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+*** START OF THE PROJECT GUTENBERG EBOOK 40288 ***
+
+  THE MODES
+
+  OF
+
+  ANCIENT GREEK MUSIC
+
+  _MONRO_
+  London
+
+  HENRY FROWDE
+
+  OXFORD UNIVERSITY PRESS WAREHOUSE
+  AMEN CORNER, E.C.
+
+  [Illustration]
+
+  New York
+
+  MACMILLAN & CO., 66, FIFTH AVENUE
+
+  _The Modes
+  of
+  Ancient Greek Music_
+
+  BY
+
+  D. B. MONRO, M.A.
+
+  PROVOST OF ORIEL COLLEGE, OXFORD
+  HONORARY DOCTOR OF LETTERS IN THE UNIVERSITY OF DUBLIN
+
+  Oxford
+
+  AT THE CLARENDON PRESS
+
+  1894
+  Oxford
+
+  PRINTED AT THE CLARENDON PRESS
+
+  BY HORACE HART, PRINTER TO THE UNIVERSITY
+  DEDICATED
+  TO THE
+  PROVOST AND FELLOWS
+  OF TRINITY COLLEGE DUBLIN
+
+  [Greek: xeinosynês heneka]
+
+
+[Blank Page]
+
+PREFACE
+
+
+The present essay is the sequel of an article on Greek music which
+the author contributed to the new edition of _Smith's Dictionary of
+Greek and Roman Antiquities_ (London, 1890-91, art. MUSICA). In that
+article the long-standing controversy regarding the nature of the
+ancient musical Modes was briefly noticed, and some reasons were
+given for dissenting from the views maintained by Westphal, and now
+very generally accepted. A full discussion of the subject would have
+taken up more space than was then at the author's disposal, and he
+accordingly proposed to the Delegates of the Clarendon Press to treat
+the question in a separate form. He has now to thank them for
+undertaking the publication of a work which is necessarily addressed
+to a very limited circle.
+
+The progress of the work has been more than once delayed by the
+accession of materials. Much of it was written before the author had
+the opportunity of studying two very interesting documents first made
+known in the course of last year in the _Bulletin de correspondance
+hellénique_ and the _Philologus_, viz. the so-called Seikelos
+ inscription from Tralles, and a fragment of the _Orestes_ of
+Euripides. But a much greater surprise was in store. The book was
+nearly ready for publication last November, when the newspapers
+reported that the French scholars engaged in excavating on the site
+of Delphi had found several pieces of musical notation, in particular
+a hymn to Apollo dating from the third century B.C. As the known
+remains of Greek music were either miserably brief, or so late as
+hardly to belong to classical antiquity, it was thought best to wait
+for the publication of the new material. The French School of Athens
+must be congratulated upon the good fortune which has attended their
+enterprise, and also upon the excellent form in which its results
+have been placed, within a comparatively short time, at the service
+of students. The writer of these pages, it will be readily
+understood, had especial reason to be interested in the announcement
+of a discovery which might give an entirely new complexion to the
+whole argument. It will be for the reader to determine whether the
+main thesis of the book has gained or lost by the new evidence.
+
+Mr. Hubert Parry prefaces his suggestive treatment of Greek music by
+some remarks on the difficulty of the subject. 'It still seems
+possible,' he observes, 'that a large portion of what has passed into
+the domain of "well-authenticated fact" is complete misapprehension,
+as Greek scholars have not time for a thorough study of music up to
+the standard required to judge securely of the matters in question,
+and musicians as a rule are not extremely intimate with Greek' (_The
+Art of Music_, p. 24). To the present writer, who has no claim to the
+title of musician, the scepticism expressed in these words appears to
+be well founded. If his interpretation of the ancient texts furnishes
+musicians like Mr. Parry with a somewhat more trustworthy basis for
+their criticism of Greek music as an art, his object will be fully
+attained.
+
+
+
+
+                        TABLE OF CONTENTS
+
+        § 1.  _Introductory._                                      PAGE
+Musical forms called [Greek: harmoniai] or [Greek: tropoi]            1
+
+
+        § 2. _Statement of the question._
+The terms Dorian, Phrygian, Lydian, &c.                               3
+
+
+        § 3. _The Authorities._
+Aristoxenus--Plato--Aristotle--Heraclides Ponticus--the
+    Aristotelian _Problems_                                           4
+
+
+        § 4. _The Early Poets._
+Pratinas--Telestes--Aristophanes                                      5
+
+
+        § 5. _Plato._
+The [Greek: harmoniai] in the _Republic_--The _Laches_                7
+
+
+        § 6. _Heraclides Ponticus._
+The three Hellenic [Greek: harmoniai]--the Phrygian and Lydian--the
+    Hypo-dorian, &c.                                                  9
+
+
+        § 7. _Aristotle--The Politics._
+The [Greek: harmoniai] in the _Politics_                             12
+
+
+        § 8. _The Aristotelian Problems._
+Hypo-dorian and Hypo-phrygian                                        14
+
+
+        § 9. _The Rhetoric._
+The [Greek: harmonia] of oratory                                     15
+
+
+        § 10. _Aristoxenus._
+The [Greek: topoi] or keys                                           16
+
+        § 11.  _Names of keys._
+The prefix Hypo- --the term [Greek: tonos]                           19
+
+
+        § 12. _Plutarch's Dialogue on Music._
+The Platonic modes--Lydian--Mixo-lydian and Syntono-lydian--the
+    Mixo-lydian octave--the keys of Sacadas--[Greek: tonos]
+    and [Greek: harmonia]                                            20
+
+
+        § 13. _Modes employed on different instruments._
+Modes on wind-instruments--on the water-organ--on the
+    cithara--on the flute                                            27
+
+
+        § 14. _Recapitulation._
+Equivalence of [Greek: harmonia] and [Greek: tonos]                  28
+
+
+        § 15._ The Systems of Greek music._
+The musical System ([Greek: systêma emmeles])                        30
+
+
+        § 16. _The standard Octachord System._
+The scale in Aristotle and Aristoxenus                               31
+
+
+        § 17. _Earlier Heptachord Scales._
+Seven-stringed scales in the _Problems_--Nicomachus                  33
+
+
+        § 18. _The Perfect System._
+The Greater and Lesser Perfect Systems--Aristoxenus--enlargement
+    of the scale--Timotheus--Pronomus--the
+    Proslambanomenos--the Hyperhypatê                                35
+
+
+        § 19. _Relation of System and Key._
+The standard System and the 'modes'--the multiplicity of
+    [Greek: harmoniai]                                               40
+
+
+        § 20. _Tonality of the Greek musical scale._
+The Mesê as a key-note--the close on the Hypatê--[Greek: archê] in
+    the _Metaphysics_                                                42
+
+
+        § 21. _The Species of a Scale._
+The seven Species ([Greek: schêmata, eidê]) of the Octave--connexion
+    with the Modes                                                   47
+
+        § 22. _The Scales as treated by Aristoxenus._
+Advance made by Aristoxenus--diagrams of the Enharmonic
+    genus--reference in Plato's _Republic_--Aristides
+    Quintilianus--the _Philebus_                                     48
+
+
+        § 23. _The Seven Species._
+Aristoxenus--the _Introductio Harmonica_                             56
+
+
+        § 24. _Relation of the Species to the Keys._
+Use of the names Dorian, &c.--treatment of musical scales
+    in Aristoxenus--Species in the different genera                  58
+
+
+        § 25. _The Ethos of Music._
+Regions of the voice--branches of lyrical poetry--kinds of
+    ethos                                                            62
+
+
+        § 26. _The Ethos of the Genera and Species._
+Ethos depending on pitch--on the genus                               66
+
+
+        § 27. _The Musical Notation._
+The instrumental notes--original form and date                       67
+
+
+        § 28. _Traces of the Species in the Notation._
+Westphal's theory                                                    75
+
+
+        § 29. _Ptolemy's Scheme of Modes._
+Reduction of the Modes to seven--nomenclature according
+    to _value_ and according to _position_                           78
+
+
+        § 30. _Nomenclature by Position._
+The term [Greek: thesis] in Aristoxenus--in the Aristotelian
+    _Problems_                                                       81
+
+
+        § 31. _Scales of the Lyre and Cithara._
+The scales on the lyre--on the cithara (viz. [Greek: tritai, tropoi,
+    parypatai, lydia, hypertropa, iastiaioliaia])                    83
+
+
+        § 32. _Remains of Greek Music._
+The hymns of Dionysius and Mesomedes--instrumental
+    passages in the _Anonymus_--Mr. Ramsay's inscription--melody
+    and accent--fragment of the _Orestes_                            87
+
+
+        § 33. _Modes of Aristides Quintilianus._
+The six Modes of Plato's _Republic_                                  94
+
+        § 34. _Credibility of Aristides Quintilianus._
+Date of Aristides--genuineness of his scales                         95
+
+
+        § 35. _Evidence for Scales of different species._
+The Hypo-dorian or common species--the Dorian--the
+    Mixo-lydian--the Phrygian and the Hypo-phrygian--Aristotle
+    on Dorian and Phrygian--the dithyramb                           101
+
+
+        § 36. _Conclusion._
+Early importance of genus and key only--change in
+    Ptolemy's time in the direction of the mediaeval Tones          108
+
+
+        § 37. _Epilogue--Speech and Song._
+Musical nature of Greek accent--relation of musical and
+    ordinary utterance--agreement of melody and accent in
+    the Seikelos inscription--rhythm of music and of prose--the
+    stress accent (_ictus_)--music influenced by language--words
+    and melody--want of harmony--the
+    non-diatonic scales                                             113
+
+
+                        APPENDIX.
+
+Table I. Scales of the seven oldest Keys, with the species
+    of the same name                                                127
+Table II. The fifteen Keys                                          128
+Music of the _Orestes_ of Euripides                                 130
+Musical part of the Seikelos inscription                            133
+The hymns recently discovered at Delphi:
+Hymn to Apollo--the scale--the changes of genus
+    and key--the 'mode' identical with the modern Minor--the
+    other fragments--the agreement of melody and
+    accent                                                          134
+Index of passages discussed or referred to                          142
+
+
+THE MODES OF ANCIENT GREEK MUSIC.
+
+
+
+
+§ 1. _Introductory._
+
+
+The modes of ancient Greek music are of interest to us, not only as
+the forms under which the Fine Art of Music was developed by a people
+of extraordinary artistic capability, but also on account of the
+peculiar ethical influence ascribed to them by the greatest ancient
+philosophers. It appears from a well-known passage in the _Republic_
+of Plato, as well as from many other references, that in ancient
+Greece there were certain kinds or forms of music, which were known
+by national or tribal names--Dorian, Ionian, Phrygian, Lydian and the
+like: that each of these was believed to be capable, not only of
+expressing particular emotions, but of reacting on the sensibility in
+such a way as to exercise a powerful and specific influence in the
+formation of character: and consequently that the choice, among these
+varieties, of the musical forms to be admitted into the education of
+the state, was a matter of the most serious practical concern. If on
+a question of this kind we are inclined to distrust the imaginative
+temper of Plato we have only to turn to the discussion of the same
+subject in the _Politics_ of Aristotle, and we shall find the
+Platonic view criticised in some important details, but treated in
+the main as being beyond controversy.
+
+The word [Greek: harmonia], 'harmony,' applied to these forms of
+music by Plato and Aristotle, means literally 'fitting' or
+'adjustment,' hence the 'tuning' of a series of notes on any
+principle, the formation of a 'scale' or 'gamut.' Other ancient
+writers use the word [Greek: tropos], whence the Latin _modus_ and
+our mood or 'mode,' generally employed in this sense by English
+scholars. The word 'mode' is open to the objection that in modern
+music it has a meaning which assumes just what it is our present
+business to prove or disprove about the 'modes' of Greek music. The
+word 'harmony,' however, is still more misleading, and on the whole
+it seems best to abide by the established use of 'mode' as a
+translation of [Greek: harmonia], trusting that the context will show
+when the word has its distinctively modern sense, and when it simply
+denotes a musical scale of some particular kind.
+
+The rhythm of music is also recognized by both Plato and Aristotle as
+an important element in its moral value. On this part of the subject,
+however, we have much less material for a judgement. Plato goes on to
+the rhythms after he has done with the modes, and lays down the
+principle that they must not be complex or varied, but must be the
+rhythms of a sober and brave life. But he confesses that he cannot
+tell which these are ([Greek: poia de poiou biou mimêmata ouk echô
+legein]), and leaves the matter for future inquiry[1].
+
+[Footnote 1: Plato, _Rep._ p. 400 _b_ [Greek: alla tauta men, ên d'
+egô, kai meta Damônos bouleusometha, tines te aneleutherias kai
+hybreôs ê manias kai allês kakias prepousai baseis, kai tinas tois
+enantiois leipteon rhythmous.]]
+
+§ 2. _Statement of the question._
+
+
+What then are the musical forms to which Plato and Aristotle ascribe
+this remarkable efficacy? And what is the source of their influence
+on human emotion and character?
+
+There are two obvious relations in which the scales employed in any
+system of music may stand to each other. They may be related as two
+keys of the same mode in modern music: that is to say, we may have to
+do with a scale consisting of a fixed succession of intervals, which
+may vary in pitch--may be 'transposed,' as we say, from one pitch or
+key to another. Or the scales may differ as the Major mode differs
+from the Minor, namely in the order in which the intervals follow
+each other. In modern music we have these two modes, and each of them
+may be in any one of twelve keys. It is evidently possible, also,
+that a name such as Dorian or Lydian might denote a particular mode
+taken in a particular key--that the scale so called should possess a
+definite pitch as well as a definite series of intervals.
+
+According to the theory which appears now to prevail among students
+of Greek music, these famous names had a double application. There
+was a Dorian mode as well as a Dorian key, a Phrygian mode and a
+Phrygian key, and so on. This is the view set forth by Boeckh in the
+treatise which may be said to have laid the foundations of our
+knowledge of Greek music (_De Metris Pindari_, lib. III. cc.
+vii-xii). It is expounded, along with much subsidiary speculation, in
+the successive volumes which we owe to the fertile pen of Westphal;
+and it has been adopted in the learned and excellent _Histoire et
+Théorie de la Musique de l'Antiquité_ of M. Gevaert. According to
+these high authorities the Greeks had a system of key ([Greek:
+tonoi]), and also a system of modes ([Greek: harmoniai]), the former
+being based solely upon difference of pitch, the latter upon the
+'form' or species ([Greek: eidos]) of the octave scale, that is to
+say, upon the order of the intervals which compose it.
+
+
+
+
+§ 3. _The Authorities._
+
+
+The sources of our knowledge are the various systematic treatises
+upon music which have come down to us from Greek antiquity, together
+with incidental references in other authors, chiefly poets and
+philosophers. Of the systematic or 'technical' writers the earliest
+and most important is Aristoxenus, a pupil of Aristotle. His treatise
+on _Harmonics_ ([Greek: harmonikê]) has reached us in a fragmentary
+condition, but may be supplemented to some extent from later works of
+the same school. Among the incidental notices of music the most
+considerable are the passages in the _Republic_ and the _Politics_
+already referred to. To these we have to add a few other references
+in Plato and Aristotle; a long fragment from the Platonic philosopher
+Heraclides Ponticus, containing some interesting quotations from
+earlier poets; a number of detached observations collected in the
+nineteenth section of the Aristotelian _Problems_; and one or two
+notices preserved in lexicographical works, such as the _Onomasticon_
+of Pollux.
+
+In these groups of authorities the scholars above mentioned find the
+double use which they believe to have been made of the names Dorian,
+Phrygian, Lydian and the rest. In Aristoxenus they recognise that
+these names are applied to a series of keys ([Greek: tonoi]), which
+differed in pitch only. In Plato and Aristotle they find the same
+names applied to scales called [Greek: harmoniai], and these scales,
+they maintain, differed primarily in the order of their intervals. I
+shall endeavour to show that there was no such double use: that in
+the earlier periods of Greek music the scales in use, whether called
+[Greek: tonoi] or [Greek: harmoniai], differed primarily in _pitch_:
+that the statements of ancient authors about them, down to and
+including Aristoxenus, agree as closely as there is reason to expect:
+and that the passages on which the opposite view is based--all of
+them drawn from comparatively late writers--either do not relate to
+these ancient scales at all, or point to the emergence in
+post-classical times of some new forms or tendencies of musical art.
+I propose in any case to adhere as closely as possible to a
+chronological treatment of the evidence which is at our command, and
+I hope to make it probable that the difficulties of the question may
+be best dealt with on this method.
+
+
+
+
+§ 4. _The Early Poets._
+
+
+The earliest of the passages now in question comes from the poet
+Pratinas, a contemporary of Aeschylus. It is quoted by Heraclides
+Ponticus, in the course of a long fragment preserved by Athenaeus
+(xiv. cc. 19-21, p. 624 _c_-626 _a_). The words are:
+
+    [Greek: mête syntonon diôke mête tan aneimenan
+    Iasti mousan, alla tan messan neôn
+    arouran aiolize tô melei.]
+
+'Follow neither a highly-strung music nor the low-pitched Ionian, but
+turning over the middle plough-land be an Aeolian in your melody.'
+Westphal takes the word [Greek: 'Iasti] with [Greek: syntonon] as
+well as with [Greek: aneimenan], and infers that there were two kinds
+of Ionian, a 'highly-strung' and a 'relaxed' or low-pitched. But this
+is not required by the words, and seems less natural than the
+interpretation which I have given. All that the passage proves is
+that in the time of Pratinas a composer had the choice of at least
+three scales: one (or more) of which the pitch was high ([Greek:
+syntonos]); another of low pitch ([Greek: aneimenê]), which was
+called _Ionian_; and a third, intermediate between the others, and
+known as _Aeolian_. Later in the same passage we are told that
+Pratinas spoke of the 'Aeolian harmony' ([Greek: prepei toi pasin
+aoidolabraktais Aiolis harmonia]). And the term is also found, with
+the epithet 'deep-sounding,' in a passage quoted from the hymn to
+Demeter of a contemporary poet, Lasus of Hermione (Athen. xiv. 624
+_e_):
+
+    [Greek: Damatra melpô Koran te Klymenoio alochon Meliboian,
+    hymnôn anagôn Aiolid' hama barybromon harmonian.]
+
+With regard to the Phrygian and Lydian scales Heraclides (_l. c._)
+quotes an interesting passage from Telestes of Selinus, in which
+their introduction is ascribed to the colony that was said to have
+followed Pelops from Asia Minor to the Peloponnesus:
+
+    [Greek: prôtoi para kratêras Hellênôn en aulois
+    synopadoi Pelopos matros oreias phrygion aeison nomon;
+    toi d' oxyphônois pêktidôn psalmois krekon
+    Dydion hymnon.]
+
+'The comrades of Pelops were the first who beside the Grecian cups
+sang with the flute ([Greek: aulos]) the Phrygian measure of the
+Great Mother; and these again by shrill-voiced notes of the _pectis_
+sounded a Lydian hymn.' The epithet [Greek: oxyphônos] is worth
+notice in connexion with other evidence of the high pitch of the
+music known as Lydian. The Lydian mode is mentioned by Pindar, _Nem._
+4. 45:
+
+    [Greek: exyphaine glykeia kai tod' autika phorminx
+    Lydia syn harmonia melos pephilêmenon.]
+
+The Dorian is the subject of an elaborate jest made at the expense of
+Cleon in the _Knights_ of Aristophanes, ll. 985-996:
+
+    [Greek: alla kai tod' egô ge thaumazô tês hyomousias
+    autou phasi gar auton hoi paides hoi xynephoitôn
+    tên Dôristi monên enarmottesthai thama tên lyran,
+    allên d' ouk ethelein labein; kata ton kitharistên
+    orgisthent' apagein keleuein, hôs harmonian ho pais
+    outos ou dynatai mathein ên mê Dôrodokêsti.]
+
+
+
+
+§ 5. _Plato._
+
+Following the order of time, we come next to the passage in the
+_Republic_ (p. 398), where Socrates is endeavouring to determine the
+kinds of music to be admitted for the use of his future 'guardians,'
+in accordance with the general principles which are to govern their
+education. First among these principles is the condemnation of all
+undue expression of grief. 'What modes of music ([Greek:
+harmoniai]),' he asks, are plaintive ([Greek: thrênôdeis])?' 'The
+_Mixo-lydian_,' Glaucon replies, 'and the _Syntono-lydian_, and
+such-like.' These accordingly Socrates excludes. 'But again,
+drunkenness and slothfulness are no less forbidden to the guardians;
+which of the modes are soft and convivial ([Greek: malakai te kai
+sympotikai])?' '_Ionian_,' says Glaucon, 'and _Lydian_, those which
+are called slack ([Greek: chalarai]).' 'Which then remain?'
+'Seemingly _Dorian_ and _Phrygian_.' 'I do not know the modes,' says
+Socrates, 'but leave me one that will imitate the tones and accents
+of a brave man enduring danger or distress, fighting with constancy
+against fortune: and also one fitted for the work of peace, for
+prayer heard by the gods, for the successful persuasion or
+exhortation of men, and generally for the sober enjoyment of ease and
+prosperity.' Two such modes, one for Courage and one for Temperance,
+are declared by Glaucon to be found in the Dorian and the Phrygian.
+In the _Laches_ (p. 188) there is a passing reference in which a
+similar view is expressed. Plato is speaking of the character of a
+brave man as being metaphorically a 'harmony,' by which his life is
+made consonant to reason--'a Dorian harmony,' he adds--playing upon
+the musical sense of the word--'not an Ionian, certainly not a
+Phrygian or a Lydian, but that one which only is truly Hellenic'
+([Greek: atechnôs Dôristi, all' ouk Iasti, oiomai de oude Phrygisti
+oude Lydisti, all' hê per monê Hellênikê estin harmonia]). The
+exclusion of Phrygian may be due to the fact that the virtue
+discussed in the _Laches_ is courage; but it is in agreement with
+Aristotle's opinion. The absence of Aeolian from both the Platonic
+passages seems to show that it had gone out of use in his time (but
+cp. p. 11).
+
+The point of view from which Plato professes to determine the right
+modes to be used in his ideal education appears clearly in the
+passage of the _Republic_. The modes first rejected are those which
+are high in pitch. The Syntono-lydian or 'high-strung Lydian' is
+shown by its name to be of this class. The Mixo-lydian is similar, as
+we shall see from Aristotle and other writers. The second group which
+he condemns is that of the 'slack' or low-pitched. Thus it is on the
+profoundly Hellenic principle of choosing the mean between opposite
+extremes that he approves of the Dorian and Phrygian pitch. The
+application of this principle was not a new one, for it had been
+already laid down by Pratinas: [Greek: mête syntonon diôke mête tan
+aneimenan].
+
+The three chapters which Aristotle devotes to a discussion of the use
+of music in the state (_Politics_ viii. cc. 5-7), and in which he
+reviews and criticises the Platonic treatment of the same subject,
+will be found entirely to bear out the view now taken. It is also
+supported by the commentary of Plutarch, in his dialogue on Music
+(cc. 15-17), of which we shall have something to say hereafter.
+Meanwhile, following the chronological order of our authorities, we
+come next to the fragment of Heraclides Ponticus already mentioned
+(Athen. xiv. p. 624 _c_-626 _a_).
+
+
+
+
+§ 6. _Heraclides Ponticus._
+
+The chief doctrine maintained by Heraclides Ponticus is that there
+are three modes ([Greek: harmoniai]), belonging to the three Greek
+races--Dorian, Aeolian, Ionian. The Phrygian and Lydian, in his view,
+had no right to the name of mode or 'harmony' ([Greek: oud' harmonian
+phêsi dein kaleisthai tên Phrygion, kathaper oude tên Lydion]). The
+three which he recognized had each a marked ethos. The Dorian
+reflected the military traditions and temper of Sparta. The Aeolian,
+which Heraclides identified with the Hypo-dorian of his own time,
+answered to the national character of the Thessalians, which was bold
+and gay, somewhat overweening and self-indulgent, but hospitable and
+chivalrous. Some said that it was called Hypo-dorian because it was
+below the Dorian on the [Greek: aulos] or flute; but Heraclides
+thinks that the name merely expressed likeness to the Dorian
+character ([Greek: Dôrion men autên ou nomizein, prosempherê de pôs
+ekeinê]). The Ionian, again, was harsh and severe, expressive of the
+unkindly disposition fostered amid the pride and material welfare of
+Miletus. Heraclides is inclined to say that it was not properly a
+distinct musical scale or 'harmony,' but a strange aberration in the
+form of the musical scale ([Greek: tropon de tina thaumaston
+schêmatos harmonias]). He goes on to protest against those who do not
+appreciate differences of kind ([Greek: tas kat' eidos diaphoras]),
+and are guided only by the high or low pitch of the notes ([Greek: tê
+tôn phthongôn exytêti kai barytêti]); so that they make a
+Hyper-mixolydian, and another again above that. 'I do not see,' he
+adds, 'that the Hyper-phrygian has a distinct ethos; and yet some say
+that they have discovered a new mode ([Greek: harmonia]), the
+Hypo-phrygian. But a mode ought to have a distinct moral or emotional
+character ([Greek: eidos echein ethous hê pathous]), as the Locrian,
+which was in use in the time of Simonides and Pindar, but went out of
+fashion again.' The Phrygian and Lydian, as we have seen, were said
+to have been brought to the Peloponnesus by the followers of Pelops.
+
+The tone as well as the substance of this extract makes it evident
+that the opinions of Heraclides on questions of theoretical music
+must be accepted with considerable reserve. The notion that the
+Phrygian and Lydian scales were 'barbarous' and opposed to Hellenic
+ethos was apparently common enough, though largely due (as we may
+gather from several indications) to national prejudice. But no one,
+except Heraclides, goes so far as to deny them the name of [Greek:
+harmonia]. The threefold division into Dorian, Aeolian and Ionian
+must also be arbitrary. It is to be observed that Heraclides obtains
+his Aeolian by identifying the Aeolian of Pratinas and other early
+poets with the mode called Hypo-dorian in his own time. The
+circumstance that Plato mentions neither Aeolian nor Hypo-dorian
+suggests rather that Aeolian had gone out of use before Hypo-dorian
+came in. The conjecture of Boeckh that Ionian was the same as the
+later Hypo-phrygian (_De Metr. Pind._ iii. 8) is open to a similar
+objection. The Ionian mode was at least as old as Pratinas, whereas
+the Hypo-phrygian was a novelty in the time of Heraclides. The
+protest which Heraclides makes against classifying modes merely
+according to their pitch is chiefly valuable as proving that the
+modes were as a matter of fact usually classified from that point of
+view. It is far from proving that there was any other principle which
+Heraclides wished to adopt--such, for example, as difference in the
+intervals employed, or in their succession. His 'differences of kind'
+([Greek: tas kat' eidos diaphoras]) are not necessarily to be
+explained from the technical use of [Greek: eidos] for the 'species'
+of the octave. What he complains of seems to be the multiplication of
+modes--Hyper-mixolydian, Hyper-phrygian, Hypo-phrygian--beyond the
+legitimate requirements of the art. The Mixo-lydian (_e.g._) is
+high-pitched and plaintive: what more can the Hyper-mixolydian be?
+The Hypo-phrygian is a new mode: Heraclides denies it a distinctive
+ethos. His view seems to be that the number of modes should not be
+greater than the number of varieties in temper or emotion of which
+music is capable. But there is nothing to show that he did not regard
+pitch as the chief element, or one of the chief elements, of musical
+expression.
+
+The absence of the name Hypo-lydian, taken with the description of
+Hypo-dorian as 'below the Dorian,' would indicate that the
+Hypo-dorian of Heraclides was not the later mode of that name, but
+was a semitone below the Dorian, in the place afterwards occupied by
+the Hypo-lydian. This is confirmed, as we shall see, by Aristoxenus
+(p. 18).
+
+
+
+
+§ 7. _Aristotle--the Politics._
+
+Of the writers who deal with music from the point of view of the
+cultivated layman, Aristotle is undoubtedly the most instructive. The
+chapters in his _Politics_ which treat of music in its relation to
+the state and to morality go much more deeply than Plato does into
+the grounds of the influence which musical forms exert upon temper
+and feeling. Moreover, Aristotle's scope is wider, not being confined
+to the education of the young; and his treatment is evidently a more
+faithful reflexion of the ordinary Greek notions and sentiment. He
+begins (_Pol._ viii. 5, p. 1340 _a_ 38) by agreeing with Plato as to
+the great importance of the subject for practical politics. Musical
+forms, he holds, are not mere _symbols_ ([Greek: sêmeia]), acting
+through association, but are an actual _copy_ or reflex of the forms
+of moral temper ([Greek: en de tois melesin autois esti mimêmata tôn
+êthôn]); and this is the ground of the different moral influence
+exercised by different modes ([Greek: harmoniai]). By some of them,
+especially by the Mixo-lydian, we are moved to a plaintive and
+depressed temper ([Greek: diatithesthai odyrtikôterôs kai
+synestêkotôs mallon]); by others, such as those which are called the
+'relaxed' ([Greek: aneimenai]), we are disposed to 'softness' of mind
+([Greek: malakôterôs tên dianoian]). The Dorian, again, is the only
+one under whose influence men are in a middle and settled mood
+([Greek: mesôs kai kathestêkotôs malista]): while the Phrygian makes
+them excited ([Greek: enthousiastikous]). In a later chapter (Pol.
+viii. 7, p. 1342 _a_ 32), he returns to the subject of the Phrygian.
+Socrates, he thinks, ought not to have left it with the Dorian,
+especially since he condemned the flute ([Greek: aulos]), which has
+the same character among instruments as the Phrygian among modes,
+both being orgiastic and emotional. The Dorian, as all agree, is the
+most steadfast ([Greek: stasimôtatê]), and has most of the ethos of
+courage; and, as compared with other modes, it has the character
+which Aristotle himself regards as the universal criterion of
+excellence, viz. that of being the mean between opposite excesses.
+Aristotle, therefore, certainly understood Plato to have approved the
+Dorian and the Phrygian as representing the mean in respect of pitch,
+while other modes were either too high or too low. He goes on to
+defend the use of the 'relaxed' modes on the ground that they furnish
+a music that is still within the powers of those whose voice has
+failed from age, and who therefore are not able to sing the
+high-pitched modes ([Greek: oion tois apeirêkosi dia chronon ou
+rhadion adein tas syntonous harmonias, alla tas aneimenas hê physis
+hypoballei tois têlikoutois]). In this passage the meaning of the
+words [Greek: syntonos] and [Greek: aneimenos] is especially clear.
+
+In the same discussion (c. 6), Aristotle refers to the distinction
+between music that is ethical, music suited to action, and music that
+inspires religious excitement ([Greek: ta men êthika, ta de praktika,
+ta ho enthousiastika]). The last of these kinds serves as a
+'purification' ([Greek: katharsis]). The excitement is calmed by
+giving it vent; and the morbid condition of the ethos is met by music
+of high pitch and exceptional 'colour' ([Greek: tôn harmoniôn
+parekbaseis kai tôn melôn ta syntona kai parakechrôsmena]).
+
+In a different connexion (_Pol._ iv. 3, p. 1290 _a_ 20), dealing with
+the opinion that all forms of government are ultimately reducible to
+two, viz. oligarchy and democracy, Aristotle compares the view of
+some who held that there are properly only two musical modes, Dorian
+and Phrygian,--the other scales being mere varieties of these two.
+Rather, he says, there is in each case a right form, or two right
+forms at most, from which the rest are declensions ([Greek:
+parekbaseis]),--on one side to 'high-pitched' and imperious
+oligarchies, on the other to 'relaxed' and 'soft' forms of popular
+government ([Greek: oligarchikas men tas syntonôteras kai
+despotikônteras, tas d' aneimenas kai malakas dêmotikas]). This is
+obviously the Platonic doctrine of two right keys, holding the mean
+between high and low.
+
+
+
+
+§ 8. _The Aristotelian Problems._
+
+Some further notices of the [Greek: harmoniai] or modes are contained
+in the so-called _Problems_,--a collection which is probably not the
+work of Aristotle himself, but can hardly be later than the
+Aristotelian age. What is said in it of the modes is clearly of the
+period before the reform of Aristoxenus. In one place (_Probl._ xix.
+48) the question is asked why the Hypo-dorian and Hypo-phrygian are
+not used in the _chorus_ of tragedy. One answer is that the
+Hypo-phrygian has the ethos of action ([Greek: êthos echei
+praktikon]), and that the Hypo-dorian is the expression of a lofty
+and unshaken character; both of these things being proper to the
+heroic personages on the stage, but not to the chorus, which
+represents the average spectator, and takes no part in the action.
+Hence the music suited to the chorus is that of emotion venting
+itself in passive complaint:--a description which fits the other
+modes, but least of all the exciting and orgiastic Hypo-phrygian. On
+the contrary (the writer adds) the passive attitude is especially
+expressed by the Mixo-lydian. The view here taken of the Hypo-dorian
+evidently agrees with that of Heraclides Ponticus (_supra_, p. 10).
+
+The relation which Plato assumes between high pitch and the
+excitement of passion, and again between lowness of pitch and
+'softness' or self-indulgence ([Greek: malakia kai argia]), is
+recognized in the _Problems_, xix. 49 [Greek: epei de ho men barys
+phthongos malakos kai êremaios estin, ho de oxys kinêtikos, k.t.l.]:
+'since a deep note is soft and calm, and a high note is exciting,
+&c.'
+
+
+
+
+§ 9. _The Rhetoric._
+
+The word [Greek: tonos] occurs several times in Aristotle with the
+sense of 'pitch,' but is not applied by him to the keys of music. The
+nearest approach to such a use may be found in a passage of the
+_Rhetoric_ (iii. 1, p. 1403 _b_ 27).
+
+Speaking of the rise of acting ([Greek: hypokrisis]), which was
+originally the business of the poet himself, but had grown into a
+distinct art, capable of theoretical as well as practical treatment,
+he observes that a similar art might be formed for oratory. 'Such an
+art would lay down rules directing how to use the voice so as to suit
+each variety of feeling,--when it should be loud, when low, when
+intermediate;--and how to use the keys, when the pitch of the voice
+should be high or low or middle ([Greek: kai pôs tois tonois, oion
+oxeia kai bareia kai mesê], sc. [Greek: phônê]); and the rhythms,
+which to use for each case. For there are three things which men
+study, viz. quantity (_i. e._ loudness of sound), tune, and rhythm
+([tria gar esti peri hôn skopousi, tauta d' esti megethos, harmonia,
+rhythmos]).' The passage is interesting as showing the value which
+Aristotle set upon pitch as an element of effect. And the use of
+[Greek: harmonia] in reference to the pitch of the voice, and as
+virtually equivalent to [Greek: tonos], is especially worthy of note.
+
+
+
+
+§ 10. _Aristoxenus._
+
+Our next source of information is the technical writer Aristoxenus, a
+contemporary and pupil of Aristotle. Of his many works on the subject
+of music three books only have survived, bearing the title [Greek:
+harmonika otoicheia][1]. In the treatment adopted by Aristoxenus the
+chapter on keys follows the chapter on 'systems' ([Greek:
+systêmata]). By a [Greek: systêma] he means a scale consisting of a
+certain succession of intervals: in other words, a series of notes
+whose relative pitch is determined. Such a system may vary in
+absolute pitch, and the [Greek: tonoi] or keys are simply the
+different degrees of pitch at which a particular system is taken
+([Greek: tous tonous eph' ôn tithemena ta systêmata melôdeitai]).
+When the system and the key are both given it is evident that the
+whole series of notes is determined.
+
+Aristoxenus is the chief authority on the keys of Greek music. In
+this department he is considered to have done for Greece what Bach's
+_Wohltemperirtes Clavier_ did for modern Europe. It is true that the
+scheme of keys which later writers ascribe to him is not given in the
+_Harmonics_ which we have: but we find there what is in some respects
+more valuable, namely, a vivid account of the state of things in
+respect of tonality which he observed in the music of his time.
+
+[Footnote 1: It is foreign to our purpose to discuss the critical
+problems presented by the text of Aristoxenus. Of the three extant
+books the first is obviously a distinct treatise, and should probably
+be entitled [Greek: peri archôn]. The other two books will then bear
+the old title [Greek: harmonika stoicheia]. They deal with the same
+subjects, for the most part, as the first book, and in the same
+order,--a species of repetition of which there are well-known
+instances in the Aristotelian writings. The conclusion is abrupt, and
+some important topics are omitted. It seems an exaggeration, however,
+to describe the _Harmonics_ of Aristoxenus as a mere collection of
+excerpts, which is the view taken by Marquard (_Die harmonischen
+Fragmente des Aristoxenus_, pp. 359-393). See Westphal's _Harmonik
+und Melopöie der Griechen_ (p. 41, ed. 1863), and the reply to
+Marquard in his _Aristoxenus von Tarent_ (pp. 165-170).]
+
+'No one,' says Aristoxenus (p. 37 Meib.), 'has told us a word about
+the keys, either how they are to be arrived at ([Greek: tina tropon
+lêpteon]), or from what point of view their number is to be
+determined. Musicians assign the place of the keys very much as the
+different cities regulate the days of the month. The Corinthians, for
+example, will be found counting a day as the tenth of the month,
+while with the Athenians it is the fifth, and in some other place the
+eighth. Some authorities on music ([Greek: harmonikoi]) say that the
+Hypo-dorian is the lowest key, the Mixo-lydian a semitone higher, the
+Dorian again a semitone higher, the Phrygian a tone above the Dorian,
+and similarly the Lydian a tone above the Phrygian. Others add the
+Hypo-phrygian flute [_i. e._ the scale of the flute so called] at the
+lower end of the list. Others, again, looking to the holes of the
+flute ([Greek: pros tên tôn aulôn trupêsin blepontes]), separate the
+three lowest keys, viz. the Hypo-phrygian, Hypo-dorian, and Dorian,
+by the interval of three-quarters of a tone ([Greek: trisi
+diesesin]), but the Phrygian from the Dorian by a tone, the Lydian
+from the Phrygian again by three-quarters of a tone, and the
+Mixo-lydian from the Lydian by a like interval. But as to what
+determines the interval between one key and another they have told us
+nothing.'
+
+It will be seen that (with one marked exception) there was agreement
+about the order of the keys in respect of pitch, and that some at
+least had reduced the intervals to the succession of tones and
+semitones which characterises the diatonic scale. The exception is
+the Mixo-lydian, which some ranked immediately below the Dorian,
+others above the Lydian. Westphal attributes this strange discrepancy
+to the accidental displacing of some words in the MSS. of
+Aristoxenus[1]. However this may be, it is plain that in the time of
+Aristoxenus considerable progress had been made towards the scheme of
+keys which was afterwards connected with his name. This may be
+represented by the following table, in which for the sake of
+comparison the later Hypo-lydian and Hypo-dorian are added in
+brackets:
+
+
+                   Mixo-lydian
+      semitone - {
+                   Lydian
+        tone   - {
+                   Phrygian
+        tone   - {
+                   Dorian
+      semitone - {
+                   Hypo-dorian [Hypo-lydian]
+        tone   - {
+                   Hypo-phrygian
+        tone   - {
+                   [Hypo-dorian]
+
+
+[Footnote 1: _Harm._ p. 37, 19 Meib. [Greek: houtô gar hoi men tôn
+harmonikôn legousi barytaton men ton Hypodôrion tôn tonôn, hêmitoniô
+de oxyteron toutou ton Mixolydion, toutou de hêmitoniô ton Dôrion,
+tou de Dôriou tonô ton Phrygion: hôsautôs de kai tou Phrygiou ton
+Lydion heterô tonô.] Westphal (_Harmonik und Melopöie_ p. 165) would
+transfer the words [Greek: hêmitoniô ... Mixolydion] to the end of
+the sentence, and insert [Greek: oxyteron] before [Greek: ton
+Dôrion]. The necessity for this insertion shows that Westphal's
+transposition is not in itself an easy one. The only reason for it is
+the difficulty of supposing that there could have been so great a
+difference in the pitch of the Mixo-lydian scale. As to this,
+however, see p. 23 (note).
+
+The words [Greek: Hypophrygion aulon] have also been condemned by
+Westphal (_Aristoxenus_, p. 453). He points out the curious
+contradiction between [Greek: pros tên tôn aulôn trypêsin blepontes]
+and the complaint [Greek: ti d' esti pros ho blepontes ... ouden
+eirêkasin]. But if [Greek: pros tên ... blepontes] was a marginal
+gloss, as Westphal suggests, it was doubtless a gloss on [Greek:
+aulon], and if so, [Greek: aulon] is presumably sound. Since the
+[Greek: aulos] was especially a Phrygian instrument, and regularly
+associated with the Phrygian mode (as we know from Aristotle, see p.
+13), nothing is more probable than that there was a variety of flute
+called Hypo-phrygian, because tuned so as to yield the Hypo-phrygian
+key, either by itself or as a modulation from the Phrygian.]
+
+In this scheme the important feature--that which marks it as an
+advance on the others referred to by Aristoxenus--is the conformity
+which it exhibits with the diatonic scale. The result of this
+conformity is that the keys stand in a certain relation to each
+other. Taking any two, we find that certain notes are common to them.
+So long as the intervals of pitch were quite arbitrary, or were
+practically irrational quantities, such as three-quarters of a tone,
+no such relation could exist. It now became possible to pass from one
+key to another, _i. e._ to employ _modulation_ ([Greek: metabolê]) as
+a source of musical effect. This new system had evidently made some
+progress when Aristoxenus wrote, though it was not perfected, and had
+not passed into general use.
+
+
+
+
+§ 11. _Names of Keys_ ([Greek: hypo-]).
+
+A point that deserves special notice at this place is the use of the
+prefix _Hypo-_ ([Greek: hypo-]) in the names of keys. In the final
+Aristoxenean system _Hypo-_ implies that a key is lower by the
+interval of a Fourth than the key to whose name it is prefixed. This
+convention served to bring out the special relation between the two
+keys, viz. to show that they are related (to use modern language) as
+the keys of a tonic and dominant. In the scheme of keys now in
+question there is only one instance of this use of _Hypo-_, namely in
+the Hypo-phrygian, the most recently introduced. It must have been on
+the analogy of this name that the term Hypo-dorian was shifted from
+the key immediately below the Dorian to the new key a Fourth below
+it, and that the new term Hypo-lydian was given to the old
+Hypo-dorian in accordance with its similar relation to the Lydian. In
+the time of Aristoxenus, then, this technical sense of _Hypo-_ had
+not yet been established, but was coming into use. It led naturally
+to the employment of _Hyper-_ in the inverse sense, viz. to denote a
+key a Fourth higher (the key of the sub-dominant). By further steps,
+of which there is no record, the Greek musicians arrived at the idea
+of a key for every semitone in the octave; and thus was formed the
+system of thirteen keys, ascribed to Aristoxenus by later writers.
+(See the scheme at the end of this book, Table II.) Whether in fact
+it was entirely his work may be doubted. In any case he had formed a
+clear conception--the want of which he noted in his predecessors--of
+the principles on which a theoretically complete scheme of keys
+should be constructed.
+
+In the discussions to which we have been referring, Aristoxenus
+invariably employs the word [Greek: tonos] in the sense of 'key.' The
+word [Greek: harmonia] in his writings is equivalent to 'Enharmonic
+genus' ([Greek: genos enarmonion]), the _genus_ of music which made
+use of the Enharmonic _diësis_ or quarter-tone. Thus he never speaks,
+as Plato and Aristotle do, of the Dorian (or Phrygian or Lydian)
+[Greek: harmonia], but only of the [Greek: tonoi] so named. There is
+indeed one passage in which certain octave scales are said by
+Aristoxenus to have been called [Greek: harmoniai]: but this, as will
+be shown, is a use which is to be otherwise explained (see p. 54).
+
+
+
+
+§ 12. _Plutarch's Dialogue on Music._
+
+After the time of Aristoxenus the technical writers on music make
+little or no use of the term [Greek: harmonia]. Their word for 'key'
+is [Greek: tonos]; and the octachord scales which are distinguished
+by the succession of their intervals are called 'species of the
+octave' ([Greek: eidê tou dia] [Greek: pasôn]). The modes of the
+classical period, however, were still objects of antiquarian and
+philosophic interest, and authors who treated them from this point of
+view naturally kept up the old designation. A good specimen of the
+writings of this class has survived in the _dialogus de musicâ_ of
+Plutarch. Like most productions of the time, it is mainly a
+compilation from earlier works now lost. Much of it comes from
+Aristoxenus, and there is therefore a special fitness in dealing with
+it in this place, by way of supplement to the arguments drawn
+directly from the Aristoxenean _Harmonics_. The following are the
+chief passages bearing on the subject of our enquiry:
+
+(1) In cc. 15-17 we find a commentary of some interest on the
+Platonic treatment of the modes. Plutarch is dwelling on the
+superiority of the older and simpler music, and appeals to the
+opinion of Plato.
+
+'The Lydian mode ([Greek: harmonia]) Plato objects to because it is
+high ([Greek: oxeia]) and suited to lamentation. Indeed it is said to
+have been originally devised for that purpose: for Aristoxenus tells
+us, in his first book on Music, that Olympus first employed the
+Lydian mode on the flute in a dirge ([Greek: epikêdeion aulêsai
+Lydisti]) over the Python. But some say that Melanippides began this
+kind of music. And Pindar in his paeans says that the Lydian mode
+([Greek: harmonia]) was first brought in by Anthippus in an ode on
+the marriage of Niobe. But others say that Torrhebus first used that
+mode, as Dionysius the Iambus relates.'
+
+'The Mixo-lydian, too, is pathetic and suitable to tragedy. And
+Aristoxenus says that Sappho was the inventor of the Mixo-lydian, and
+that from her the tragic poets learned it. They combined it with the
+Dorian, since that mode gives grandeur and dignity, and the other
+pathos, and these are the two elements of tragedy. But in his
+Historical Treatise on Music ([Greek: historika tês harmonias
+hypomnêmata]) he says that Pythoclides the flute-player was the
+discoverer of it. And Lysis says that Lamprocles the Athenian,
+perceiving that in it the disjunctive tone ([Greek: diazeuxis]) is
+not where it was generally supposed to be, but is at the upper end of
+the scale, made the form of it to be that of the octave from Paramesê
+to Hypatê Hypatôn ([Greek: toiouton autês apergasasthai to schêma
+hoion to apo paramesês epi hypatên hypatôn]). Moreover, it is said
+that the relaxed Lydian ([Greek: epaneimenên Lydisti]), which is the
+opposite of the Mixo-lydian, being similar to the Ionian ([Greek:
+paraplêsian ousan tê Iadi]), was invented by Damon the Athenian.'
+
+'These modes then, the one plaintive, the other relaxed ([Greek:
+eklelymenê]), Plato properly rejected, and chose the Dorian, as
+befitting warlike and temperate men.'
+
+In this passage the 'high-pitched Lydian' ([Greek: Syntonolydisti])
+of Plato is called simply Lydian. There is every reason to suppose
+that it is the mode called Lydian by Aristotle and Heraclides
+Ponticus[1]. If this is so, it follows almost of necessity that the
+Lydian of Plato, called slack ([Greek: chalara]) by him--Plutarch's
+[Greek: epaneimenê Lydisti]--is to be identified with the later
+Hypo-lydian.
+
+[Footnote 1: An objection to this identification has been based on
+the words of Pollux, _Onom._ iv. 78 [Greek: kai harmonia men aulêtikê
+Dôristi, Phrygisti, Lydios kai Iônikê, kai syntonos Lydisti ên
+Anthippos exeure]. The source of this statement, or at least of the
+latter part of it, is evidently the same as that of the notice in
+Plutarch. The agreement with Plato's list makes it probable that this
+source was some comment on the passage in the _Republic_. If so, it
+can hardly be doubted that Pollux gives the original terms, the
+Platonic [Greek: Lydisti] and [Greek: Syntonolydisti], and
+consequently that the later Lydian is not to be found in his [Greek:
+Lydios] (which is a 'relaxed' mode), but in his [Greek: syntonos
+Lydisti]. There is no difficulty in supposing that the mode was
+called [Greek: syntonos] merely in contrast to the other.]
+
+The point, however, is not free from difficulty: for (as we have
+seen, p. 18), the name Hypo-lydian is not in the list of keys given
+by Aristoxenus--the key which was ultimately called Hypo-lydian being
+known to him as the Hypo-dorian. If, however, the confusion in the
+nomenclature of the keys was as great as Aristoxenus himself
+describes, such a contradiction as this cannot be taken to prove
+much[1].
+
+The statement that the 'relaxed Lydian' was the opposite of the
+Mixo-lydian, and similar to the Ionian, has given rise to much
+speculation. In what sense, we naturally ask, can a key or a mode be
+said to be 'opposite' or 'similar' to another? I venture to think
+that it is evidently a mere paraphrase of Plato's language. The
+relaxed Lydian is opposed to the Mixo-lydian because it is at the
+other end of the scale in pitch; and it is similar to the Ionian
+because the two are classed together (as [Greek: chalarai]) by Plato.
+
+The Mixo-lydian, according to Aristoxenus, was employed by the tragic
+poets in close union with the Dorian mode ([Greek: labontas syzeuxai
+tê Dôristi]). The fact that the Mixo-lydian was just a Fourth higher
+than the Dorian must have made the transition from the one to the
+other a natural and melodious one. As Aristoxenus suggested, it would
+be especially used to mark the passage from grandeur and dignity to
+pathos which is the chief characteristic of tragedy ([Greek: hê men
+to megaloprepes kai axiômatikon apodidôsin, hê de to pathêtikon,
+memiktai de dia toutôn tragôdia]). It is worth noticing that this
+relation obtained in the scheme of the musicians who did not arrange
+the keys according to the diatonic scale, but in some way suggested
+by the form of the flute ([Greek: hoi pros tên tôn aulôn trypêsin
+blepontes]). It may therefore be supposed to have been established
+before the relative pitch of other keys had been settled.
+
+[Footnote 1: It seems not impossible that this difficulty with regard
+to the 'slack Lydian' and Hypo-lydian may be connected with the
+contradiction in the statement of Aristoxenus about the schemes of
+keys in his time (p. 18). According to that account, if the text is
+sound, some musicians placed the Mixo-lydian a semitone below the
+Dorian--the Hypo-dorian being again a semitone lower. In this scheme,
+then, the Mixo-lydian held the place of the later Hypo-lydian. The
+conjecture may perhaps be hazarded, that this lower Mixo-lydian
+somehow represents Plato's 'slack Lydian,' and eventually passed into
+the Hypo-lydian.]
+
+So far the passage of Plutarch goes to confirm the view of the
+Platonic modes according to which they were distinguished chiefly, if
+not wholly, by difference of pitch. We come now, however, to a
+statement which apparently tends in the opposite direction, viz. that
+a certain Lamprocles of Athens noticed that in the Mixo-lydian mode
+the Disjunctive Tone ([Greek: diazeuxis]) was at the upper end of the
+scale ([Greek: epi to oxy]), and reformed the scale accordingly. This
+must refer to an octave scale of the form _b c d e f g a b_,
+consisting of the two tetrachords _b-e_ and _e-a_, and the tone
+_a-b_. Such an octave may or may not be in the Mixo-lydian key: it is
+certainly of the Mixo-lydian species (p. 57).
+
+In estimating the value of this piece of evidence it is necessary to
+remark, in the first place, that the authority is no longer that of
+Aristoxenus, but of a certain Lysis, of whom nothing else seems to be
+known. That he was later than Aristoxenus is made probable by his way
+of describing the Mixo-lydian octave, viz. by reference to the notes
+in the Perfect System by which it is exemplified (Hypatê Hypatôn to
+Paramesê). In Aristoxenus, as we shall see (p. 31), the primitive
+octave (from Hypatê to Nêtê) is the only scale the notes of which are
+mentioned by name. But even if the notice is comparatively early, it
+is worth observing that the Mixo-lydian scale thus ascribed to
+Lamprocles consists of two tetrachords of the normal type, viz. with
+the semitone or [Greek: pyknon] at the lower end of the scale
+(Diatonic _e f g a_, Enharmonic _e e* f a_). The difference is that
+they are conjunct, whereas in the primitive standard octave (_e - e_)
+the tetrachords are disjunct (_e-a b-e_). This, however, is a variety
+which is provided for by the tetrachord Synêmmenôn in the Perfect
+System, and which may have been allowed in the less complete scales
+of earlier times. In any case the existence of a scale of this
+particular form does not prove that the octaves of other species were
+recognised in the same way.
+
+(2) In another passage (c. 6) Plutarch says of the ancient music of
+the cithara that it was characterised by perfect simplicity. It was
+not allowed, he tells us, to change the mode ([Greek: metapherein tas
+harmonias]) or the rhythm: for in the primitive lyrical compositions
+called 'Nomes' ([Greek: nomoi]) they preserved in each its proper
+pitch ([Greek: tên oikeian tasin]). Here the word [Greek: tasis]
+indicates that by [Greek: harmoniai] Plutarch (or the older author
+from whom he was quoting) meant particular _keys_. This is fully
+confirmed by the use of [Greek: tonos] in a passage a little further
+on (c. 8), where Plutarch gives an account of an innovation in this
+matter made by Sacadas of Argos (fl. 590 B.C.). 'There being three
+keys ([Greek: tonoi]) in the time of Polymnastus and Sacadas, viz.
+the Dorian, Phrygian and Lydian, it is said that Sacadas composed a
+strophe in each of these keys, and taught the chorus to sing them,
+the first in the Dorian, the second in the Phrygian, and the third in
+the Lydian key: and this composition was called the "three-part Nome"
+([Greek: nomos trimerês]) on account of the change of key.' In
+Westphal's _Harmonik und Melopöie_ (ed. 1863, p. 76, cp. p. 62) he
+explains this notice of the ancient modes ([Greek: harmoniai],
+_Tonarten_), observing that the word [Greek: tonos] is there used
+improperly for what the technical writers call [Greek: eidos tou dia
+pasôn].
+
+(3) In a somewhat similar passage of the same work (c. 19) Plutarch
+is contending that the fewness of the notes in the scales used by the
+early musicians did not arise from ignorance, but was characteristic
+of their art, and necessary to its peculiar ethos. Among other points
+he notices that the tetrachord Hypatôn was not used in Dorian music
+([Greek: en tois Dôriois]), and this, he says, was not because they
+did not know of that tetrachord--for they used it in other keys
+([Greek: tonoi])--but they left it out in the Dorian key for the sake
+of preserving its ethos, the beauty of which they valued ([Greek: dia
+dê tên tou êthous phylakên aphêroun tou Dôriou tonou, timôntes to
+kalon autou]). Here again Westphal (_Aristoxenus_, p. 476) has to
+take [Greek: tonos] to mean [Greek: harmonia] or 'mode' (in his
+language _Tonart_, not _Transpositionsscala_). For in the view of
+those who distinguish [Greek: harmonia] from [Greek: tonos] it is the
+[Greek: harmonia] upon which the ethos of music depends. Plutarch
+himself had just been saying (in c. 17) that Plato preferred the
+Dorian [Greek: harmonia] on account of its grave and elevated
+character ([Greek: epei poly to semnon estin en tê Dôristi, tautên
+proutimêsen]). On the other hand the usual sense of [Greek: tonos] is
+supported by the consideration that the want of the tetrachord
+Hypatôn would affect the pitch of the scale rather than the
+succession of its intervals.
+
+It seems to follow from a comparison of these three passages that
+Plutarch was not aware of any difference of meaning between the words
+[Greek: tonos] and [Greek: harmonia], or any distinction in the
+scales of Greek music such as has been supposed to be conveyed by
+these words. Another synonym of [Greek: tonos] which becomes very
+common in the later writers on music is the word [Greek: tropos][1].
+In the course of the passage of Plutarch already referred to (_De
+Mus._ c. 17) it is applied to the Dorian mode, which Plutarch has
+just called [Greek: harmonia]. As [Greek: tropos] is always used in
+the later writers of the keys ([Greek: tonoi]) of Aristoxenus, this
+may be added to the places in which [Greek: harmonia] has the same
+meaning.
+
+
+
+
+§ 13. _Modes employed on different Instruments._
+
+In the anonymous treatise on music published by Bellermann[2] (c.
+28), we find the following statement regarding the use of the modes
+or keys in the scales of different instruments:
+
+'The Phrygian mode ([Greek: harmonia]) has the first place on
+wind-instruments: witness the first discoverers--Marsyas, Hyagnis,
+Olympus--who were Phrygians. Players on the water-organ ([Greek:
+hydraulai]) use only six modes ([Greek: tropoi]), viz. Hyper-lydian,
+Hyper-ionian, Lydian, Phrygian, Hypo-lydian, Hypo-phrygian. Players
+on the cithara tune their instrument to these four, viz.
+Hyper-ionian, Lydian, Hypo-lydian, Ionian. Flute-players employ
+seven, viz. Hyper-aeolian, Hyper-ionian, Hypo-lydian, Lydian,
+Phrygian, Ionian, Hypo-phrygian. Musicians who concern themselves
+with orchestic (choral music) use seven, viz. Hyper-dorian, Lydian,
+Phrygian, Dorian, Hypo-lydian, Hypo-phrygian, Hypo-dorian.
+
+[Footnote 1: Aristides Quintilianus uses [Greek: tropos] as the
+regular word for 'key:' e.g. in p. 136 [Greek: en tê tôn tropôn, hous
+kai tonous ekalesamen, ekthesei]. So Alypius (p. 2 Meib.) [Greek:
+dielein eis tous legomenous tropous te kai tonous, ontas pentekaideka
+ton arithmon]. Also Bacchius in his catechism (p. 12 Meib.) [Greek:
+hoi tous treis tropous adontes tinas adousi; Lydion, Phrygion,
+Dôrion; hoi de tous hepta tinas; Mixolydion, Lydion, Phrygion,
+Dôrion, Hypolydion, Hypophrygion, Hypodôrion, toutôn poios estin
+oxyteros? ho Mixolydios, k.t.l.] And Gaudentius (p. 21, l. 2) [Greek:
+kath' hekaston tropon hê tonon]. Cp. Dionys. Hal. _De Comp. Verb._ c.
+19.]
+
+[Footnote 2: _Anonymi scriptio de Musica_ (Berlin. 1841).]
+
+In this passage it is evident that we have to do with keys of the
+scheme attributed to Aristoxenus, including the two (Hyper-aeolian
+and Hyper-lydian) which were said to have been added after his time.
+The number of scales mentioned is sufficient to prove that the
+reference is not to the seven species of the octave. Yet the word
+[Greek: harmonia] is used of these keys, and with it, seemingly as an
+equivalent, the word [Greek: tropos].
+
+Pollux (_Onom._ iv. 78) gives a somewhat different account of the
+modes used on the flute: [Greek: kai harmonia men aulêtikê Dôristi,
+Phrygisti, Lydios kai Iônikê, kai syntonos Lydisti hên Anthippos
+exeure]. But this statement, as has been already pointed out (p. 22),
+is a piece of antiquarian learning, and therefore takes no notice of
+the more recent keys, as Hyper-aeolian and Hyper-ionian, or even
+Hypo-phrygian (unless that is the Ionian of Pollux). The absence of
+Dorian from the list given by the _Anonymus_ is curious: but it seems
+that at that time it was equally unknown to the cithara and the
+water-organ. There is therefore no reason to think that the two lists
+are framed with reference to different things. That is to say,
+[Greek: harmonia] in Pollux has the same meaning as [Greek: harmonia]
+in the _Anonymus_, and is equivalent to [Greek: tonos].
+
+
+
+
+§ 14. _Recapitulation--[Greek: harmonia] and [Greek: tonos]._
+
+The inquiry has now reached a stage at which we may stop to consider
+what result has been reached, especially in regard to the question
+whether the two words [Greek: harmonia] and [Greek: tonos] denote two
+sets of musical forms, or are merely two different names for the same
+thing. The latter alternative appears to be supported by several
+considerations.
+
+1. From various passages, especially in Plato and Aristotle, it has
+been shown that the modes anciently called [Greek: harmoniai]
+differed in pitch, and that this difference in pitch was regarded as
+the chief source of the peculiar ethical character of the modes.
+
+2. The list of [Greek: harmoniai] as gathered from the writers who
+treat of them, viz. Plato, Aristotle, and Heraclides Ponticus, is
+substantially the same as the list of [Greek: tonoi] described by
+Aristoxenus (p. 18): and moreover, there is an agreement in detail
+between the two lists which cannot be purely accidental. Thus
+Heraclides says that certain people had found out a new [Greek:
+harmonia], the Hypo-phrygian; and Aristoxenus speaks of the
+Hypo-phrygian [Greek: tonos] as a comparatively new one. Again, the
+account which Aristoxenus gives of the Hypo-dorian [Greek: tonos] as
+a key immediately below the Dorian agrees with what Heraclides says
+of the Hypo-dorian [Greek: harmonia], and also with the mention of
+Hypo-dorian and Hypo-phrygian (but not Hypo-lydian) in the
+Aristotelian _Problems_. Once more, the absence of Ionian from the
+list of [Greek: tonoi] in Aristoxenus is an exception which proves
+the rule: since the name of the Ionian [Greek: harmonia] is similarly
+absent from Aristotle.
+
+3. The usage of the words [Greek: harmonia] and [Greek: tonos] is
+never such as to suggest that they refer to different things. In the
+earlier writers, down to and including Aristotle, [Greek: harmonia]
+is used, never [Greek: tonos]. In Aristoxenus and his school we find
+[Greek: tonos], and in later writers [Greek: tropos], but not [Greek:
+harmonia]. The few writers (such as Plutarch) who use both [Greek:
+tonos] and [Greek: harmonia] do not observe any consistent
+distinction between them. Those who (like Westphal) believe that
+there was a distinction, are obliged to admit that [Greek: harmonia]
+is occasionally used for [Greek: tonos] and conversely.
+
+4. If a series of names such as Dorian, Phrygian, Lydian and the rest
+were applied to two sets of things so distinct from each other, and
+at the same time so important in the practice of music, as what we
+now call modes and keys, it is incredible that there should be no
+trace of the double usage. Yet our authors show no sense even of
+possible ambiguity. Indeed, they seem to prefer, in referring to
+modes or keys, to use the adverbial forms [Greek: dôristi], [Greek:
+phrygisti], &c., or the neuter [Greek: ta dôria], [Greek: ta
+phrygia], &c., where there is nothing to show whether 'mode' or
+'key,' [Greek: harmonia] or [Greek: tonos], is intended.
+
+
+
+
+§ 15. _The Systems of Greek Music._
+
+The arguments in favour of identifying the primitive national Modes
+([Greek: harmoniai]) with the [Greek: tonoi] or keys may be
+reinforced by some considerations drawn from the history and use of
+another ancient term, namely [Greek: systêma].
+
+A System ([Greek: systêma]) is defined by the Greek technical writers
+as a group or complex of intervals ([Greek: to ek pleionôn ê henos
+diastêmatôn synkeimenon] Ps. Eucl.). That is to say, any three or
+more notes whose _relative_ pitch is fixed may be regarded as forming
+a particular System. If the notes are such as might be used in the
+same melody, they are said to form a _musical_ System ([Greek:
+systêma emmeles]). As a matter of abstract theory it is evident that
+there are very many combinations of intervals which in this sense
+form a musical System. In fact, however, the variety of systems
+recognised in the theory of Greek music was strictly limited. The
+notion of a small number of scales, of a particular compass,
+available for the use of the musician, was naturally suggested by the
+ancient lyre, with its fixed and conventional number of strings. The
+word for _string_ ([Greek: chordê]) came to be used with the general
+sense of a _note_ of music; and in this way the several strings of
+the lyre gave their names to the notes of the Greek gamut[1].
+
+
+
+
+§ 16. _The Standard Octachord System._
+
+In the age of the great melic poets the lyre had no more than seven
+strings: but the octave was completed in the earliest times of which
+we have accurate information. The scale which is assumed as matter of
+common knowledge in the Aristotelian _Problems_ and the _Harmonics_
+of Aristoxenus consists of eight notes, named as follows from their
+place on the lyre:
+
+
+      Nêtê ([Greek: neatê] or [Greek: nêtê], lit. 'lowest,' our 'highest').
+      Paranêtê  ([Greek: paranêtê], 'next to Nêtê').
+      Tritê ([Greek: tritê], _i.e._ 'third' string).
+      Paramesê ([Greek: paramesê] or [Greek: paramesos], 'next to Mesê').
+      Mesê ([Greek: mesê], 'middle string').
+      Lichanos ([Greek: lichanos], _i.e._ 'forefinger' string).
+      Parhypatê ([Greek: parypatê]).
+      Hypatê ([Greek: hypatê], lit. 'uppermost,' our 'lowest').
+
+
+It will be seen that the conventional sense of high and low in the
+words [Greek: hypatê] and [Greek: neatê] was the reverse of the
+modern usage.
+
+The musical scale formed by these eight notes consists of two
+_tetrachords_ or scales of four notes, and a major tone. The lower of
+the tetrachords consists of the notes from Hypatê to Mesê, the higher
+of those from Paramesê to Nêtê: the interval between Mesê and
+Paramesê being the so-called _Disjunctive Tone_ ([Greek: tonos
+diazeuktikos]). Within each tetrachord the intervals depend upon the
+_Genus_ ([Greek: genos]). Thus the four notes just mentioned--Hypatê,
+Mesê, Paramesê, Nêtê--are the same for every genus, and accordingly
+are called the 'standing' or 'immoveable' notes ([Greek: phthongoi
+hestôtes, akinêtoi]), while the others vary with the genus, and are
+therefore 'moveable' ([Greek: pheromenoi]).
+
+[Footnote 1: This is especially evident in the case of the Lichanos;
+as was observed by Aristides Quintilianus, who says (p. 10 Meib.):
+[Greek: hai kai tô genei lichanoi prosêgoreuthêsan, homônymôs tô
+plêttonti daktylô tên êchousan autas chordên onomastheisai]. But
+Tritê also is doubtless originally the 'third string' rather than the
+'third note.']
+
+In the ordinary Diatonic genus the intervals of the tetrachords are,
+in the ascending order, semitone + tone + tone: _i.e._ Parhypatê is a
+semitone above Hypatê, and Lichanos a tone above Parhypatê. In the
+Enharmonic genus the intervals are two successive quarter-tones
+([Greek: diesis]) followed by a ditone or major Third: consequently
+Parhypatê is only a quarter of a tone above Hypatê, and Lichanos
+again a quarter of a tone above Parhypatê. The group of three notes
+separated in this way by small intervals (viz. two successive
+quarter-tones) is called a [Greek: pyknon]. If we use an asterisk to
+denote that a note is raised a quarter of a tone, these two scales
+may be represented in modern notation as follows:
+
+
+        _Diatonic._              _Enharmonic._
+
+      e  =Nêtê=      \           e  =Nêtê=      \
+      d  Paranêtê          }        ( c  Paranêtê          }
+      c  Tritê             }    +---( b* Tritê             }
+      b  =Paramesê=  /     |   ( b  =Paramesê=  /
+      a  =Mesê=      \     |     a  =Mesê=      \
+      g  Lichanos          }    |   ( f  Lichanos          }
+      f  Parhypatê         }    | +-( e* Parhypatê         }
+      e  =Hypatê=    /     | | ( e  =Hypatê=    /
+                                | |
+                  [Greek: pyknon] [Greek: pyknon]
+
+
+In the Chromatic genus and its varieties the division is of an
+intermediate kind. The interval between Lichanos and Mesê is more
+than one tone, but less than two: and the two other intervals, as in
+the enharmonic, are equal.
+
+The most characteristic feature of this scale, in contrast to those
+of the modern Major and Minor, is the place of the small intervals
+(semitone or [Greek: pyknon]), which are always the lowest intervals
+of a tetrachord. It is hardly necessary to quote passages from
+Aristotle and Aristoxenus to show that this is the succession of
+intervals assumed by them. The question is asked in the Aristotelian
+_Problems_ (xix. 4), why Parhypatê is difficult to sing, while Hypatê
+is easy, although there is only a diesis between them ([Greek: kaitoi
+diesis hekateras]). Again (_Probl._ xix. 47), speaking of the old
+heptachord scale, the writer says that the Paramesê was left out, and
+consequently the Mesê became the lowest note of the upper [Greek:
+pyknon], _i.e._ the group of 'close' notes consisting of Mesê, Tritê,
+and Paranêtê. Similarly Aristoxenus (_Harm._ p. 23) observes that the
+'space' of the Lichanos, _i.e._ the limit within which it varies in
+the different genera, is a tone while the space of the Parhypatê is
+only a diesis, for it is never nearer Hypatê than a diesis or further
+off than a semitone.
+
+
+
+
+§ 17. _Earlier Heptachord Scales._
+
+Regarding the earlier seven-stringed scales which preceded this
+octave our information is scanty and somewhat obscure. The chief
+notice on the subject is the following passage of the Aristotelian
+_Problems_:
+
+
+     _Probl._ xix. 47 [Greek: dia ti hoi archaioi heptachordous
+     poiountes tas harmonias tên hypatên all' ou tên nêtên
+     katelipon: hê ou tên] [Greek: hypatên] (leg. [Greek: nêtên]),
+     [Greek: alla tên nyn paramesên kaloumenên aphêroun kai to
+     toniaion diastêma; echrônto de tê eschatê mesê tou epi to oxy
+     pyknou; did kai mesên autên prosêloreusan [hê] oti ên tou men
+     anô tetrachordon teleutê, tou de katô archê, kai meson eiche
+     logon tonô tôn akrôn?]
+
+     'Why did the ancient seven-stringed scales include Hypatê but
+     not Nêtê? Or should we say that the note omitted was not Nêtê,
+     but the present Paramesê and the interval of a tone (_i.e._
+     the disjunctive tone)? The Mesê, then, was the lowest note of
+     the upper [Greek: pyknon]: whence the name [Greek: mesê],
+     because it was the end of the upper tetrachord and beginning
+     of the lower one, and was in pitch the middle between the
+     extremes.'
+
+
+This clearly implies two conjunct tetrachords--
+
+[Music: _e f g a a# c d_ \---- /\----- /]
+
+In another place (_Probl._ xix. 32) the question is asked, why the
+interval of the octave is called [Greek: dia pasôn], not [Greek: di'
+oktô],--as the Fourth is [Greek: dia tessarôn], the Fifth [Greek: dia
+pente]. The answer suggested is that there were anciently seven
+strings, and that Terpander left out the Tritê and added the Nêtê.
+That is to say, Terpander increased the compass of the scale from the
+ancient two tetrachords to a full Octave; but he did not increase the
+number of strings to eight. Thus he produced a scale like the
+standard octave, but with one note wanting; so that the term [Greek:
+di oktô] was inappropriate.
+
+Among later writers who confirm this account we may notice
+Nicomachus, p. 7 Meib. [Greek: mesê dia tessarôn pros amphotera en tê
+heptachordô kata to palaion diestôsa]: and p. 20 [Greek: tê toinyn
+archaiotropô lyra toutesti tê heptachordô, kata synaphên ek duo
+tetrachordôn synestôsê k.t.l.]
+
+It appears then that two kinds of seven-stringed scales were known,
+at least by tradition: viz. (1) a scale composed of two conjunct
+tetrachords, and therefore of a compass less than an octave by one
+tone; and (2) a scale of the compass of an octave, but wanting a
+note, viz. the note above Mesê. The existence of this incomplete
+scale is interesting as a testimony to the force of the tradition
+which limited the number of strings to seven.
+
+
+
+
+§ 18. _The Perfect System._
+
+The term 'Perfect System' ([Greek: systêma teleion]) is applied by
+the technical writers to a scale which is evidently formed by
+successive additions to the heptachord and octachord scales explained
+in the preceding chapter. It may be described as a combination of two
+scales, called the Greater and Lesser Perfect System.
+
+The Greater Perfect System ([Greek: systêma teleion meizon]) consists
+of two octaves formed from the primitive octachord System by adding a
+tetrachord at each end of the scale. The new notes are named like
+those of the adjoining tetrachord of the original octave, but with
+the name of the tetrachord added by way of distinction. Thus below
+the original Hypatê we have a new tetrachord Hypatôn ([Greek:
+tetrachordon hypatôn]), the notes of which are accordingly called
+Hypatê Hypatôn, Parhypatê Hypatôn, and Lichanos Hypatôn: and
+similarly above Nêtê we have a tetrachord Hyperbolaiôn. Finally the
+octave downwards from Mesê is completed by the addition of a note
+appropriately called Proslambanomenos.
+
+The Lesser Perfect System ([Greek: systêma teleion elasson]) is
+apparently based upon the ancient heptachord which consisted of two
+'conjunct' tetrachords meeting in the Mesê. This scale was extended
+downwards in the same way as the Greater System, and thus became a
+scale of three tetrachords and a tone.
+
+These two Systems together constitute the Perfect and 'unmodulating'
+System ([Greek: systêma teleion ametabolon]), which may be
+represented in modern notation[1] as follows:
+
+
+      a  Nêtê Hyperbolaiôn     \  Tetrachord
+      g  Paranêtê Hyperbolaiôn  } Hyperbolaiôn
+      f  Tritê Hyperbolaiôn    /
+      e  Nêtê Diezeugmenôn
+      d  Paranêtê Diezeugmenôn \  Tetrachord
+      c  Tritê Diezeugmenôn     } Diezeugmenôn
+      b  Paramesê              /
+            d  Nêtê Synêmmenôn       \ Tetrachord
+            c  Paranêtê Synêmmenôn    } Synêmmenôn
+            b flat   Tritê Synêmmenôn/
+      a  Mesê            \
+      g  Lichanos Mesôn   } Tetrachord
+      f  Parhypatê Mesôn  } Mesôn
+      e  Hypatê Mesôn    /
+      d  Lichanos Hypatôn  \ Tetrachord
+      c  Parhypatê Hypatôn  }  Hypatôn
+      b  Hypatê Hypatôn    /
+      a  Proslambanomenos
+
+
+[Footnote 1: The correspondence between ancient and modern musical
+notation was first determined in a satisfactory way by Bellermann
+(_Die Tonleitern und Musiknoten der Griechen_), and Fortlage (_Das
+musicalische System der Griechen_).]
+
+No account of the Perfect System is given by Aristoxenus, and there
+is no trace in his writings of an extension of the standard scale
+beyond the limits of the original octave. In one place indeed
+(_Harm._ p. 8, 12 Meib.) Aristoxenus promises to treat of Systems,
+'and among them of the perfect System' ([Greek: peri te tôn allôn kai
+tou teleiou]). But we cannot assume that the phrase here had the
+technical sense which it bore in later writers. More probably it
+meant simply the octave scale, in contrast to the tetrachord and
+pentachord--a sense in which it is used by Aristides Quintilianus, p.
+11 Meib. [Greek: synêmmenôn de eklêthê to holon systêma hoti tô
+prokeimenô teleiô tô mechri mesês synêptai], 'the whole scale was
+called conjunct because it is conjoined to the complete scale that
+reaches up to Mesê' (_i.e._ the octave extending from
+Proslambanomenos to Mesê). So p. 16 [Greek: kai ha men autôn esti
+teleia, ha d' ou, atelê men tetrachordon, pentachordon, teleion de
+oktachordon.] This is a use of [Greek: teleios] which is likely
+enough to have come from Aristoxenus. The word was doubtless applied
+in each period to the most complete scale which musical theory had
+then recognised.
+
+Little is known of the steps by which this enlargement of the Greek
+scale was brought about. We shall not be wrong in conjecturing that
+it was connected with the advance made from time to time in the form
+and compass of musical instruments[1]. Along with the lyre, which
+kept its primitive simplicity as the instrument of education and
+everyday use, the Greeks had the cithara ([Greek: kithara]), an
+enlarged and improved lyre, which, to judge from the representations
+on ancient monuments, was generally seen in the hands of professional
+players ([Greek: kitharôdoi]). The development of the cithara showed
+itself in the increase, of which we have good evidence even before
+the time of Plato, in the number of the strings.
+
+[Footnote 1: This observation was made by ancient writers, _e.g._ by
+Adrastus (Peripatetic philosopher of the second cent. A.D.): [Greek:
+epêuxêmenês de tês mousikês kai polychordôn kai polyphthongôn
+gegonotôn organôn tô proslêphthênai kai epi to bary kai epi to oxy
+tois pro[:y]parchousin oktô phthongois allous pleionas, homôs k.t.l.
+(Theon Smyrn. c. 6).]
+
+The poet Ion, the contemporary of Sophocles, was the author of an
+epigram on a certain ten-stringed lyre, which seems to have had a
+scale closely approaching that of the Lesser Perfect System[1]. A
+little later we hear of the comic poet Pherecrates attacking the
+musician Timotheus for various innovations tending to the loss of
+primitive simplicity, in particular the use of twelve strings[2].
+According to a tradition mentioned by Pausanias, the Spartans
+condemned Timotheus because in his cithara he had added four strings
+to the ancient seven. The offending instrument was hung up in the
+Scias (the place of meeting of the Spartan assembly), and apparently
+was seen there by Pausanias himself (Paus. iii. 12, 8).
+
+[Footnote 1: The epigram is quoted in the pseudo-Euclidean
+_Introductio_, p. 19 (Meib.): [Greek: ho de] (sc. [Greek: Iôn])
+[Greek: en dekachordô lyra] (_i.e._ in a poem on the subject of the
+ten-stringed lyre):--
+
+              [Greek: tên dekabamona taxin echousa
+      tas symphônousas harmonias triodous;
+    prin men s' heptatonon psallon dia tessara pantes
+      Hellênes, spanian mousan aeiramenoi.]
+
+'The triple ways of music that are in concord' must be the three
+conjunct tetrachords that can be formed with ten notes (_b c d e f g
+a b-flat c d_). This is the scale of the Lesser Perfect System before
+the addition of the Proslambanomenos.]
+
+[Footnote 2: Pherecrates [Greek: cheirôn] fr. 1 (quoted by Plut. _de
+Mus._ c. 30). It is needless to refer to the other traditions on the
+subject, such as we find in Nicomachus (_Harm._ p. 35) and Boethius.]
+
+A similar or still more rapid development took place in the flute
+([Greek: aulos]). The flute-player Pronomus of Thebes, who was said
+to have been one of the instructors of Alcibiades, invented a flute
+on which it was possible to play in all the modes. 'Up to his time,'
+says Pausanias (ix. 12, 5), 'flute-players had three forms of flute:
+with one they played Dorian music; a different set of flutes served
+for the Phrygian mode ([Greek: harmonia]); and the so-called Lydian
+was played on another kind again. Pronomus was the first who devised
+flutes fitted for every sort of mode, and played melodies different
+in mode on the same flute.' The use of the new invention soon became
+general, since in Plato's time the flute was the instrument most
+distinguished by the multiplicity of its notes: cp. Rep. p. 399
+[Greek: ti de? aulopoious ê aulêtas paradexei eis tên polin? ê ou
+touto polychordotaton?] Plato may have had the invention of Pronomus
+in mind when he wrote these words.
+
+With regard to the order in which the new notes obtained a place in
+the schemes of theoretical musicians we have no trustworthy
+information. The name [Greek: proslambanomenos], applied to the
+lowest note of the Perfect System, points to a time when it was the
+last new addition to the scale. Plutarch in his work on the _Timaeus_
+of Plato ([Greek: peri tês en Timaiô psychogonias]) speaks of the
+Proslambanomenos as having been added in comparatively recent times
+(p. 1029 _c_ [Greek: hoi de neôteroi ton proslambanomenon tonô
+diapheronta tês hypatês epi to bary taxantes to men holon diastêma
+dis dia pasôn epoiêsan]). The rest of the Perfect System he ascribes
+to 'the ancients' ([Greek: tous palaious ismen hypatas men dyo, treis
+de nêtas, mian de mesên kai mian paramesên tithemenous]). An earlier
+addition--perhaps the first made to the primitive octave--was a note
+called Hyperhypatê, which was a tone below the old Hypatê, in the
+place afterwards occupied on the Diatonic scale by Lichanos Hypatôn.
+It naturally disappeared when the tetrachord Hypatôn came into use.
+It is only mentioned by one author, Thrasyllus (quoted by Theon
+Smyrnaeus, cc. 35-36[1]).
+
+[Footnote 1: The term [Greek: hyperypatê] had all but disappeared
+from the text of Theon Smyrnaeus in the edition of Bullialdus (Paris,
+1644), having been corrupted into [Greek: hypatê] or [Greek:
+parypatê] in every place except one (p. 141, 3). It has been restored
+from MSS. in the edition of Hiller (Teubner, Leipzig, 1878). The word
+occurs also in Aristides Quintilianus (p. 10 Meib.), where the plural
+[Greek: hyperypatai] is used for the notes below Hypatê, and in
+Boethius (_Mus._ i. 20).
+
+It may be worth noticing also that Thrasyllus uses the words [Greek:
+diezeugmenê] and [Greek: hyperbolaia] in the sense of [Greek: nêtê
+diezeugmenôn] and [Greek: nêtê hyperbolaiôn] (Theon Smyrn. _l. c._).]
+
+The notes of the Perfect System, with the intervals of the scale
+which they formed, are fully set out in the two treatises that pass
+under the name of the geometer Euclid, viz. the _Introductio
+Harmonica_ and the _Sectio Canonis_. Unfortunately the authorship of
+both these works is doubtful[1]. All that we can say is that if the
+Perfect System was elaborated in the brief interval between the time
+of Aristotle and that of Euclid, the materials for it must have
+already existed in musical practice.
+
+[Footnote 1: _The Introduction to Harmonics_ ([Greek: eisagôgê
+harmonikê]) which bears the name of Euclid in modern editions
+(beginning with J. Pena, Paris, 1557) cannot be his work. In some
+MSS. it is ascribed to Cleonides, in others to Pappus, who was
+probably of the fourth century A.D. The author is one of the [Greek:
+harmonikoi] or Aristoxeneans, who adopt the method of equal
+temperament. He may perhaps be assigned to a comparatively early
+period on the ground that he recognises only the thirteen keys
+ascribed to Aristoxenus--not the fifteen keys given by most later
+writers (Aristides Quint., p. 22 Meib.). For some curious evidence
+connecting it with the name of the otherwise unknown writer
+Cleonides, see K. von Jan, _Die Harmonik des Aristoxenianers
+Kleonides_ (Landsberg, 1870). The _Section of the Canon_ ([Greek:
+kanonos katatomê]) belongs to the mathematical or Pythagorean school,
+dividing the tetrachord into two major tones and a [Greek: leimma]
+which is somewhat less than a semitone. In point of form it is
+decidedly Euclidean: but we do not find it referred to by any writer
+before the third century A.D.--the earliest testimony being that of
+Porphyry (pp. 272-276 in Wallis' edition).]
+
+
+
+
+§ 19. _Relation of System and Key._
+
+Let us now consider the relation between this fixed or standard scale
+and the varieties denoted by the terms [Greek: harmonia] and [Greek:
+tonos].
+
+With regard to the [Greek: tonoi] or Keys of Aristoxenus we are not
+left in doubt. A system, as we have seen, is a series of notes whose
+_relative_ pitch is fixed. The key in which the System is taken fixes
+the absolute pitch of the series. As Aristoxenus expresses it, the
+Systems are melodies set at the pitch of the different keys ([Greek:
+tous tonous, eph' hôn tithemena ta systêmata melôdeitai]). If then we
+speak of Hypatê or Mesê (just as when we speak of a moveable Do), we
+mean as many different notes as there are keys: but the Dorian Hypatê
+or the Lydian Mesê has an ascertained pitch. The Keys of Aristoxenus,
+in short, are so many transpositions of the scale called the Perfect
+System.
+
+Such being the relation of the standard System to the key, can we
+suppose any different relation to have subsisted between the standard
+System and the ancient 'modes' known to Plato and Aristotle under the
+name of [Greek: harmoniai]?
+
+It appears from the language used by Plato in the _Republic_ that
+Greek musical instruments differed very much in the variety of modes
+or [Greek: harmoniai] of which they were susceptible. After Socrates
+has determined, in the passage quoted above (p. 7), that he will
+admit only two modes, the Dorian and Phrygian, he goes on to observe
+that the music of his state will not need a multitude of strings, or
+an instrument of all the modes ([Greek: panarmonion])[1]. 'There will
+be no custom therefore for craftsmen who make triangles and harps and
+other instruments of many notes and many modes. How then about makers
+of the flute ([Greek: aulos]) and players on the flute? Has not the
+flute the greatest number of notes, and are not the scales which
+admit all the modes simply imitations of the flute? There remain then
+the lyre and the cithara for use in our city; and for shepherds in
+the country a syrinx (pan's pipes).' The lyre, it is plain, did not
+admit of changes of mode. The seven or eight strings were tuned to
+furnish the scale of one mode, not of more. What then is the relation
+between the mode or [Greek: harmonia] of a lyre and the standard
+scale or [Greek: systêma] which (as we have seen) was based upon the
+lyre and its primitive gamut?
+
+[Footnote 1: Plato, Rep. p. 399: [Greek: ouk ara, ên d' egô,
+polychordias ge oude panarmoniou hêmin deêsei en tais ôdais te kai
+melesin. Ou moi, ephê, phainetai. Trigônôn ara kai pêktidôn kai
+pantôn organôn hosa polychorda kai polyarmonia dêmiourgous ou
+threpsomen. Ou phainometha. Ti de? aulopoious ê aulêtas paradexei eis
+tên polin? ê ou touto polychordotaton, kai auta ta panarmonia aulou
+tynchanei onta mimêma? Dêla dê, ê d' hos. Lyra dê soi, ên d' egô, kai
+kithara leipetai, kai kata polin chrêsima; kai au kat' agrous tois
+nomeusi syrinx an tis eiê.]
+
+The [Greek: aulos] was not exactly a flute. It had a mouthpiece which
+gave it the character rather of the modern oboe or clarinet: see the
+_Dictionary of Antiquities_, S. V. TIBIA. The [Greek: panarmonion] is
+not otherwise known, and the passage in Plato does not enable us to
+decide whether it was a real instrument or only a scale or
+arrangement of notes.]
+
+If [Greek: harmonia] means 'key,' there is no difficulty. The scale
+of a lyre was usually the standard octave from Hypatê to Nêtê: and
+that octave might be in any one key. But if a mode is somehow
+characterised by a particular succession of intervals, what becomes
+of the standard octave? No one succession of intervals can then be
+singled out. It may be said that the standard octave is in fact the
+scale of a particular mode, which had come to be regarded as the
+type, viz. the Dorian. But there is no trace of any such prominence
+of the Dorian mode as this would necessitate. The philosophers who
+recognise its elevation and Hellenic purity are very far from
+implying that it had the chief place in popular regard. Indeed the
+contrary was evidently the case[1].
+
+[Footnote 1: The passage quoted above from the _Knights_ of
+Aristophanes (p. 7) is sufficient to show that a marked preference
+for the Dorian mode would be a matter for jest.]
+
+
+
+
+§ 20. _Tonality of the Greek musical scale._
+
+It may be said here that the value of a series of notes as the basis
+of a distinct mode--in the modern sense of the word--depends
+essentially upon the _tonality_. A single scale might yield music of
+different modes if the key-note were different. It is necessary
+therefore to collect the scanty notices which we possess bearing upon
+the tonality of Greek music. The chief evidence on the subject is a
+passage of the _Problems_, the importance of which was first pointed
+out by Helmholtz[1]. It is as follows:
+
+
+     Arist. _Probl._ xix. 20: [Greek: Dia ti ean men tis tên mesên
+     kinêsê hêmôn, harmosas tas allas chordas, kai chrêtai tô
+     organô, ou monon hotan kata ton tês mesês genêtai phthongon
+     lypei kai phainetai anarmoston, alla kai kata tên allên
+     melôdian, ean de tên lichanon ê tina allon phthongon, tote
+     phainetai diapherein monon hotan kakeinê tis chrêtai? ê
+     eulogôs touto symbainei? panta gar ta chrêsta melê pollakis tê
+     mesê chrêtai, kai pantes hoi agathoi poiêtai pykna pros tên
+     mesên apantôsi, kan apelthôsi tachy epanerchontai, pros de
+     allên houtôs oudemian. kathaper ek tôn logôn eniôn
+     exairethentôn syndesmôn ouk estin ho logos Hellênikos, hoion
+     to te kai to kai, enioi de outhen lypousi, dia to tois men
+     anankaion einai chrêsthai pollakis, ei estai logos, tois de
+     mê, houtô kai tôn phthongôn hê mesê hôsper syndesmos esti, kai
+     malista tôn kalôn, dia to pleistakis enyparchein ton phthongon
+     autês.]
+
+     'Why is it that if the Mesê is altered, after the other
+     strings have been tuned, the instrument is felt to be out of
+     tune, not only when the Mesê is sounded, but through the whole
+     of the music,--whereas if the Lichanos or any other note is
+     out of tune, it seems to be perceived only when that note is
+     struck? Is it to be explained on the ground that all good
+     melodies often use the Mesê, and all good composers resort to
+     it frequently, and if they leave it soon return again, but do
+     not make the same use of any other note? just as language
+     cannot be Greek if certain conjunctions are omitted, such as
+     [Greek: te] and [Greek: kai], while others may be dispensed
+     with, because the one class is necessary for language, but not
+     the other: so with musical sounds the Mesê is a kind of
+     'conjunction,' especially of beautiful sounds, since it is
+     most often heard among these.'
+
+
+[Footnote 1: _Die Lehre von den Tonempfindungen_, p. 367, ed. 1863.]
+
+In another place (xix. 36) the question is answered by saying that
+the notes of a scale stand in a certain relation to the Mesê, which
+determines them with reference to it ([Greek: hê taxis hê hekastês
+êdê di' ekeinên]): so that the loss of the Mesê means the loss of the
+ground and unifying element of the scale ([Greek: arthentos tou
+aitiou tou hêrmosthai kai tou synechontos])[1].
+
+These passages imply that in the scale known to Aristotle, viz. the
+octave _e - e_, the Mesê _a_ had the character of a Tonic or
+key-note. This must have been true _a fortiori_ of the older
+seven-stringed scale, in which the Mesê united the two conjunct
+tetrachords. It was quite in accordance with this state of things
+that the later enlargement completed the octaves from Mesê downwards
+and upwards, so that the scale consisted of two octaves of the form
+_a-a_. As to the question how the Tonic character of the Mesê was
+shown, in what parts of the melody it was necessarily heard, and the
+like, we can but guess. The statement of the _Problems_ is not
+repeated by any technical writer, and accordingly it does not appear
+that any rules on the subject had been arrived at. It is significant,
+perhaps, that the frequent use of the Mesê is spoken of as
+characteristic of _good_ melody ([Greek: panta ta chrêsta melê
+pollakis tê mesê chrêtai]), as though tonality were a merit rather
+than a necessity.
+
+Another passage of the _Problems_ has been thought to show that in
+Greek music the melody ended on the Hypatê. The words are these
+(_Probl._ xix. 33):
+
+
+  [Greek: Dia ti euarmostoteron apo tou oxeos epi to bary ê apo
+  tou]
+
+
+[Footnote 1: So in the Euclidean _Sectio Canonis_ the propositions
+which deal with the 'movable' notes, viz. Paranêtê and Lichanos
+(Theor. xvii) and Parhypatê and Tritê (Theor. xviii), begin by
+postulating the Mesê ([Greek: estô gar mesê ho B k.t.l.]).]
+
+
+     [Greek: bareos epi to oxy; poteron hoti to apo tês archês
+     ginetai archesthai? hê gar mesê kai hêgemôn oxytatê tou
+     tetrachordou; to de ouk ap' archês all' apo teleutês.]
+
+     'Why is a descending scale more musical than an ascending one?
+     Is it that in this order we begin with the beginning,--since
+     the Mesê or leading note[1] is the highest of the
+     tetrachord,--but with the reverse order we begin with the
+     end?'
+
+
+There is here no explicit statement that the melody ended on the
+Hypatê, or even that it began with the Mesê. In what sense, then, was
+the Mesê a 'beginning' ([Greek: archê]), and the Hypatê an 'end'? In
+Aristotelian language the word [Greek: archê] has various senses. It
+might be used to express the relation of the Mesê to the other notes
+as the basis or ground-work of the scale. Other passages, however,
+point to a simpler explanation, viz. that the order in question was
+merely conventional. In _Probl._ xix. 44 it is said that the Mesê is
+the beginning ([Greek: archê]) of one of the two tetrachords which
+form the ordinary octave scale (viz. the tetrachord Mesôn); and again
+in _Probl._ xix. 47 that in the old heptachord which consisted of two
+conjunct tetrachords (_e-a-d_) the Mesê (_a_) was the end of the
+upper tetrachord and the beginning of the lower one ([Greek: hoti ên
+tou men anô tetrachordou teleutê, tou de katô archê]). In this last
+passage it is evident that there is no reference to the beginning or
+end of the melody.
+
+[Footnote 1: The term [Greek: hêgemôn] or 'leading note' of the
+tetrachord Mesôn, here applied to the Mesê, is found in the same
+sense in Plutarch, _De Mus._ c. 11, where [Greek: ho peri ton
+hêgemona keimenos tonos] means the disjunctive tone. Similarly
+Ptolemy (_Harm._ i. 16) speaks of the tones in a diatonic scale as
+being [Greek: en tois hêgoumenois topois], the semitones [Greek: en
+tois hepomenois] (sc. of the tetrachord): and again of the ratio 5:4
+(the major Third) as the 'leading' one of an Enharmonic tetrachord
+([Greek: ton epitetarton hos estin hêgoumenos tou enarmoniou
+genous]).]
+
+Another instance of the use of [Greek: archê] in connexion with the
+musical scale is to be found in the _Metaphysics_ (iv. 11, p. 1018
+_b_ 26), where Aristotle is speaking of the different senses in which
+things may be prior and posterior:
+
+
+     [Greek: Ta de kata taxin; tauta d' estin hosa pros ti hen
+     hôrismenon diestêke kata ton logon, hoion parastatês
+     tritostatou proteron, kai paranêtê nêtês; entha men gar ho
+     koryphaios, entha de hê mesê archê.]
+
+     'Other things [are prior and posterior] in _order_: viz. those
+     which are at a varying interval from some one definite thing;
+     as the second man in the rank is prior to the third man, and
+     the Paranêtê to the Nêtê: for in the one case the coryphaeus
+     is the starting-point, in the other the Mesê.'
+
+
+Here the Mesê is again the [Greek: archê] or beginning, but the order
+is the ascending one, and consequently the Nêtê is the end. The
+passage confirms what we have learned of the relative importance of
+the Mesê: but it certainly negatives any inference regarding the note
+on which the melody ended.
+
+It appears, then, that the Mesê of the Greek standard System had the
+functions of a key-note in that System. In other words, the music was
+in the _mode_ (using that term in the modern sense) represented by
+the octave _a-a_ of the natural key--the Hypo-dorian or Common
+Species. We do not indeed know how the predominant character of the
+Mesê was shown--whether, for example, the melody ended on the Mesê.
+The supposed evidence for an ending on the Hypatê has been shown to
+be insufficient. But we may at least hold that as far as the Mesê was
+a key-note, so far the Greek scale was that of the modern Minor mode
+(descending). The only way of escape from this conclusion is to deny
+that the Mesê of _Probl._ xix. 20 was the note which we have
+understood by the term--the Mesê of the standard System. This, as we
+shall presently see, is the plea to which Westphal has recourse.
+
+
+
+
+§ 21. _The Species of a Scale._
+
+The object of the preceding discussion has been to make it clear that
+the theory of a system of modes--in the modern sense of the
+word--finds no support from the earlier authorities on Greek music.
+There is, however, evidence to show that Aristoxenus, and perhaps
+other writers of the time, gave much thought to the varieties to be
+obtained by taking the intervals of a scale in different order. These
+varieties they spoke of as the _forms_ or _species_ ([Greek:
+schêmata, eidê]) of the interval which measured the compass of the
+scale in question. Thus, the interval of the Octave ([Greek: dia
+pasôn]) is divided into seven intervals, and these are, in the
+Diatonic genus, five tones and two semitones, in the Enharmonic two
+ditones, four quarter-tones, and a tone. As we shall presently see in
+detail, there are seven species of the Octave in each genus. That is
+to say, there are seven admissible octachord scales ([Greek:
+systêmata emmelê]), differing only in the succession of the intervals
+which compose them.
+
+Further, there is evidence which goes to connect the seven species of
+the Octave with the Modes or [Greek: harmoniai]. In some writers
+these species are described under names which are familiar to us in
+their application to the modes. A certain succession of intervals is
+called the Dorian species of the Octave, another succession is called
+the Phrygian species, and so on for the Lydian, Mixo-lydian,
+Hypo-dorian, Hypo-phrygian, and Hypo-lydian. It seems natural to
+conclude that the species or successions of intervals so named were
+characteristic in some way of the modes which bore the same names,
+consequently that the modes were not keys, but modes in the modern
+sense of the term.
+
+In order to estimate the value of this argument, it is necessary to
+ask, (1) how far back we can date the use of these names for the
+species of the Octave, and (2) in what degree the species of the
+Octave can be shown to have entered into the practice of music at any
+period. The answer to these questions must be gathered from a careful
+examination of all that Aristoxenus and other early writers say of
+the different musical scales in reference to the order of their
+intervals.
+
+
+
+
+§ 22. _The Scales as treated by Aristoxenus._
+
+The subject of the musical scales ([Greek: systêmata]) is treated by
+Aristoxenus as a general problem, without reference to the scales in
+actual use. He complains that his predecessors dealt only with the
+octave scale, and only with the Enharmonic genus, and did not address
+themselves to the real question of the melodious sequence of
+intervals. Accordingly, instead of beginning with a particular scale,
+such as the octave, he supposes a scale of indefinite compass,--just
+as a mathematician postulates lines and surfaces of unlimited
+magnitude. His problem virtually is, given any interval known to the
+particular genus supposed, to determine what intervals can follow it
+on a musical scale, either ascending or descending. In the Diatonic
+genus, for example, a semitone must be followed by two tones, so as
+to make up the interval of a Fourth. In the Enharmonic genus the
+dieses or quarter-tones can only occur two together, and every such
+pair of dieses ([Greek: pyknon]) must be followed in the ascending
+order by a ditone, in the descending order by a ditone or a tone. By
+these and similar rules, which he deduces mathematically from one or
+two general principles of melody, Aristoxenus in effect determines
+all the possible scales of each genus, without restriction of compass
+or pitch[1]. But whenever he refers for the purpose of illustration
+to a scale in actual use, it is always the standard octave already
+described (from Hypatê to Nêtê), or a part of it. Thus nothing can be
+clearer than the distinction which he makes between the theoretically
+infinite scale, subject only to certain principles or laws
+determining the succession of intervals, and the eight notes, of
+fixed relative pitch, which constituted the gamut of practical music.
+
+The passages in which Aristoxenus dwells upon the advance which he
+has made upon the methods of his predecessors are of considerable
+importance for the whole question of the species of the Octave. There
+are three or four places which it will be worth while to quote.
+
+
+     1. Aristoxenus, _Harm._ p. 2, 15 Meib.: [Greek: ta gar
+     diagrammata autois tôn enarmoniôn] ([Greek: harmoniôn] MSS.)
+     [Greek: ekkeitai monon systêmatôn, diatonôn d' ê chrômatikôn
+     oudeis pôpoth' heôraken; kaitoi ta diagrammata g' autôn edêlou
+     tên pasan tês melôdias taxin, en hois peri systêmatôn
+     oktachordôn enarmoniôn] ([Greek: harmoniôn] MSS.) [Greek:
+     monon elegon, peri de tôn allôn genôn te kai schêmatôn en autô
+     te tô genei tontô kai tois loipois oud' epecheirei oudeis
+     katamanthanein.]
+
+
+[Footnote 1: The investigation occupies a considerable space in his
+_Harmonics_, viz. pp. 27-29 Meib. (from the words [Greek: peri de
+synecheias kai tou hexês]), and again pp. 58-72 Meib.]
+
+
+     'The diagrams of the earlier writers set forth Systems in the
+     Enharmonic genus only, never in the Diatonic or Chromatic: and
+     yet these diagrams professed to give the whole scheme of their
+     music, and in them they treated of Enharmonic octave Systems
+     only; of other genera and other forms of this or any genus no
+     one attempted to discover anything.'
+
+     2. Ibid. p. 6, 20 Meib.: [Greek: tôn d' allôn katholou men
+     kathaper emprosthen eipomen oudeis hêptai, henos de systêmatos
+     Eratoklês epecheirêse kath' hen genos exarithmêsai ta schêmata
+     tou dia pasôn apodeiktikôs tê periphora tôn diastêmatôn
+     deiknys; ou katamathôn hoti, mê prosapodeichthentôn] (qu.
+     [Greek: proapod.]) [Greek: tôn de tou dia pente schêmatôn kai
+     tôn tou dia tessarôn pros de toutois kai tês syntheseôs autôn
+     tis pot' esti kath' hên emmelôs syntithentai, pollaplasia tôn
+     hepta symbainein gignesthai deiknytai.]
+
+     'The other Systems no one has dealt with by a general method:
+     but Eratocles has attempted in the case of one System, in one
+     genus, to enumerate the forms or _species_ of the Octave, and
+     to determine them mathematically by the periodic recurrence of
+     the intervals: not perceiving that unless we have first
+     demonstrated the forms of the Fifth and the Fourth, and the
+     manner of their melodious combination, the forms of the Octave
+     will come to be many more than seven.'
+
+
+The 'periodic recurrence of intervals' here spoken of may be
+illustrated on the key-board of a piano. If we take successive
+octaves of white notes, _a-a_, _b-b_, and so on, we obtain each time
+a different order of intervals (_i.e._ the semitones occur in
+different places), until we reach _a-a_ again, when the series begins
+afresh. In this way it is shown that only seven species of the Octave
+can be found on any particular scale. Aristoxenus shows how to prove
+this from first principles, viz. by analysing the Octave as the
+combination of a Fifth with a Fourth.
+
+3. Ibid. p. 36, 29 Meib.: [Greek: tôn de systêmatôn tas diaphoras hoi
+men holôs ouk epecheiroun exarithmein, alla peri autôn monon tôn
+heptachordôn ha ekaloun harmonias tên episkepsin epoiounto, hoi de
+epicheirêsantes oudena tropon exêrithmounto.]
+
+For [Greek: heptachordôn] Meibomius and other editors read [Greek:
+hepta oktachordôn]--a correction strongly suggested by the parallel
+words [Greek: systêmatôn oktachordôn] in the first passage quoted.
+
+'Some did not attempt to enumerate the differences of the Systems,
+but confined their view to the seven octachord Systems which they
+called [Greek: harmoniai]; others who did make the attempt did not
+succeed.'
+
+It appears from these passages that before the time of Aristoxenus
+musicians had framed diagrams or tables showing the division of the
+octave scale according to the Enharmonic genus: and that a certain
+Eratocles--of whom nothing else is known--had recognised seven forms
+or species of the octachord scale, and had shown how the order of the
+intervals in the several species passes through a sort of cycle.
+Finally, if the correction proposed in the third passage is right,
+the seven species of the Octave were somehow shown in the diagrams of
+which the first passage speaks. In what respect Eratocles failed in
+his treatment of the seven species can hardly be conjectured.
+
+Elsewhere the diagrams are described by Aristoxenus somewhat
+differently, as though they exhibited a division into Enharmonic
+dieses or quarter-tones, without reference to the melodious character
+of the scale. Thus we find him saying--. _Harm._ p. 28 Meib.: [Greek:
+zêtêteon de to syneches ouch hôs hoi harmonikoi en tais tôn
+diagrammatôn katapyknôsesin apodidonai peirôntai, toutous
+apophainontes tôn phthongôn hexês allêlôn keisthai hois symbebêke to
+elachiston diastêma diechein aph' hautôn. ou gar to mê dynasthai
+dieseis oktô kai eikosin hexês melôdeisthai tês phônês estin, alla
+tên tritên diesin panta poiousa ouch hoia t' esti prostithenai.]
+
+'We must seek continuity of succession, not as theoretical musicians
+do in filling up their diagrams with small intervals, making those
+notes successive which are separated from each other by the least
+interval. For it is not merely that the voice cannot sing
+twenty-eight successive dieses: with all its efforts it cannot sing a
+third diesis[1].'
+
+[Footnote 1: This point is one which Aristoxenus is fond of insisting
+upon: cp. p. 10, 16 [Greek: ou pros tên katapyknôsin blepontas hôsper
+hoi harmonikoi]: p. 38, 3 [Greek: hoti de estin hê katapyknôsis
+ekmelês kai panta tropon achrêstos phaneron]: p. 53, 3 [Greek: kata
+tên tou melous physin zêtêteon to hexês kai ouch hôs hoi eis tên
+katapyknôsin blepontes eiôthasin apodidonai to hexês].
+
+The statement that the ancient diagrams gave a series of twenty-eight
+successive dieses or quarter-tones has not been explained. The number
+of quarter-tones in an octave is only twenty-four. Possibly it is a
+mere error of transcription ([Greek: [=kê]] for [Greek: [=kd]]). If
+not, we may perhaps connect it with the seven intervals of the
+ordinary octave scale, and the simple method by which the enharmonic
+intervals were expressed in the instrumental notation. It has been
+explained that raising a note a quarter of a tone was shown by
+turning it through a quarter of a circle. Thus, our _c_ being denoted
+by [Symbols: E], _c_* was [Symbols: w], and _c_[Symbols: c] was
+[Symbols: 3]. Now the ancient diagrams, which divided every tone into
+four parts, must have had a character for _c_[Symbols: S]*, or the
+note three-quarters of a tone above _c_. Naturally this would be the
+remaining position of [Symbols: E], namely [Symbols: m]. Again, we
+have seen that when the interval between two notes on the diatonic
+scale is only a semitone, the result of the notation is to produce a
+certain number of duplicates, so to speak. Thus: [Symbols: K] stands
+for _b_, and therefore [Symbols:)1] for _c_: but _c_ is a note of the
+original scale, and as such is written [Symbols: q]. It may be that
+the diagrams to which Aristoxenus refers made use of these
+duplicates: that is to say, they may have made use of all four
+positions of a character (such as [Symbols: K 7g]) whether the
+interval to be filled was a tone or a semitone. If so, the seven
+intervals would give twenty-eight characters (besides the upper
+octave-note), and apparently therefore twenty-eight dieses. Some
+traces of this use of characters in four positions have been noticed
+by Bellermann (_Tonleitern_, p. 65).]
+
+This representation of the musical diagrams is borne out by the
+passage in the _Republic_ in which Plato derides the experimental
+study of music:
+
+_Rep._ p. 531 a [Greek: tas gar akouomenas au symphônias kai
+phthongous allêlois anametrountes anênyta, hôsper hoi astronomoi,
+ponousin. Nê tous theous, ephê, kai geloiôs ge, pyknômat' atta
+onomazontes kai paraballontes ta ôta, hoion ek geitonôn phônên
+thêreuomenoi, hoi men phasin eti katakouein en mesô tina êchên kai
+smikrotaton einai touto diastêma, hô metrêteon, hoi de k.t.l.]
+
+Here Socrates is insisting that the theory of music should be studied
+as a branch of mathematics, not by observation of the sounds and
+concords actually heard, about which musicians spend toil in vain.
+'Yes,' says Glaucon, 'they talk of the close-fitting of intervals,
+and put their ears down to listen for the smallest possible interval,
+which is then to be the measure.' The smallest interval was of course
+the Enharmonic diesis or quarter of a tone, and this accordingly was
+the measure or unit into which the scale was divided. A group of
+notes separated by a diesis was called 'close' ([Greek: pyknon], or a
+[Greek: pyknôma]), and the filling up of the scale in that way was
+therefore a [Greek: katapyknôsis tou diagrammatos]--a filling up with
+'close-set' notes, by the division of every tone into four equal
+parts.
+
+An example of a diagram of this kind has perhaps survived in a
+comparatively late writer, viz. Aristides Quintilianus, who gives a
+scale of two octaves, one divided into twenty-four dieses, the next
+into twelve semitones (_De Mus._ p. 15 Meib.). The characters used
+are not otherwise known, being quite different from the ordinary
+notation: but the nature of the diagram is plain from the
+accompanying words: [Greek: hautê estin hê para tois archaiois kata
+dieseis harmonia, heôs [=kd] dieseôn to proteron diagousa dia pasôn,
+to deuteron dia tôn hêmitoniôn auxêsasa]: 'this is the [Greek:
+harmonia] (division of the scale) according to dieses in use among
+the ancients, carried in the case of the first octave as far as
+twenty-four dieses, and dividing the second into semitones[1].'
+
+The phrase [Greek: hê kata dieseis harmonia], used for the division
+of an octave scale into quarter-tones, serves to explain the
+statement of Aristoxenus (in the third of the passages above quoted)
+that the writers who treated of octave Systems called them
+'harmonies' ([Greek: ha ekaloun harmonias]). That statement has
+usually been taken to refer to the ancient Modes called [Greek:
+harmoniai] by Plato and Aristotle, and has been used accordingly as
+proof that the scales of these Modes were based upon the different
+species ([Greek: eidê]) of the Octave. But the form of the
+reference--'which _they called_ [Greek: harmoniai]'--implies some
+forgotten or at least unfamiliar use of the word by the older
+technical writers. It is very much more probable that the [Greek:
+harmoniai] in question are divisions of the octave scale, as shown in
+theoretical diagrams, and had no necessary connexion with the Modes.
+Apparently some at least of these diagrams were not musical scales,
+but tables of all the notes in the compass of an octave; and the
+Enharmonic diesis was used, not merely on account of the importance
+of that genus, but because it was the smallest interval, and
+therefore the natural unit of measurement[2].
+
+[Footnote 1: The fullest account of this curious fragment of notation
+is that given by Bellermann in his admirable book, _Die Tonleitern
+und Musiknoten der Griechen_, pp. 61-65. His conjectures as to its
+origin do not claim a high degree of probability. See the remarks on
+pp. 97-99.]
+
+[Footnote 2: Cp. Plato, _Rep._ p. 531: [Greek: kai smikrotaton einai
+touto diastêma, hô metrêteon.] It may even be that this sense of
+[Greek: harmonia] was connected with the use for the Enharmonic
+genus. It is at least worth notice that the phrase [Greek: ha ekaloun
+harmonias] in this passage answers to the adjective [Greek:
+enarmoniôn] in the passage first quoted (compare the words [Greek:
+peri autôn monon tôn hepta oktachordôn ha ekaloun harmonias] with
+[Greek: peri systêmatôn oktachordôn enarmoniôn monon]).]
+
+The use of [Greek: harmonia] as an equivalent for 'System' or
+'division of the scale' appears in an important passage in Plato's
+_Philebus_ (p. 17): [Greek: all', ô phile, epeidan labês ta
+diastêmata hoposa esti ton arithmon tês phônês oxytêtos te peri kai
+barytêtos, kai hopoia, kai tous horous tôn diastêmatôn, kai ta ek
+toutôn hosa systêmata gegonen, ha katidontes hoi prosthen paredosan
+hêmin tois hepomenois ekeinois kalein auta harmonias, k.t.l.] In this
+passage,--which has an air of technical accuracy not usual in Plato's
+references to music (though perhaps characteristic of the
+_Philebus_),--there is a close agreement with the technical writers,
+especially Aristoxenus. The main thought is the application of limit
+or measure to matter which is given as unlimited or indefinite--the
+distinction drawn out by Aristoxenus in a passage quoted below (p.
+81). The treatment of the term 'System' is notably Aristoxenean (cp.
+_Harm._ p. 36 [Greek: ta systêmata theôrêsai posa te esti kai poia
+atta, kai pôs ek te tôn diastêmatôn kai phthongôn synestêkota]).
+Further, the use of [Greek: harmonia] for [Greek: systêma], or rather
+of the plural [Greek: harmoniai] for the [Greek: systêmata] observed
+by the older musical theorists, is exactly what is noticed by
+Aristoxenus as if it were more or less antiquated. Even in the time
+of Plato it appears as a word of traditional character ([Greek: hoi
+prosthen paredosan]), his own word being [Greek: systêma]. It need
+not be said that there is no such hesitation, either in Plato or in
+Aristotle, about the use of [Greek: harmoniai] for the modes.
+
+The same use of [Greek: harmonia] is found in the Aristotelian
+_Problems_ (xix. 26), where the question is asked, [Greek: dia ti
+mesê kaleitai en tais harmoniais, tôn de oktô ouk esti meson], _i.e._
+how can we speak of the Mesê or 'middle note' of a scale of eight
+notes?
+
+We have now reviewed all the passages in Aristoxenus which can be
+thought to bear upon the question whether the [Greek: harmoniai] or
+Modes of early Greek music are the same as the [Greek: tonoi] or Keys
+discussed by Aristoxenus himself. The result seems to be that we have
+found nothing to set against the positive arguments for the
+identification already urged. It may be thought, perhaps, that the
+variety of senses ascribed to the word [Greek: harmonia] goes beyond
+what is probable. In itself however the word meant simply 'musical
+scale[1].' The Pythagorean use of it in the sense of 'octave scale,'
+and the very similar use in reference to diagrams which represented
+the division of that scale, were antiquated in the time of
+Aristoxenus. The sense of 'key' was doubtless limited in the first
+instance to the use in conjunction with the names Dorian, &c., which
+suggested a distinction of pitch. From the meaning 'Dorian scale' to
+'Dorian key' is an easy step. Finally, in reference to genus [Greek:
+harmonia] meant the Enharmonic scale. It is not surprising that a
+word with so many meanings did not keep its place in technical
+language, but was replaced by unambiguous words, viz. [Greek: tonos]
+in one sense, [Greek: systêma] in another, [Greek: genos enarmonion]
+in a third. Naturally, too, the more precise terms would be first
+employed by technical writers.
+
+[Footnote 1: So in Plato, _Leg._ p. 665 a: [Greek: tê dê tês kinêseôs
+taxei rhythmos onoma eiê, tê d' au tês phônês, tou te oxeos hama kai
+bareos synkerannymenôn, harmonia onoma prosagoreuoito.]]
+
+
+
+
+§ 23. _The Seven Species._
+
+(See the Appendix, Table I.)
+
+In the _Harmonics_ of Aristoxenus an account of the seven species of
+the Octave followed the elaborate theory of Systems already referred
+to (p. 48), and doubtless exhibited the application of that general
+theory to the particular cases of the Fourth, Fifth, and Octave.
+Unfortunately the existing manuscripts have only preserved the first
+few lines of this chapter of the Aristoxenean work (p. 74, ll. 10-24
+Meib.).
+
+The next source from which we learn anything of this part of the
+subject is the pseudo-Euclidean _Introductio Harmonica_. The writer
+enumerates the species of the Fourth, the Fifth, and the Octave,
+first in the Enharmonic and then in the Diatonic genus. He shows that
+if we take Fourths on a Diatonic scale, beginning with Hypatê Hypatôn
+(our _b_), we get successively _b c d e_ (a scale with the intervals
+1/2 1 1), _c d e f_ (1 1 1/2) and _d e f g_ (1 1/2 1). Similarly on
+the Enharmonic scale we get--
+
+
+    Hypatê Hypatôn to Hypatê Mesôn    _b  b* c  e_  (1/4  1/4  2  )
+    Parhypatê  "    " Parhypatê "     _b* c  e  e*_ (1/4  2    1/4)
+    Lichanos   "    " Lichanos  "     _c  e  e* f_  (2    1/4  1/4)
+
+
+In the case of the Octave the species is distinguished on the
+Enharmonic scale by the place of the tone which separates the
+tetrachords, the so-called Disjunctive Tone ([Greek: tonos
+diazeuktikos]). Thus in the octave from Hypatê Hypatôn to Paramesê
+(_b-b_) this tone (_a-b_) is the highest interval; in the next
+octave, from Parhypatê Hypatôn to Tritê Diezeugmenôn (_c-c_), it is
+the second highest; and so on. These octaves, or species of the
+Octave, the writer goes on to tell us, were anciently called by the
+same names as the seven oldest Keys, as follows:
+
+
+    Mixo-lydian      _b - b_      1/4  1/4  2    1/4  1/4  2    1
+    Lydian           _b*- b*_     1/4  2    1/4  1/4  2    1    1/4
+    Phrygian         _c - c_      2    1/4  1/4  2    1    1/4  1/4
+    Dorian           _e - e_      1/4  1/4  2    1    1/4  1/4  2
+    Hypo-lydian      _e*- e*_     1/4  2    1    1/4  1/4  2    1/4
+    Hypo-phrygian    _f - f_      2    1    1/4  1/4  2    1/4  1/4
+    Hypo-dorian      _a - a_      1    1/4  1/4  2    1/4  1/4  2
+
+
+On the Diatonic scale, according to the same writer, the species of
+an Octave is distinguished by the places of the two semitones. Thus
+in the first species, _b-b_, the semitones are the first and fourth
+intervals (_b-c_ and _e-f_): in the second, _c-c_, they are the third
+and the seventh, and so on. He does not however say, as he does in
+the case of the Enharmonic scale, that these species were known by
+the names of the Keys. This statement is first made by Gaudentius (p.
+20 Meib.), a writer of unknown date. If we adopt it provisionally,
+the species of the Diatonic octave will be as follows:
+
+
+    [Mixo-lydian]      _b - b_    1/2  1    1    1/2  1    1    1
+    [Lydian]           _c - c_    1    1    1/2  1    1    1    1/2
+    [Phrygian]         _d - d_    1    1/2  1    1    1    1/2  1
+    [Dorian]           _e - e_    1/2  1    1    1    1/2  1    1
+    [Hypo-lydian]      _f - f_    1    1    1    1/2  1    1    1/2
+    [Hypo-phrygian]    _g - g_    1    1    1/2  1    1    1/2  1
+    [Hypo-dorian]      _a - a_    1    1/2  1    1    1/2  1    1
+
+
+
+
+§ 24. _Relation of the Species to the Keys._
+
+Looking at the octaves which on our key-board, as on the Greek scale,
+exhibit the several species, we cannot but be struck with the
+peculiar relation in which they stand to the Keys. In the tables
+given above the keys stand in the order of their pitch, from the
+Mixo-lydian down to the Hypo-dorian: the species of the same names
+follow the reverse order, from _b-b_ upwards to _a-a_. This, it is
+obvious, cannot be an accidental coincidence. The two uses of this
+famous series of names cannot have originated independently. Either
+the naming of the species was founded on that of the keys, or the
+converse relation obtained between them. Which of these two uses,
+then, was the original and which the derived one? Those who hold that
+the species were the basis of the ancient Modes or [Greek: harmoniai]
+must regard the keys as derivative. Now Aristoxenus tells us, in one
+of the passages just quoted, that the seven species had long been
+recognised by theorists. If the scheme of keys was founded upon the
+seven species, it would at once have been complete, both in the
+number of the keys and in the determination of the intervals between
+them. But Aristoxenus also tells us that down to his time there were
+only six keys,--one of them not yet generally recognised,--and that
+their relative pitch was not settled. Evidently then the keys, which
+were scales in practical use, were still incomplete when the species
+of the Octave had been worked out in the theory of music.
+
+If on the other hand we regard the names Dorian, &c. as originally
+applied to keys, we have only to suppose that these names were
+extended to the species after the number of seven keys had been
+completed. This supposition is borne out by the fact that
+Aristoxenus, who mentions the seven species as well known, does not
+give them names, or connect them with the keys. This step was
+apparently taken by some follower of Aristoxenus, who wished to
+connect the species of the older theorists with the system of keys
+which Aristoxenus had perfected.
+
+The view now taken of the seven species is supported by the whole
+treatment of musical scales ([Greek: systêmata]) as we find it in
+Aristoxenus. That treatment from first to last is purely abstract and
+theoretical. The rules which Aristoxenus lays down serve to determine
+the sequence of intervals, but are not confined to scales of any
+particular compass. His Systems, accordingly, are not scales in
+practical use: they are parts taken anywhere on an ideal unlimited
+scale. And the seven species of the Octave are regarded by
+Aristoxenus as a scheme of the same abstract order. They represent
+the earlier teaching on which he had improved. He condemned that
+teaching for its want of generality, because it was confined to the
+compass of the Octave and to the Enharmonic genus, and also because
+it rested on no principles that would necessarily limit the species
+of the Octave to seven. On the other hand the diagrams of the earlier
+musicians were unscientific, in the opinion of Aristoxenus, on the
+ground that they divided the scale into a succession of
+quarter-tones. Such a division, he urged, is impossible in practice
+and musically wrong ([Greek: ekmeles]). All this goes to show that
+the earlier treatment of Systems, including the seven Species, had
+the same theoretical character as his own exposition. The only System
+which he recognises for practical purposes is the old standard
+octave, from Hypatê to Nêtê: and that System, with the enlargements
+which turned it into the Perfect System, kept its ground with all
+writers of the Aristoxenean school.
+
+Even in the accounts of the pseudo-Euclid and the later writers, who
+treat of the Species of the Octave under the names of the Keys, there
+is much to show that the species existed chiefly or wholly in musical
+theory. The seven species of the Octave are given along with the
+three species of the Fourth and the four species of the Fifth,
+neither of which appear to have had any practical application.
+Another indication of this may be seen in the seventh or Hypo-dorian
+species, which was also called Locrian and Common (ps. Eucl. p. 16
+Meib.). Why should this species have more than one name? In the
+Perfect System it is singular in being exemplified by two different
+octaves, viz. that from Proslambanomenos to Mesê, and that from Mesê
+to Nêtê Hyperbolaiôn. Now we have seen that the higher the octave
+which represents a species, the lower the key of the same name. In
+this case, then, the upper of the two octaves answers to the
+Hypo-dorian key, and the lower to the Locrian. But if the species has
+its two names from these two keys, it follows that the names of the
+species are derived from the keys. The fact that the Hypo-dorian or
+Locrian species was also called Common is a further argument to the
+same purpose. It was doubtless 'common' in the sense that it
+characterised the two octaves which made up the Perfect System. Thus
+the Perfect System was recognised as the really important scale.
+
+Another consideration, which has been overlooked by Westphal and
+those who follow him, is the difference between the species of the
+Octave in the several genera, especially the difference between the
+Diatonic and the Enharmonic. This is not felt as a difficulty with
+all the species. Thus the so-called Dorian octave _e - e_ is in the
+Enharmonic genus _e e* f a b b* c e_, a scale which may be regarded
+as the Diatonic with _g_ and _d_ omitted, and the semitones divided.
+But the Phrygian _d-d_ cannot pass in any such way into the
+Enharmonic Phrygian _c e e* f a b b* c_, which answers rather to the
+Diatonic scale of the species _c-c_ (the Lydian). The scholars who
+connect the ancient Modes with the species generally confine
+themselves to octaves of the Diatonic genus. In this they are
+supported by later Greek writers--notably, as we shall see, by
+Ptolemy--and by the analogy of the mediaeval Modes or Tones. But on
+the other side we have the repeated complaints of Aristoxenus that
+the earlier theorists confined themselves to Enharmonic octave
+scales. We have also the circumstance that the writer or compiler of
+the pseudo-Euclidean treatise, who is our earliest authority for the
+names of the species, gives these names for the Enharmonic genus
+only. Here, once more, we feel the difference between theory and
+practice. To a theorist there is no great difficulty in the terms
+Diatonic Phrygian and Enharmonic Phrygian meaning essentially
+different things. But the 'Phrygian Mode' in practical music must
+have been a tolerably definite musical form.
+
+
+
+
+§ 25. _The Ethos of Music._
+
+From Plato and Aristotle we have learned some elements of what may be
+called the gamut of sensibility. Between the higher keys which in
+Greece, as in Oriental countries generally, were the familiar vehicle
+of passion, especially of the passion of grief, and the lower keys
+which were regarded, by Plato at least, as the natural language of
+ease and license, there were keys expressive of calm and balanced
+states of mind, free from the violent extremes of pain and pleasure.
+In some later writers on music we find this classification reduced to
+a more regular form, and clothed in technical language. We find also,
+what is still more to our purpose, an attempt to define more
+precisely the musical forms which answered to the several states of
+temper or emotion.
+
+Among the writers in question the most instructive is Aristides
+Quintilianus. He discusses the subject of musical ethos under the
+first of the usual seven heads, that which deals with sounds or notes
+([Greek: peri phthongôn]). Among the distinctions to be drawn in
+regard to notes he reckons that of ethos: the ethos of notes, he
+says, is different as they are higher or lower, and also as they are
+in the place of a Parhypatê or in the place of a Lichanos (p. 13
+Meib. [Greek: hetera gar êthê tois oxyterois, hetera tois baryterois
+epitrechei, kai hetera men parypatoeidesin, hetera de
+lichanoeidesin]). Again, under the seventh head, that of [Greek:
+melopoiia] or composition, he treats of the 'regions of the voice'
+([Greek: topoi tês phônês]). There are three kinds of composition, he
+tells us (p. 28), viz. that which is akin to Hypatê ([Greek:
+hypatoeidês]), that which is akin to Mesê ([Greek: mesoeidês]), and
+that which is akin to Nêtê ([Greek: nêtoeidês]). The first part of
+the art of composition is the choice ([Greek: lêpsis]) which the
+musician is able to make of the region of the voice to be employed
+([Greek: lêpsis men di' hês heuriskein tô mousikô perigignetai apo
+poiou tês phônês to systêma topou poiêteon, poteron hypatoeidous ê
+tôn loipôn tinos]). He then proceeds to connect these regions, or
+different parts of the musical scale, with different branches of
+lyrical poetry. 'There are three styles of musical composition
+([Greek: tropoi tês melopoiias]), viz. the Nomic, the Dithyrambic,
+and the Tragic; and of these the Nomic is netoid, the Dithyrambic is
+mesoid, and the Tragic is hypatoid.... They are called styles
+([Greek: tropoi]) because according to the melody adopted they
+express the ethos of the mind. Thus it happens that composition
+([Greek: melopoiia]) may differ in _genus_, as Enharmonic, Chromatic:
+in _System_, as Hypatoid, Mesoid, Netoid: in _key_, as Dorian,
+Phrygian: in _style_, as Nomic, Dithyrambic: in _ethos_, as we call
+one kind of composition "contracting" ([Greek: systaltikê]), viz.
+that by which we move painful feelings; another "expanding" ([Greek:
+diastaltikê]), that by which we arouse the spirit ([Greek: thymos]);
+and another "middle" ([Greek: mesê]), that by which we bring round
+the soul to calmness.'
+
+This passage does not quite explicitly connect the three kinds of
+ethos--the diastaltic, the systaltic, the intermediate--with the
+three regions of the voice; but the connexion was evidently implied,
+and is laid down in express terms in the pseudo-Euclidean
+_Introductio_ (p. 21 Meib.). According to this Aristoxenean writer,
+'the diastaltic ethos of musical composition is that which expresses
+grandeur and manly elevation of soul ([Greek: megaloprepeia kai
+diarma psychês andrôdes]), and heroic actions; and these are employed
+by tragedy and all poetry that approaches the tragic type. The
+systaltic ethos is that by which the soul is brought down into a
+humble and unmanly frame; and such a disposition will be fitting for
+amatory effusions and dirges and lamentations and the like. And the
+hesychastic or tranquilly disposed ethos ([Greek: hêsychastikon
+êthos]) of musical composition is that which is followed by calmness
+of soul and a liberal and peaceful disposition: and this temper will
+fit hymns, paeans, laudations, didactic poetry and the like.' It
+appears then that difference in the 'place' ([Greek: topos]) of the
+notes employed in a composition--difference, that is to say, of
+pitch--was the element which chiefly determined its ethos, and (by
+consequence) which distinguished the music appropriate to the several
+kinds of lyrical poetry.
+
+A slightly different version of this piece of theory is preserved in
+the anonymous treatise edited by Bellermann (§§ 63, 64), where the
+'regions of the voice' are said to be four in number, viz. the three
+already mentioned, and a fourth which takes its name from the
+tetrachord Hyperbolaiôn ([Greek: topos hyperboloeidês]). In the same
+passage the boundaries of the several regions are laid down by
+reference to the keys. 'The lowest or hypatoid region reaches from
+the Hypo-dorian Hypatê Mesôn to the Dorian Mesê; the intermediate or
+mesoid region from the Phrygian Hypatê Mesôn to the Lydian Mesê; the
+netoid region from the Lydian Mesê to the Nêtê Synemmenôn; the
+hyperboloid region embracing all above the last point.' The text of
+this passage is uncertain; but the general character of the [Greek:
+topoi] or regions of the voice is clearly enough indicated.
+
+The three regions are mentioned in the catechism of Bacchius (p. 11
+Meib.): [Greek: topous] (MSS. [Greek: tropous]) [Greek: de tês phônês
+posous legomen einai? treis. tinas? toutous; oxyn, meson, baryn.] The
+varieties of ethos also appear (p. 14 Meib.): [Greek: hê de metabolê
+kata êthos? hotan ek tapeinou eis megaloprepes; ê ex hêsychou kai
+synnou eis parakekinêkos.] 'What is change of ethos? when a change is
+made from the humble to the magnificent; or from the tranquil and
+sober to violent emotion.'
+
+When we compare the doctrine of musical ethos as we find it in these
+later writers with the indications to be gathered from Plato and
+Aristotle, the chief difference appears to be that we no longer hear
+of the ethos of particular modes, but only of that of three or (at
+the most) four portions of the scale. The principle of the division,
+it is evident, is simply difference of pitch. But if that was the
+basis of the ethical effect of music in later times, the circumstance
+goes far to confirm us in the conclusion that it was the pitch of the
+music, rather than any difference in the succession of the intervals,
+that principally determined the ethical character of the older modes.
+
+
+
+
+§ 26. _The Ethos of the Genera and Species._
+
+Although the pitch of a musical composition--as these passages
+confirm us in believing--was the chief ground of its ethical
+character, it cannot be said that no other element entered into the
+case.
+
+In the passage quoted above from Aristides Quintilianus (p. 13 Meib.)
+it is said that ethos depends first on pitch ([Greek: hetera êthê
+tois oxyterois, hetera tois baryterois]), and secondly on the
+moveable notes, that is to say, on the _genus_. For that is evidently
+involved in the words that follow: [Greek: kai hetera men
+parypatoeidesin, hetera de lichanoeidesin.] By [Greek:
+parypatoeideis] and [Greek: lichanoeideis] he means all the moveable
+notes ([Greek: phthongoi pheromenoi]): the first are those which hold
+the place of Parhypatê in their tetrachord, viz. the notes called
+Parhypatê or Tritê: the second are similarly the notes called
+Lichanos or Paranêtê. These moveable notes, then, give an ethos to
+the music because they determine the genus of the scale. Regarding
+the particular ethos belonging to the different genera, there is a
+statement of the same author (p. 111) to the effect that the Diatonic
+is masculine and austere ([Greek: arrhenôpon d' esti kai
+austêroteron]), the Chromatic sweet and plaintive ([Greek: hêdiston
+te kai goeron]), the Enharmonic stirring and pleasing ([Greek:
+diegertikon d' esti touto kai êpion]). The criticism doubtless came
+from some earlier source.
+
+Do we ever find ethos attributed to this or that _species_ of the
+Octave? I can find no passage in which this source of ethos is
+indicated. Even Ptolemy, who is the chief authority (as we shall see)
+for the value of the species, and who makes least of mere difference
+of pitch, recognises only two forms of modulation in the course of a
+melody, viz. change of genus and change of pitch[1].
+
+
+
+
+§ 27. _The Musical Notation._
+
+As the preceding argument turns very much upon the practical
+importance of the scale which we have been discussing, first as the
+single octave from the original Hypatê to Nêtê, then in its enlarged
+form as the Perfect System, it may be worth while to show that some
+such scale is implied in the history of the Greek musical notation.
+
+The use of written characters ([Greek: sêmeia]) to represent the
+sounds of music appears to date from a comparatively early period in
+Greece. In the time of Aristoxenus the art of writing down a melody
+([Greek: parasêmantikê]) had come to be considered by some persons
+identical with the science of music ([Greek: harmonikê]),--an error
+which Aristoxenus is at some pains to refute. It is true that the
+authorities from whom we derive our knowledge of the Greek notation
+are post-classical. But the characters themselves, as we shall
+presently see, furnish sufficient evidence of their antiquity.
+
+[Footnote 1: Ptol. _Harm._ ii. 6. After drawing a distinction between
+difference of key as affecting the whole of a melody or piece of
+music and as a means of change in the course of it--the distinction,
+in short, between transposition and modulation proper--he says of the
+latter: [Greek: hautê de hôsper ekpiptein autên] (sc. [Greek: tên
+aisthêsin]) [Greek: poiei tou synêthous kai prosdokômenou melous,
+hotan epi pleon men syneirêtai to akolouthon, metabainê de pê pros
+heteron eidos, êtoi kata to genos ê kata tên tasin.] That is to say,
+the sense of change is produced by a change of genus or of pitch. A
+change of _species_ is not suggested. So Dionys. Hal. _De Comp.
+Verb._ c. 19 [Greek: hoi de ge dithyrambopoioi kai tous tropous]
+(keys) [Greek: meteballon, Dôrikous te kai Phrygious kai Lydious en
+tô autô asmati poiountes; kai tas melôdias exêllatton, tote men
+enarmonious poiountes, k.t.l.]]
+
+The Greek musical notation is curiously complicated. There is a
+double set of characters, one for the note assigned to the singer,
+the other for those of the lyre or other instrument. The notes for
+the voice are obviously derived from the letters of the ordinary
+Ionic alphabet, multiplied by the use of accents and other
+diacritical marks. The instrumental notes were first explained less
+than thirty years ago by Westphal. In his work _Harmonik und Melopöie
+der Griechen_ (c. viii _Die Semantik_) he showed, in a manner as
+conclusive as it is ingenious, that they were originally taken from
+the first fourteen letters of an alphabet of archaic type, akin to
+the alphabets found in certain parts of Peloponnesus. Among the
+letters which he traces, and which point to this conclusion, the
+most-significant are the digamma, the primitive crooked iota
+[Symbols: Li], and two forms of lambda, [Symbols: <] and [Symbols:
+F], the latter of which is peculiar to the alphabet of Argos. Of the
+other characters [Symbols: M], which stands for alpha, is best
+derived from the archaic form [Symbols: NJ]. For beta we find
+[Symbols: c], which may come from an archaic form of the letter[1].
+The character [Symbols: El], as Westphal shows, is for [Symbols:7],
+or delta with part of one side left out. Similarly the ancient
+[Symbols: O], when the circle was incomplete, yielded the character
+[Symbols: C]. The crooked iota ([Symbols:'-i]) appears as
+[Symbols:h]. The two forms of lambda serve for different notes, thus
+bringing the number of symbols up to fifteen. Besides these there are
+two characters, [Symbols: O] and [Symbols: 6], which cannot be
+derived in the same way from any alphabet. As they stand for the
+lowest notes of the scale, they are probably an addition, later than
+the rest of the system. At the upper end, again, the scale is
+extended by the simple device of using the same characters for notes
+an octave higher, distinguishing them in this use by an accent. The
+original fifteen characters, with the letters from which they are
+derived, and the corresponding notes in the modern musical scale, are
+as follows:
+
+
+    [Symbols: H h E  r P F C K r l < E N Z M]
+    [Greek: ê i e l^1 g m [digamma] th k d l^2 b n z a]
+    _a b c d e f g a b c d e f g a_
+
+
+[Footnote 1: Since this was written I have learned from Mr. H. S.
+Jones that the form [Symbols:E] for beta occurs on an inscription
+dated about 500 B.C., viz. Count Tyszkiewicz's bronze plate,
+published simultaneously by Robert in the _Monumenti Antichi
+pubblicati per cura della reale Accademia dei Lincei_, i. pp. 593
+(with plate), and Fröhner in the _Revue Archéologique_, 1891
+July-August, pp. 51 ff. Pl. xix. Mr. Jones points out that this
+[Symbols:E] connects the crescent beta ([Symbols: C]) of Naxos,
+Delos, &c. with the common form, and is evidently therefore an early
+form of the letter.
+
+I take this opportunity of thanking Mr. Jones for other help,
+especially in regard to the subject of this section.]
+
+These notes, it will be seen, compose two octaves of the Diatonic
+scale, identical with the two octaves of the Greater Perfect System.
+They may be regarded as answering to the white notes of the modern
+keyboard,--those which form the complete scale in the so-called
+'natural' key.
+
+The other notes, viz. those which are required not only in different
+keys of the Diatonic scale, but also in all Enharmonic and Chromatic
+scales, are represented by the same characters modified in some
+simple way. Usually a character is turned half round backwards to
+raise it by one small interval (as from Hypatê to Parhypatê), and
+reversed to raise it by both (Hypatê to Lichanos). Thus the letter
+epsilon, [Symbols: E], stands for our _c_: and accordingly [Symbols:
+W] ([Symbols: E] [Greek: anestrammenon] or [Greek: hyption]) stands
+for _c*_, and [Symbols: 3] ([Symbols: E] [Greek: apestrammenon]) for
+_c[Symbols: #]_. The Enharmonic scale _c-c*-c[Symbols: #]-f_ is
+therefore written [Symbols: E W 3 f'], the two modifications of the
+letter [Symbols: E] representing the two 'moveable' notes of the
+tetrachord. Similarly we have the triads [Symbols: h I rl, F "q, Cup,
+KY>1, <V>, CUm]. As some letters do not admit of this kind of
+differentiation, other methods are employed. Thus [Symbols: D] is
+made to yield the forms [Symbols: ri] (for [Symbols: 7]) [Symbols: L
+A]: from [Symbols: H] (or [Symbols: B]) are obtained the forms
+[Symbols: Li] and [Symbols: R]: and from [Symbols: Z] (or [Symbols:
+i]) the forms [Symbols: A] and [Symbols: A]. The modifications of
+[Symbols: N] are [Symbols: /] and [Symbols: \]: those of [Symbols:
+'I] are [Symbols: A] and [Symbols: N].
+
+The method of writing a Chromatic tetrachord is the same, except that
+the higher of the two moveable notes is marked by a bar or accent.
+Thus the tetrachord _c c[Symbols: #] d f_ is written [Symbols: E W 3'
+/`'].
+
+In the Diatonic genus we should have expected that the original
+characters would have been used for the tetrachords _b c d e_ and _e
+f g a_; and that in other tetrachords the second note, being a
+semitone above the first, would have been represented by a reversed
+letter ([Greek: gramma apestrammenon]). In fact, however, the
+Diatonic Parhypatê and Tritê are written with the same character as
+the Enharmonic. That is to say, the tetrachord _b c d e_ is not
+written [Symbols: h E H r], but [Symbols: Fix I-r]: and _d e[Symbols:
+b] f g_ is not [Symbols: I], but [Symbols: I-tl F].
+
+Let us now consider how this scheme of symbols is related to the
+Systems already described and the Keys in which those Systems may be
+set ([Greek: tonoi eph' hôn tithemena ta systêmata melôdeitai]).
+
+The fifteen characters, it has been noticed, form two diatonic
+octaves. It will appear on a little further examination that the
+scheme must have been constructed with a view to these two octaves.
+The successive notes are not expressed by the letters of the alphabet
+in their usual order (as is done in the case of the vocal notes). The
+highest note is represented by the first letter, [Greek: A]: and then
+the remaining fourteen notes are taken in pairs, each with its
+octave: and each of the pairs of notes is represented by two
+successive letters--the two forms of lambda counting as one such pair
+of letters. Thus:
+
+
+  The higher and lower _e_ are denoted by [Greek: b]  and  [Greek: g]
+      "     "     "    _c_     "     "    [Greek: d]   "   [Greek: e]
+      "     "     "    _g_     "     "    [Symbol: digamma] "  [Greek: z]
+      "     "     "    _a_     "     "    [Greek: ê]   "   [Greek: th]
+      "     "     "    _b_     "     "    [Greek: i]   "   [Greek: k]
+      "     "     "    _d_     "     "    [Greek: l^1] "   [Greek: l^2]
+      "     "     "    _f_     "     "    [Greek: m]   "   [Greek: n]
+
+
+On this plan the alphabetical order of the letters serves as a series
+of links connecting the highest and lowest notes of every one of the
+seven octaves that can be taken on the scale. It is evident that the
+scheme cannot have grown up by degrees, but is the work of an
+inventor who contrived it for the practical requirements of the music
+of his time.
+
+Two questions now arise, which it is impossible to separate. What is
+the scale or System for which the notation was originally devised?
+And how and when was the notation adapted to exhibit the several keys
+in which any such System might be set?
+
+The enquiry must start from the remarkable fact that the two octaves
+represented by the fifteen original letters are in the _Hypo-lydian_
+key--the key which down to the time of Aristoxenus was called the
+Hypo-dorian. Are we to suppose that the scheme was devised in the
+first instance for that key only? This assumption forms the basis of
+the ingenious and elaborate theory by which M. Gevaert explains the
+development of the notation (_Musique de l'Antiquité_, t. I. pp. 244
+ff.). It is open to the obvious objection that the Hypo-lydian (or
+Hypo-dorian) cannot have been the oldest key. M. Gevaert meets this
+difficulty by supposing that the original scale was in the Dorian
+key, and that subsequently, from some cause the nature of which we
+cannot guess, a change of pitch took place by which the Dorian scale
+became a semitone higher. It is perhaps simpler to conjecture that
+the original Dorian became split up, so to speak, into two keys by
+difference of local usage, and that the lower of the two came to be
+called Hypo-dorian, but kept the original notation. A more serious
+difficulty is raised by the high antiquity which M. Gevaert assigns
+to the Perfect System. He supposes that the inventor of the notation
+made use of an instrument (the _magadis_) which 'magadised' or
+repeated the notes an octave higher. But this would give us a
+repetition of the primitive octave _e - e_, rather than an
+enlargement by the addition of tetrachords at both ends.
+
+M. Gevaert regards the adaptation of the scheme to the other keys as
+the result of a gradual process of extension. Here we may distinguish
+between the recourse to the modified characters--which served
+essentially the same purpose as the 'sharps' and 'flats' in the
+signature of a modern key--and the additional notes obtained either
+by means of new characters ([Symbols: a] and [Symbols: e]), or by the
+use of accents ([Symbols:?'], &c.). The Hypo-dorian and
+Hypo-phrygian, which employ the new characters [Symbols: a] and
+[Symbols: e], are known to be comparatively recent. The Phrygian and
+Lydian, it is true, employ the accented notes; but they do so only in
+the highest tetrachord (Hyperbolaiôn), which may not have been
+originally used in these high keys. The modified characters doubtless
+belong to an earlier period. They are needed for the three oldest
+keys--Dorian, Phrygian, Lydian--and also for the Enharmonic and
+Chromatic genera. If they are not part of the original scheme, the
+musician who devised them may fairly be counted as the second
+inventor of the instrumental notation.
+
+In setting out the scales of the several keys it will be unnecessary
+to give more than the standing notes ([Greek: phthongoi hestôtes]),
+which are nearly all represented by original or unmodified
+letters--the moveable notes being represented by the modified forms
+described above. The following list includes the standing notes, viz.
+Proslambanomenos, Hypatê Hypatôn, Hypatê Mesôn, Mesê, Paramesê, Nêtê
+Diezeugmenôn and Nêtê Hyperbolaiôn in the seven oldest keys: the two
+lowest are marked as doubtful:--
+
+
+    TABLE LEGEND:
+    Column A = Prosl.
+    Column B = Hyp. Hypatôn.
+    Column C = Hyp. Mesôn.
+    Column D = Mesê.
+    Column E = Par.
+    Column F = Nêtê Diez.
+    Column G = Nêtê Hyperb.
+
+                             A    B   C   D   E   F   G
+
+    Mixo-lydian    [Symbols] 4    id  D   >   N   \       = _e[Symbol: b] - e[Symbol: b]_
+    Lydian         [Symbols] I-   r   c   <   c   m       = _d - d_
+    Phrygian       [Symbols] E    I-  F   11  <   Z       = _c - c_
+    Dorian         [Symbols] R    E   I'  D   ri  N   \   = _b[Symbol: b] - b[Symbol: b]_
+    Hypo-lydian    [Symbols] H    h   r   C   I<  c   M   = _a - a_
+    [Hypo-phrygian [Symbols]      H   I-  F   C   <   Z   = _g - g_
+    [Hypo-dorian   [Symbols]          E  /4   F   11  N   = _f - f_
+
+
+It will be evident that this scheme of notation tallies fairly well
+with what we know of the compass of Greek instruments about the end
+of the fifth century, and also with the account which Aristoxenus
+gives of the keys in use up to his time. We need only refer to what
+has been said above on p. 17 and p. 37.
+
+It would be beyond the scope of this essay to discuss the date of the
+Greek musical notation. A few remarks, however, may be made,
+especially with reference to the high antiquity assigned to it by
+Westphal.
+
+The alphabet from which it was derived was certainly an archaic one.
+It contained several characters, in particular [Symbols: F] for
+digamma, [Symbols: LI] for iota, and [Symbols: I-] for lambda, which
+belong to the period before the introduction of the Ionian alphabet.
+Indeed if we were to judge from these letters alone we should be led
+to assign the instrumental notation (as Westphal does) to the time of
+Solon. The three-stroke iota ([Symbols: I]), in particular, does not
+occur in any alphabet later than the sixth century B.C. On the other
+hand, when we find that the notation implies the use of a musical
+System in advance of any scale recognised in Aristotle, or even in
+Aristoxenus, such a date becomes incredible. We can only suppose
+either (1) that the use of [Symbols: Li] in the fifth century was
+confined to localities of which we have no complete epigraphic
+record, or (2) that [Symbols: i] as a form of iota was still
+known--as archaic forms must have been--from the older public
+inscriptions, and was adopted by the inventor of the notation as
+being better suited to his purpose than [Symbols: 1].
+
+With regard to the place of origin of the notation the chief fact
+which we have to deal with is the use of the character [Symbols: I-]
+for lambda, which is distinctive of the alphabet of Argos, along with
+the commoner form [Symbols: <]. Westphal indeed asserts that both
+these forms are found in the Argive alphabet. But the inscription (C.
+I. 1) which he quotes[1] for [Symbols: <] really contains only
+[Symbols: t-] in a slightly different form. We cannot therefore say
+that the inventor of the notation derived it entirely from the
+alphabet of Argos, but only that he shows an acquaintance with that
+alphabet. This is confirmed by the fact that the form [Symbols: Li]
+for iota is not found at Argos. Probably therefore the inventor drew
+upon more than one alphabet for his purpose, the Argive alphabet
+being one.
+
+[Footnote 1: _Harmonik und Melopöie_, p. 286 (ed. 1863). The true
+form of the letter is given by Mr. Roberts, _Greek Epigraphy_, p.
+109.]
+
+The special fitness of the notation for the scales of the Enharmonic
+genus may be regarded as a further indication of its date. We shall
+see presently that that genus held a peculiar predominance in the
+earliest period of musical theory--that, namely, which was brought to
+an end by Aristoxenus.
+
+If the author of the notation--or the second author, inventor of the
+modified characters--was one of the musicians whose names have come
+down to us, it would be difficult to find a more probable one than
+that of Pronomus of Thebes. One of the most striking features of the
+notation, at the time when it was framed, must have been the
+adjustment of the keys. Even in the time of Aristoxenus, as we know
+from the passage so often quoted, that adjustment was not universal.
+But it is precisely what Pronomus of Thebes is said to have done for
+the music of the flute (_supra_, p. 38). The circumstance that the
+system was only used for instrumental music is at least in harmony
+with this conjecture. If it is thought that Thebes is too far from
+Argos, we may fall back upon the notice that Sacadas of Argos was the
+chief composer for the flute before the time of Pronomus[1], and
+doubtless Argos was one of the first cities to share in the advance
+which Pronomus made in the technique of his art.
+
+[Footnote 1: Pausanias (iv. 27, 4) says of the founding of Messene:
+[Greek: eirgazonto de kai hypo mousuiês allês men oudemias, aulôn de
+Boiôtiôn kai Argeiôn; ta te Sakada kai Pronomou melê tote dê
+proêchthê malista eis hamillan.]]
+
+
+
+
+§ 28. _Traces of the Species in the Notation._
+
+Before leaving this part of the subject it will be well to notice the
+attempt which Westphal makes to connect the species of the Octave
+with the form of the musical notation.
+
+The basis of the notation, as has been explained (p. 69), is formed
+by two Diatonic octaves, denoted by the letters of the alphabet from
+[Greek: a] to [Greek: n], as follows:
+
+
+    [Greek: ê i e l g m [digamma] th k d l b n z a]
+    _     a b c d e f g            a b c d e f g a_
+
+In this scale, as has been pointed out (p. 71), the notes which are
+at the distance of an octave from each other are always expressed by
+two _successive_ letters of the alphabet. Thus we find--
+
+
+  [Greek: b - g] is the octave _e - e_, the Dorian species.
+  [Greek: d - e]     "    "    _c - c_, the Lydian species.
+  [Greek: [digamma] - z]"     "    _g - g_, the Hypo-phrygian species.
+  [Greek: ê - th]    "    "    _a - a_, the Hypo-dorian species.
+
+
+Westphal adopts the theory of Boeckh (as to which see p. 11) that the
+Hypo-phrygian and Hypo-dorian species answered to the ancient Ionian
+and Aeolian modes. On this assumption he argues that the order of the
+pairs of letters representing the species agrees with the order of
+the Modes in the historical development of Greek music. For the
+priority of Dorian, Ionian, and Aeolian he appeals to the authority
+of Heraclides Ponticus, quoted above (p. 9). The Lydian, he supposes,
+was interposed in the second place on account of its importance in
+education,--recognised, as we have seen, by Aristotle in the
+_Politics_ (viii. 7 _ad fin._). Hence he regards the notation as
+confirming his theory of the nature and history of the Modes.
+
+The weakness of this reasoning is manifold. Granting that the
+Hypo-dorian and Hypo-phrygian answer to the old Aeolian and Ionian
+respectively, we have to ask what is the nature of the priority which
+Heraclides Ponticus claims for his three modes, and what is the value
+of his testimony. What he says is, in substance, that these are the
+only kinds of music that are truly Hellenic, and worthy of the name
+of modes ([Greek: harmoniai]). It can hardly be thought that this is
+a criticism likely to have weighed with the inventor of the notation.
+But if it did, why did he give an equally prominent place to Lydian,
+one of the modes which Heraclides condemned? In fact, the
+introduction of Lydian goes far to show that the coincidence--such as
+it is--with the views of Heraclides is mere accident. Apart, however,
+from these difficulties, there are at least two considerations which
+seem fatal to Westphal's theory:
+
+1. The notation, so far as the original two octaves are concerned,
+must have been devised and worked out at some one time. No part of
+these two octaves can have been completed before the rest. Hence the
+order in which the letters are taken for the several notes has no
+historical importance.
+
+2. The notation does not represent only the _species_ of a scale,
+that is to say, the relative pitch of the notes which compose it, but
+it represents also the absolute pitch of each note. Thus the octaves
+which are defined by the successive pairs of letters, [Greek:b-g,
+d-e], and the rest, are octaves of definite notes. If they were
+framed with a view to the ancient modes, as Westphal thinks, they
+must be the actual scales employed in these modes. If so, the modes
+followed each other, in respect of pitch, in an order exactly the
+reverse of the order observed in the keys. It need hardly be said
+that this is quite impossible. § 29. _Ptolemy's Scheme of Modes._
+
+The first writer who takes the Species of the Octave as the basis of
+the musical scales is the mathematician Claudius Ptolemaeus (fl.
+140-160 A.D.). In his _Harmonics_ he virtually sets aside the scheme
+of keys elaborated by Aristoxenus and his school, and adopts in their
+place a system of scales answering in their main features to the
+mediaeval Tones or Modes. The object of difference of key, he says,
+is not that the music as a whole may be of a higher or lower pitch,
+but that a melody may be brought within a certain compass. For this
+purpose it is necessary to vary the succession of intervals (as a
+modern musician does by changing the signature of the clef). If, for
+example, we take the Perfect System ([Greek: systêma ametabolon]) in
+the key of _a_ minor--which is its natural key,--and transpose it to
+the key of _d_ minor, we do so, according to Ptolemy, not in order to
+raise the general pitch of our music by a Fourth, but because we wish
+to have a scale with _b_ flat instead of _b_ natural. The flattening
+of this note, however, means that the two octaves change their
+species. They are now of the species _e - e_. Thus, instead of
+transposing the Perfect System into different keys, we arrive more
+directly at the desired result by changing the species of its
+octaves. And as there are seven possible species of the Octave, we
+obtain seven different Systems or scales. From these assumptions it
+follows, as Ptolemy shows in some detail, that any greater number of
+keys is useless. If a key is an octave higher than another, it is
+superfluous because it gives us a mere repetition of the same
+intervals[1].
+
+[Footnote 1: _Harm._ ii. 8 [Greek: hoi de hyperekpiptontes tou dia
+pasôn tous ap' autou tou dia pasôn apôterô parelkontôs hypotithentai,
+tous autous aei ginomenous tois proeilêmmenois.]]
+
+If we interpose a key between (_e.g._) the Hypo-dorian and the
+Hypo-phrygian, it must give us over again either the Hypo-dorian or
+the Hypo-phrygian scale[1]. Thus the fifteen keys of the
+Aristoxeneans are reduced to seven, and these seven are not
+transpositions of a single scale, but are all of the same pitch. See
+the table at the end of the book.
+
+With this scheme of Keys Ptolemy combined a new method of naming the
+individual notes. The old method, by which a note was named from its
+relative place in the Perfect System, must evidently have become
+inconvenient. The Lydian Mesê, for example, was two tones higher than
+the Dorian Mesê, because the Lydian scale as a whole was two tones
+higher than the Dorian. But when the two scales were reduced to the
+same compass, the old Lydian Mesê was no longer in the middle of the
+scale, and the name ceased to have a meaning. It is as though the
+term 'dominant' when applied to a Minor key were made to mean the
+dominant of the relative Major key. On Ptolemy's method the notes of
+each scale were named from their places in it. The old names were
+used, Proslambanomenos for the lowest, Hypatê Hypatôn for the next,
+and so on, but without regard to the intervals between the notes.
+Thus there were two methods of naming, that which had been in use
+hitherto, termed 'nomenclature according to _value_' ([Greek:
+onomasia kata dynamin]), and the new method of naming from the
+various scales, termed 'nomenclature according to _position_'
+([Greek: onomasia kata thesin]). The former was in effect a retention
+of the Perfect System and the Keys: the latter put in their place a
+scheme of seven different standard Systems.
+
+[Footnote 1: _Harm._ ii. 11 [Greek: hôste mêd' an heteron eti doxai
+tô eidei ton tonon para ton proteron, all' hypodôrion palin, ê ton
+auton hypophrygion, oxyphônoteron tinos ê baryphônoteron monon.]]
+
+In illustration of his theory Ptolemy gives tables showing in numbers
+the intervals of the octaves used in the different keys and genera.
+He shows two octaves in each key, viz. that from Hypatê Mesôn
+([Greek: kata thesin]) to Nêtê Diezeugmenôn (called the octave
+[Greek: apo nêtês]), and that from Proslambanomenos to Mesê (the
+octave [Greek: apo mesês]). As he also gives the divisions of five
+different 'colours' or varieties of genus, the whole number of
+octaves is no less than seventy.
+
+Ptolemy does not exclude difference of pitch altogether. The whole
+instrument, he says, may be tuned higher or lower at pleasure[1].
+Thus the pitch is treated by him as modern notation treats the
+_tempo_, viz. as something which is not absolutely given, but has to
+be supplied by the individual performer.
+
+Although the language of Ptolemy's exposition is studiously
+impersonal, it may be gathered that his reduction of the number of
+keys from fifteen to seven was an innovation proposed by himself[2].
+If this is so, the rest of the scheme,--the elimination of the
+element of pitch, and the 'nomenclature by position,'--must also be
+due to him. Here, however, we find ourselves at issue with Westphal
+and those who agree with him on the main question of the Modes.
+According to Westphal the nomenclature by position is mentioned by
+Aristoxenus, and is implied in at least one important passage of the
+Aristotelian _Problems_. We have now to examine the evidence which he
+adduces to support his contention.
+
+[Footnote 1: _Harm._ ii. 7 [Greek: pros tên toiautên diaphoran hê tôn
+organôn holôn epitasis ê palin anesis aparkei.]]
+
+[Footnote 2: This may be traced in the occasionally controversial
+tone; as _Harm._ ii. 7 [Greek: hoi men ep' elatton tou dia pasôn
+phthasantes, hoi d' ep' auto monon, hoi de epi to meizon toutou,
+prokopên tina schedon toiautên aei tôn neôterôn para tous
+palaioterous thêrômenôn, anoikeion tês peri to hêrmosmenon physeôs te
+kai apokatastaseôs; hê monê perainein anankaion esti tên tôn esomenôn
+akrôn tonôn diastasin]. We may compare c. 11.]
+
+
+
+
+§ 30. _Nomenclature by Position._
+
+Two passages of Aristoxenus are quoted by Westphal in support of his
+contention. The first (p. 6 Meib.) is one in which Aristoxenus
+announces his intention to treat of Systems, their number and nature:
+'setting out their differences in respect of compass ([Greek:
+megethos]), and for each compass the differences in form and
+composition and position ([Greek: tas te kata schêma kai kata
+synthesin kai kata thesin]), so that no element of melody,--either
+compass or form or composition or position,--may be unexplained.' But
+the word [Greek: thesis], when applied to Systems, does not mean the
+'position' of single notes, but of groups of notes. Elsewhere (p. 54
+Meib.) he speaks of the position of tetrachords towards each other
+([Greek: tas tôn tetrachordôn pros allêla theseis]), laying it down
+that any two tetrachords in the same System must be consonant either
+with each other or with some third tetrachord. The other passage
+quoted by Westphal (p. 69 Meib.) is also in the discussion of
+Systems. Aristoxenus is pointing out the necessity of recognising
+that some elements of melodious succession are fixed and limited,
+others are unlimited:
+
+
+     [Greek: kata men oun ta megethê tôn diastêmatôn kai tas tôn
+     phthongôn taseis apeira pôs phainetai einai ta peri melos,
+     kata de tas dynameis kai kata ta eidê kai kata tas theseis
+     peperasmena te kai tetagmena.]
+
+     'In the size of the intervals and the pitch of the notes the
+     elements of melody seem to be infinite; but in respect of the
+     values (_i.e._ the relative places of the notes) and in
+     respect of the forms (_i.e._ the succession of the intervals)
+     and in respect of the positions they are limited and settled.'
+
+
+Aristoxenus goes on to illustrate this by supposing that we wish to
+continue a scale downwards from a [Greek: pyknon] or pair of small
+intervals (Chromatic or Enharmonic). In this case, as the [Greek:
+pyknon] forms the lower part of a tetrachord, there are two
+possibilities. If the next lower tetrachord is disjunct, the next
+interval is a tone; if it is conjunct, the next interval is the large
+interval of the genus ([Greek: hê men gar kata tonon eis diazeuxin
+agei to tou systêmatos eidos, hê de kata thateron diastêma ho ti
+dêpot' echei megethos eis synaphên]). Thus the succession of
+intervals is determined by the relative position of the two
+tetrachords, as to which there is a choice between two definite
+alternatives. This then is evidently what is meant by the words
+[Greek: kata tas theseis][1]. On the other hand the [Greek: thesis]
+of Ptolemy's nomenclature is the absolute pitch (_Harm._ ii. 5
+[Greek: pote men par' autên tên thesin, to oxyteron haplôs ê
+baryteron, onomazomen]), and this is one of the elements which
+according to Aristoxenus are indefinite.
+
+[Footnote 1: So Bacch. p. 19 Meib. [Greek: theseis de tetrachordôn
+hois to melos horizetai eisin hepta? synaphê, diazeuxis,
+hypodiazeuxis, k.t.l.] (see the whole passage).]
+
+Westphal also finds the nomenclature by position implied in the
+passage of the Aristotelian _Problems_ (xix. 20) which deals with the
+peculiar relation of the Mesê to the rest of the musical scale. The
+passage has already been quoted and discussed (_supra_, p. 43), and
+it has been pointed out that if the Mesê of the Perfect System
+([Greek: mesê kata dynamin]) is the key-note, the scale must have
+been an octave of the _a_-species. If octaves of other species were
+used, as Westphal maintains, it becomes necessary to take the Mesê of
+this passage to be the [Greek: mesê kata thesin], or Mesê by
+position. That is, Westphal is obliged by his theory of the Modes to
+take the term Mesê in a sense of which there is no other trace before
+the time of Ptolemy. But--
+
+(1) It is highly improbable that the names of the notes--Mesê,
+Hypatê, Nêtê and the rest--should have had two distinct meanings.
+Such an ambiguity would have been intolerable, and only to be
+compared with the similar ambiguity which Westphal's theory implies
+in the use of the terms Dorian, &c.
+
+(2) If the different species of the octave were the practically
+important scales, as Westphal maintains, the position of the notes in
+these scales must have been correspondingly important. Hence the
+nomenclature by position must have been the more usual and familiar
+one. Yet, as we have shown, it is not found in Aristotle, Aristoxenus
+or Euclid--to say nothing of later writers.
+
+(3) The nomenclature by position is an essential part of the scheme
+of Keys proposed by Ptolemy. It bears the same relation to Ptolemy's
+octaves as the nomenclature by 'value' bears to the old standard
+octave and the Perfect System. It was probably therefore devised
+about the time of Ptolemy, if not actually by him.
+
+
+
+
+§ 31. _Scales of the Lyre and Cithara._
+
+The earliest evidence in practical music of any octaves other than
+those of the standard System is to be found in the account given by
+Ptolemy of certain scales employed on the lyre and cithara. According
+to this account the scales of the lyre (the simpler and commoner
+instrument) were of two kinds. One was Diatonic, of the 'colour' or
+variety which Ptolemy recognises as the prevailing one, viz. the
+'Middle Soft' or 'Tonic' ([Greek: diatonon toniaion])[1].
+
+[Footnote 1: We may think of this as a scale in which the semitones
+are considerably smaller, _i.e._ in which _c_ and _f_ are nearly a
+quarter of a tone flat.]
+
+The other was a 'mixture' of this Diatonic with the standard
+Chromatic ([Greek: chrôma suntonon]): that is to say, the octave
+consisted of a tetrachord of each genus. These octaves apparently
+might be of any _species_, according to the key chosen[1]. On the
+cithara,--which was a more elaborate form of lyre, confined in
+practice to professional musicians,--six different octave scales were
+employed, each of a particular species and key. They are enumerated
+and described by Ptolemy in two passages (_Harm._ i. 16 and ii. 16),
+which in some points serve to correct each other.[2]
+
+[Footnote 1: Ptol. _Harm._ ii. 16 [Greek: periechetai de ta men en tê
+lyra kaloumena sterea tonou tinos hypo tôn tou toniaiou diatonou
+arithmôn tou autou tonou, ta de malaka hypo tôn en tô migmati tou
+malakou chrômatos apithmôn tou autou tonou]. Here [Greek: tonou
+tinos] evidently means 'of any given key,' and [Greek: tou autou
+tonou] 'of that key.' There is either no restriction, or none that
+Ptolemy thought worth mentioning, in the choice of the key and
+species.]
+
+[Footnote 2: The two passages enumerate the scales in a slightly
+different manner. In i. 16 they are arranged in view of the genus or
+colour into--
+
+
+          Pure Middle Soft Diatonic, viz.--
+                   [Greek: sterea], of the lyre.
+                   [Greek: tritai]      }  of the cithara.
+                   [Greek: hypertropa]  }
+
+          Mixture of Chromatic, viz.--
+                   [Greek: malaka], of the lyre.
+                   [Greek: tropika], of the cithara.
+
+          Mixture of Soft Diatonic, viz.--
+                   [Greek: parypatai], of the cithara.
+
+          Mixture of [Greek: diatonon syntonon], viz.--
+                   [Greek: lydia]  }  of the cithara.
+                   [Greek: iastia] }
+
+
+It is added, however, that in their use of this last 'mixture'
+musicians are in the habit of tuning the cithara in the Pythagorean
+manner, with two Major tones and a [Greek: leimma] (called [Greek:
+diatonon ditoniaion]).
+
+In the second passage (ii. 16) the scales of the lyre are given
+first, then those of the cithara with the key of each. The order is
+the same, except that [Greek: parypatai] comes before [Greek:
+tropika] (now called [Greek: tropoi]), and [Greek: lydia] is placed
+last. The words [Greek: ta de lydia hoi tou toniaiou diatonou] [sc.
+[Greek: arithmoi periechousi]] [Greek: tou dôriou] cannot be correct,
+not merely because they contradict the statement of the earlier
+passage that [Greek: lydia] denoted a mixture with [Greek: diatonon
+syntonon] (or in practice [Greek: diatonon ditoniaion]), but also
+because the scales that do not admit mixture are placed first in the
+list in both passages. Hence we should doubtless read [Greek: ta de
+lydia hoi <tou migmatos> tou <di>toniaiou diatonou tou Dôriou].]
+
+Of the six scales two are of the Hypo-dorian or Common species
+(_a-a_). One of these, called [Greek: tritai], is purely Diatonic of
+the Middle Soft variety; the intervals expressed by fractions are as
+follows:
+
+
+      _a_ 9/8 _b_ 28/27 _c_ 8/7 _d_ 9/8 _e_ 28/27 _f_ 8/7 _g_ 9/8 _a_
+
+
+The other, called [Greek: tropoi] or [Greek: tropika], is a mixture,
+Middle Soft Diatonic in the upper tetrachord, and Chromatic in the
+lower:
+
+
+_a_ 9/8 _b_ 22/21 _c_ 12/11 _c_[Symbols: sharp] 7/6 _e_ 28/27 _f_ 8/7
+_g_ 9/8 _a_
+
+
+Two scales are of the Dorian or _e_-species, viz. [Greek: parypatai],
+a combination of Soft and Middle Soft Diatonic:
+
+
+      _e_ 21/20 _f_ 10/9 _g_ 8/7 _a_ 9/8 _b_ 28/27 _c_ 8/7 d 9/8 _e_
+
+
+and [Greek: lydia], in which the upper tetrachord is of the strict or
+'highly strung' Diatonic ([Greek: diatonon syntonon]--our 'natural'
+temperament):
+
+
+      _e_ 28/27 _f_ 8/7 _g_ 9/8 _a_ 9/8 _b_ 16/15 _c_ 9/8 _d_ 10/9 _e_
+
+
+     Westphal (_Harmonik und Melopöie_, 1863, p. 255) supposes a
+     much deeper corruption. He would restore [Greek: ta de lydia
+     [kai iastia hoi tou migmatos tou syntonou diatonou tou ... ta
+     de ...] hoi tou toniaiou diatonou tou Dôriou]. This introduces
+     a serious discrepancy between the two passages, as the number
+     of scales in the second list is raised to eight (Westphal
+     making [Greek: iastia] and [Greek: iastiaioliaia] distinct
+     scales, and furthermore inserting a new scale, of unknown
+     name). Moreover the (unknown) scale of unmixed [Greek:
+     diatonon toniaion] is out of its place at the end of the list.
+     Westphal's objection to [Greek: lydia] as the name of a scale
+     of the _Dorian_ species of course only holds good on his
+     theory of the Modes.
+
+     The only other differences between the two passages are:
+
+     (1) In the scales of the lyre called [Greek: malaka] the
+     admixture, according to i. 16, is one of [Greek: chrômatikon
+     syntonon], according to ii. 16 of [Greek: chr. malakon]. But,
+     as Westphal shows, Soft Chromatic is not admitted by Ptolemy
+     as in practical use. It would seem that in the second passage
+     the copyist was led astray by the word [Greek: malaka] just
+     before.
+
+     (2) The [Greek: iastia] of i. 16 is called [Greek:
+     iastiaioliaia] in ii. 16. We need not suppose the text to be
+     faulty, since the two forms may have been both in use.
+
+     Another point overlooked in Westphal's treatment is that
+     [Greek: diatonon syntonon] and [Greek: d. ditoniaion] are not
+     really distinguished by Ptolemy. In one passage (i. 16) he
+     gives his [Greek: lydia] and [Greek: iastia] as a mixture with
+     [Greek: d. syntonon], adding that in practice it was [Greek:
+     d. ditoniaion]. In the other (ii. 16) he speaks at once of
+     [Greek: d. ditoniaion]. This consideration brings the two
+     places into such close agreement that any hypothesis involving
+     discrepancy is most improbable.
+
+
+In practice it appears that musicians tuned the tetrachord _b-e_ of
+this scale with the Pythagorean two Major tones and [Greek: leimma].
+
+Of the remaining scales one, called [Greek: hypertropa], is Phrygian
+in species (_d-d_), and of the standard genus:
+
+
+      _d_ 9/8 _e_ 28/27 _f_ 8/7 _g_ 9/8 _a_ 9/8 _b_ 28/27 _c_ 8/7 _d_
+
+
+One, called [Greek: iastia], or [Greek: iastiaioliaia], is of the
+Hypo-phrygian or _g_-species, the tetrachord _b-e_ being 'highly
+strung' Diatonic or (in practice) Pythagorean, viz.:
+
+
+      _g_ 9/8 _a_ 9/8 _b_ 256/243 _c_ 9/8 _d_ 9/8 _e_ 28/27 _f_ 8/7 _g_
+
+
+Regarding the tonality of these scales there is not very much to be
+said. In the case of the Hypo-dorian and Dorian octaves it will be
+generally thought probable that the key-note is _a_ (the [Greek: mesê
+kata dynamin]). If so, the difference between the two species is not
+one of 'mode,'--in the modern sense,--but consists in the fact that
+in the Hypo-dorian the compass of the melody is from the key-note
+upwards, while in the Dorian it extends a Fourth below the key-note.
+It is possible, however, that the lowest note (_e_) of the Dorian
+octave was sometimes the key-note: in which case the _mode_ was
+properly Dorian. In the Phrygian octave of Ptolemy's description the
+key-note cannot be the Fourth or Mesê [Greek: kata thesin] (_g_),
+since the interval _g-c_ is not consonant (9/8 × 9/8 × 28/27 being
+less than 4/3). Possibly the lowest note (_d_) is the key-note; if so
+the scale is of the Phrygian mode (in the modern sense). In the
+Hypo-phrygian octave there is a similar objection to regarding the
+Mesê [Greek: kata thesin] (_c_) as the key-note, and some probability
+in favour of the lowest note (_g_). If the Pythagorean division of
+the tetrachord _g-c_ were replaced by the natural temperament, which
+the language used by Ptolemy[1] leads us to regard as the true
+division, the scale would exhibit the intervals--
+
+
+          _g_ 5/4 _b_ 6/5 _d_ 7/6 _f_ 8/7 _g_
+
+
+which give the natural chord of the Seventh. This however is no more
+than a hypothesis.
+
+It evidently follows from all this that Ptolemy's octaves do not
+constitute a system of _modes_. They are merely the groups of notes,
+of the compass of an octave, which are most likely to be used in the
+several keys, and which Ptolemy or some earlier theorist chose to
+call by the names of those keys.
+
+[Footnote 1: _Harm._ i. 16 [Greek: plên kathoson adousi men
+akolouthôs tô dedeigmenô syntonô diatonikô, kathaper exestai skopein
+apo tês tôn oikeiôn autou logôn parabolês, harmozontai de heteron ti
+genos] (sc. the Pythagorean), [Greek: xynengizon men ekeinô, k.t.l.]]
+
+
+
+
+§ 32. _Remains of Greek Music._
+
+The extant specimens of Greek music are mostly of the second century
+A.D., and therefore nearly contemporary with Ptolemy. The most
+considerable are the melodies of three lyrical pieces or hymns, viz.
+(1) a hymn to Calliope, (2) a hymn to Apollo (or Helios),--both
+ascribed to a certain Dionysius,--and (3) a hymn to Nemesis, ascribed
+to Mesomedes[2]. Besides these there are (4) some short instrumental
+passages or exercises given by Bellermann's _Anonymus_ (pp. 94-96).
+And quite recently the list has been increased by (5) an inscription
+discovered by Mr. W. M. Ramsay, which gives a musical setting of four
+short gnomic sentences, and (6) a papyrus fragment (now in the
+collection of the Arch-duke Rainer) of the music of a chorus in the
+_Orestes_ of Euripides. These two last additions to our scanty stock
+of Greek music are set out and discussed by Dr. Wessely of Vienna and
+M. Ruelle in the _Revue des Études Grecques_ (V. 1892, pp. 265-280),
+also by Dr. Otto Crusius in the _Philologus_, Vol. LII, pp.
+160-200[1].
+
+[Footnote 2: It seems needless to set out these melodies here. The
+first satisfactory edition of them is that of Bellermann, _Die Hymnen
+des Dionysius und Mesomedes_ (Berlin, 1840). They are given by
+Westphal in his _Musik des griechischen Alterthumes_ (1883), and by
+Gevaert, _Musique de l'Antiquité_, vol. i. pp. 445 ff.; also in Mr.
+W. Chappell's _History of Music_ (London, 1874), where the melodies
+of the first and third hymns will be found harmonised by the late Sir
+George Macfarren.
+
+The melody published by Kircher (_Musurgia_, i. p. 541) as a fragment
+of the first Pythian ode of Pindar has no attestation, and is
+generally regarded as a forgery.]
+
+The music of the three hymns is noted in the Lydian key (answering to
+the modern scale with one [symbol: flat]). The melody of the second
+hymn is of the compass of an octave, the notes being those of the
+Perfect System from Parhypatê Hypatôn to Tritê Diezeugmenôn (_f - f_
+with one [symbol: flat]). The first employs the same octave with a
+lower note added, viz. Hypatê Hypatôn (_e_): the third adds the next
+higher note, Paranêtê Diezeugmenôn (_g_). Thus the Lydian key may be
+said, in the case of the second hymn, and less exactly in the case of
+the two others, to give the Lydian or _c_-species of the octave in
+the most convenient part of the scale; just as on Ptolemy's system of
+Modes we should expect it to do.
+
+This octave, however, represents merely the _compass_ (_ambitus_ or
+_tessitura_) of the melody: it has nothing to do with its _tonality_.
+In the first two hymns, as Bellermann pointed out, the key-note is
+the Hypatê Mesôn; and the mode--in the modern sense of that word--is
+that of the octave _e - e_ (the Dorian mode of Helmholtz's theory).
+In the third hymn the key-note appears to be the Lichanos Mesôn, so
+that the mode is that of _g-g_, viz. the Hypo-phrygian.
+
+[Footnote 1: Of the discovery made at Delphi, after most of this book
+was in type, I hope to say something in the _Appendix_.]
+
+Of the instrumental passages given by the _Anonymus_ three are
+clearly in the Hypo-dorian or common mode, the Mesê (_a_) being the
+key-note. (See Gevaert, i. p. 141.) A fourth (§ 104) also ends on the
+Mesê, but the key-note appears to be the Parhypatê Mesôn (_f_).
+Accordingly Westphal and Gevaert assign it to the Hypo-lydian species
+(_f - f_). In Westphal's view the circumstance of the end of the
+melody falling, not on the key-note, but on the Third or Mediant of
+the octave, was characteristic of the Modes distinguished by the
+prefix _syntono-_, and accordingly the passage in question is
+pronounced by him to be Syntono-lydian. All those passages, however,
+are mere fragments of two or three bars each, and are quoted as
+examples of certain peculiarities of rhythm. They can hardly be made
+to lend much support to any theory of the Modes.
+
+The music of Mr. Ramsay's inscription labours under the same defect
+of excessive shortness. If, however, we regard the four brief
+sentences as set to a continuous melody, we obtain a passage
+consisting of thirty-six notes in all, with a compass of less than an
+octave, and ending on the lowest note of that compass. Unlike the
+other extant specimens of Greek music it is written in the Ionian
+key--a curious fact which has not been noticed by Dr. Wessely.
+
+
+INSCRIPTION WITH MUSICAL NOTES.
+
+[Music:
+
+    [Greek: hos-on zês phai-nou.
+    mê-den hol-ôs sy ly-pou.
+    pros o-li-gon es-ti to zên.
+    to te-los ho chro-nos a-pai-tei.]
+
+]
+
+The notes which enter into this melody form the scale _f[Symbols:
+sharp]-g-a-b-c[Symbols: sharp]-d-e[-f[Symbols: sharp]]_, which is an
+octave of the Dorian species (_e - e_ on the white notes). Hence if
+_f_[Symbols: sharp], on which the melody ends, is the key-note, the
+_mode_ is the Dorian. On the other hand the predominant notes are
+those of the triad _a-c[Symbols: sharp]-e_, which point to the key of
+_a_ major, with the difference that the Seventh is flat (_g_ instead
+of _g_[Symbols: sharp]). On this view the music would be in the
+Hypo-phrygian mode.
+
+However this may be, the most singular feature of this fragment
+remains to be mentioned, viz. the agreement between the musical notes
+and the _accentuation_ of the words. We know from the grammarians
+that an acute accent signified that the vowel was sounded with a rise
+in the pitch of the voice, and that a circumflex denoted a rise
+followed on the same syllable by a lower note--every such rise and
+fall being quite independent both of syllabic quantity and of stress
+or _ictus_. Thus in ordinary speech the accents formed a species of
+melody,--[Greek: logôdes ti melos], as it is called by
+Aristoxenus[1]. When words were _sung_ this 'spoken melody' was no
+longer heard, being superseded by the melody proper. Dionysius of
+Halicarnassus is at pains to explain (_De Comp. Verb._, c. 11), that
+the melody to which words are set does not usually follow or resemble
+the quasi-melody of the accents, _e.g._ in the following words of a
+chorus in the _Orestes_ of Euripides (ll. 140-142):--
+
+    [Greek: siga siga leukon ichnos arbylês
+    tithete, mê ktypeite;
+    apoprobat' ekeis' apopro moi koitas,]
+
+[Footnote 1: _Harm._ p. 18 Meib. [Greek: legetai gar dê kai logôdes
+ti melos, to synkeimenon ek tôn prosôdiôn, to en tois onomasi;
+physikon gar to epiteinein kai anienai en tô dialegesthai].]
+
+he notices that the melody differs in several points from the spoken
+accents: (1) the three first words are all on the same note, in spite
+of the accents; (2) the last syllable of [Greek: arbylês] is as high
+as the second, though that is the only accented syllable: (3) the
+first syllable of [Greek: tithete] is lower than the two others,
+instead of being higher: (4) the circumflex of [Greek: ktypeite] is
+lost ([Greek: êphanistai]), because the word is all on the same
+pitch; (5) the fourth syllable of [Greek: apoprobate] is higher in
+pitch, instead of the third. In Mr. Ramsay's inscription, however,
+the music follows the accents as closely as possible. Every acute
+accent coincides with a rise of pitch, except in [Greek: hoson],
+which begins the melody, and in [Greek: esti], for which we should
+perhaps read the orthotone [Greek: esti]. Of the four instances of
+the circumflex accent three exhibit the two notes and the falling
+pitch which we expect. The interval is either a major or a minor
+Third. In the other case ([Greek: zês) the next note is a Third
+lower: but it does not seem to belong to the circumflexed syllable.
+All this cannot be accidental. It leads us to the conclusion that the
+musical notes represent a kind of recitative, or imitation of spoken
+words, rather than a melody in the proper sense of the term.
+
+If any considerable specimen of the music of Euripides had survived,
+it might have solved many of the problems with which we have been
+dealing. The fragment before us extends over about six lines in
+dochmiac metre (_Orestes_ 338-343), with the vocal notation: but no
+single line is entire. The key is the Lydian. The genus is either
+Enharmonic or Chromatic. Assuming that it is Enharmonic--the
+alternative adopted by Dr. Wessely--the characters which are still
+legible may be represented in modern notation as follows:
+
+[Music: [_Euripides_, _Orestes 338-344_.
+
+    [Greek: (katolo)phy-ro-mai; ma-te-ros (haima sas ho d' ana)bak-cheu-ei;
+    ho me-gas (olbos ou monimo)s en bro-tois;
+    a-na (de laiphos hôs ti)s a-ka-tou tho-as ti-na(xas daimôn)
+    kat-e-kly-sen (deinôn ponon) hôs pon-tou labrois k.t.l.
+
+]
+
+It should be observed that in the fragment the line [Greek:
+katolophyromai katolophyromai] comes before 338 ([Greek: materos
+k.t.l.]), not after it, as in our texts[1].
+
+[Footnote 1: I need not repeat what is said by Dr. Wessely and M.
+Ruelle in defence of the genuineness of our fragment. They justly
+point to the remarkable coincidence that the music of this very play
+is quoted by Dionysius of Halicarnassus (_l. c._). It would almost
+seem as if it was the only well-known specimen of music of the
+classical period of tragedy.
+
+The transcription of Dr. Crusius, with his conjectural restorations,
+will be found in the _Appendix_. I have only introduced one of his
+corrections here, viz. the note on the second syllable of [Greek:
+kateklysen].]
+
+The notes employed, according to the interpretation given above, give
+the scale _g-a-a*-a#-d-e-e*_. If the genus is Chromatic, as M. Ruelle
+is disposed to think, they are _g-a-a#-b-d-e-f_. When these scales
+are compared with the Perfect System we find that they do not
+entirely agree with it. Whether the genus is Enharmonic or Chromatic
+the notes from _a_ to _e*_ (or _f_) answer to those of the Perfect
+System (of the same genus) from Hypatê Mesôn to Tritê Diezeugmenôn.
+But in either case the lowest note (_g_) finds no place in the
+System, since it can only be the Diatonic Lichanos Hypatôn. It is
+possible, however, that the scale belongs to the period when the
+original octave had been extended by the addition of a tone below the
+Hypatê--the note, in fact, which we have already met with under the
+name of Hyper-hypatê (p. 39). Thus the complete scale may have
+consisted of the disjunct tetrachords _a-d_ and _e-a_, with the tone
+_g-a_. It may be observed here that although the scale in question
+does not fit into the Perfect System, it conforms to the general
+rules laid down by Aristoxenus for the melodious succession of
+intervals. It is unnecessary therefore to suppose (as Dr. Wessely and
+M. Ruelle do) that the scale exhibits a _mixture_ of different
+genera.
+
+It must be vain to attempt to discover the tonality of a short
+fragment which has neither beginning nor end. The only group of notes
+which has the character of a cadence is that on the word
+[Greek:(olo)phypomai], and again on the words [Greek: en brotois],
+viz. the notes _a# a* a_ (if the genus is the Enharmonic). The same
+notes occur in reversed order on [Greek: akatou] and [Greek:
+(kat)eklusen]. This seems to bear out the common view of the
+Enharmonic as produced by the introduction of an 'accidental' or
+passing note. It will be seen, in fact, that the Enharmonic notes
+(_a*_ and _e*_) only occur before or after the 'standing' notes (_a_
+and _e_).
+
+Relying on the fact that the lowest note is _g_, Dr. Wessely and M.
+Ruelle pronounce the mode to be the Phrygian (_g-g_ in the key with
+one [Symbols: flat], or _d-d_ in the natural key). I have already put
+forward a different explanation of this _g_, and will only add here
+that it occurs twice in the fragment, both times on a short
+syllable[1]. The important notes, so far as the evidence goes, are
+_a_, which twice comes at the end of a verse (with a pause in the
+sense), and _e_, which once has that position. If _a_ is the
+key-note, the mode--in the modern sense--is Dorian (the _e_-species).
+If _e_ is the key-note, it is Mixo-lydian (the _b_-species).
+
+[Footnote 1: Dr. Crusius, however, detects a [Symbols: phi]; (the
+sign for _g_) over the first syllable of [Greek: kateklusen] and the
+second syllable of [Greek: pontou]. There is little trace of them in
+his facsimile.]
+
+
+
+
+§ 33. _Modes of Aristides Quintilianus._
+
+The most direct testimony in support of the view that the ancient
+Modes were differentiated by the succession of their intervals has
+still to be considered. It is the account given by Aristides
+Quintilianus (p. 21 Meib.) of the six Modes ([Greek: harmoniai]) of
+Plato's _Republic_. After describing the genera and their varieties
+the 'colours,' he goes on to say that there were other divisions of
+the tetrachord ([Greek: tetrachordikai diaireseis]) which the most
+ancient musicians used for the [Greek: harmoniai], and that these
+were sometimes greater in compass than the octave, sometimes less. He
+then gives the intervals of the scale for each of the six Modes
+mentioned by Plato, and adds the scales in the ancient notation. They
+are of the Enharmonic genus, and may be represented by modern notes
+as follows:--
+
+
+      Mixo-lydian      _b-b*-c-d-e-e*-f-b_
+      Syntono-lydian   _e-e*-f-a-c_
+      Phrygian         _d-e-e*-f-a-b-b*-c-d_
+      Dorian           _d-e-e*-f-a-b-b*-c-e_
+      Lydian           _e*-f-a-b-b*-c-e-e*_
+      Ionian           _e-e*-f-a-c-d_
+
+
+Comparing these scales with the Species of the Octave, we find a
+certain amount of correspondence. As has been already noticed (p.
+22), the names Syntono-lydian and Lydian answer to the ordinary
+Lydian and Hypo-lydian respectively. Accordingly the Lydian of
+Aristides agrees with the Hypo-lydian species as given in the
+pseudo-Euclidean _Introductio_. The Dorian of Aristides is the Dorian
+species of the _Introductio_, but with an additional note, a tone
+below the Hypatê.
+
+The Phrygian of Aristides is not the Enharmonic Phrygian species; but
+it is derived from the diatonic Phrygian octave _d-e-f-g-a-b-c-d_ by
+inserting the enharmonic notes _e*_ and _b*_, and omitting the
+diatonic _g_. By a similar process the Mixo-lydian of Aristides may
+be derived from the diatonic octave _b-b_, except that _a_ as well as
+_g_ is omitted, and on the other hand _d_ is retained. If the scale
+of the Syntono-lydian is completed by the lower _c_ (as analogy would
+require), it will answer similarly to the Lydian species (_c-c_).
+
+
+
+
+§ 34. _Credibility of Aristides Quintilianus._
+
+But what weight can be given to Aristides as an authority on the
+music of the time of Plato? The answer to this question depends upon
+several considerations.
+
+1. The date of Aristides is unknown. He is certainly later than
+Cicero, since he quotes the _De Republica_ (p. 70 Meib.). From the
+circumstance that he makes no reference to the musical innovations of
+Ptolemy it has been supposed that he was earlier than that writer.
+But, as Aristides usually confines himself to the theory of
+Aristoxenus and his school, the argument from silence is not of much
+value. On the other hand he gives a scheme of notation containing two
+characters, [Symbol: [] and [Symbol: *], which extend the scale two
+successive semi-tones beyond the lowest point of the notation given
+by Alypius[1]. For this reason it is probable that Aristides is one
+of the latest of the writers on ancient music.
+
+[Footnote 1: This argument is used, along with some others not so
+cogent, in Mr. W. Chappell's _History of Music_ (p. 130).]
+
+2. The manner in which Aristides introduces his information about the
+Platonic Modes is highly suspicious. He has been describing the
+various divisions of the tetrachord according to the theory of
+Aristoxenus, and adds that there were anciently other divisions in
+use. So far Aristides is doubtless right, since Aristoxenus himself
+says that the divisions of the tetrachord are theoretically infinite
+in number (p. 26 Meib.),--that it is possible, for example, to
+combine the Parhypatê of the Soft Chromatic with the Lichanos of the
+Diatonic (p. 52 Meib.). But all this concerns the genus of the scale,
+and has nothing to do with the species of the Octave, with which
+Aristides proceeds to connect it. It follows either that there is
+some confusion in the text, or that Aristides was compiling from
+sources which he did not understand.
+
+3. The Platonic Modes were a subject of interest to the early musical
+writers, and were discussed by Aristoxenus himself (Plut. _de Mus._
+c. 17). If Aristoxenus had had access to such an account as we have
+in Aristides, we must have found some trace of it, either in the
+extant _Harmonics_ or in the quotations of Plutarch and other
+compilers.
+
+4. Of the four scales which extend to the compass of an octave, only
+one, viz. the Dorian, conforms to the rules which are said by
+Aristoxenus to have prevailed in early Greek music. The Phrygian
+divides the Fourth _a-d_ into four intervals instead of three, by the
+sequence _a b b* c d_. As has been observed, it is neither the
+Enharmonic Phrygian species (_c e e* f a b b* c_), nor the Diatonic
+_d-d_, but a mixture of the two. Similarly the Mixo-lydian divides
+the Fourth _b_-_e_ into four intervals (_b b* c d e_), by introducing
+the purely Diatonic note _d_. The Lydian is certainly the Lydian
+Enharmonic species of the pseudo-Euclid; but we can hardly suppose
+that it existed in practical music. Aristoxenus lays it down
+emphatically that a quarter-tone is always followed by another: and
+we cannot imagine a scale in which the highest and lowest notes are
+in no harmonic relation to the rest.
+
+5. Two of the scales are incomplete, viz. the Ionian, which has six
+notes and the compass of a Seventh, and the Syntono-lydian, which
+consists of five notes, with the compass of a Minor Sixth. We
+naturally look for parallels among the defective scales noticed in
+the _Problems_ and in Plutarch's dialogues. But we find little that
+even illustrates the modes of Aristides. The scales noticed in the
+_Problems_ (xix. 7, 32, 47) are hepta-chord, and generally of the
+compass of an octave. In one passage of Plutarch (_De Mus._ c. 11)
+there is a description--quoted from Aristoxenus--of an older kind of
+Enharmonic, in which the semitones had not yet been divided into
+quarter-tones. In another chapter (c. 19) he speaks of the omission
+of the Tritê and also of the Nêtê as characteristic of a form of
+music called the [Greek: spondeiakos tropos]. It may be said that in
+the Ionian and Syntono-lydian of Aristides the Enharmonic Tritê
+(_b*_) and the Nêtê (_e_) are wanting. But the Paramesê (_b_) is also
+wanting in both these modes. And the Ionian is open to the
+observation already made with regard to the Phrygian, viz. that the
+two highest notes (_c d_) involve a mixture of Diatonic with
+Enharmonic scale. We may add that Plutarch (who evidently wrote with
+Aristoxenus before him) gives no hint that the omission of these
+notes was characteristic of any particular modes.
+
+6. It is impossible to decide the question of the modes of Aristides
+without some reference to another statement of the same author. In
+the chapter which treats of Intervals (pp. 13-15 Meib.) he gives the
+ancient division of two octaves, the first into dieses or
+quarter-tones, the second into semitones. The former of these
+([Greek: hê para tois archaiois kata dieseis harmonia]) is as
+follows:
+
+
+                [1] 2  3  4  5  6  7  8  9  10 11 12
+
+      [Symbols:    -o  <  6 1-1 9  L  J  A  V  E  3]
+      [Symbols:     o- >  9  n  6  J  r- v  0  3  E]
+
+                13  14  15  16 17 18 19  20  21  22 23  24
+
+      [Symbols: 3..  N 1-1  3  E   , '-  cc   >   <  Y   Y]
+      [Symbols: r   a..1-1  E  3   A ,'- 33   <          Y]
+
+
+After every allowance has been made for the probability that these
+signs or some of them have reached us in a corrupt form, it is
+impossible to reduce them to the ordinary notation, as Meibomius
+sought to do. The scholar who first published them as they stand in
+the MSS. (F. L. Perne, see Bellermann, _Tonleitern_, p. 62) regarded
+them as a relic of a much older system of notation. This is in
+accordance with the language of Aristides, and indeed is the only
+view consistent with a belief in their genuineness. They are too like
+the ordinary notation to be quite independent, and cannot have been
+put forward as an improvement upon it. Are they, then, earlier?
+Bellermann has called our attention to a peculiarity which seems
+fatal to any such claim. They consist, like the ordinary signs, of
+two sets, one written above the other, and in every instance one of
+the pair is simply a reversed or inverted form of the other. With the
+ordinary signs this is not generally the case, since the two sets,
+the vocal and instrumental notes, are originally independent. But it
+is the case with the three lowest notes, viz. those which were added
+to the series at a later time. When these additional signs were
+invented the vocal and instrumental notes had come to be employed
+together. The inventor therefore devised a pair of signs in each
+case, and not unnaturally made them correspond in form. In the scale
+given by Aristides this correspondence runs through the whole series,
+which must therefore be of later date. But if this is so, the
+characters can hardly represent a genuine system of notation. In
+other words, Aristides must have been imposed upon by a species of
+forgery.
+
+7. Does the fragment of the _Orestes_ tell for or against the Modes
+described by Aristides?
+
+The scale which is formed by the notes of the fragment agrees, so far
+as it extends, with two of the scales now in question, viz. the
+Phrygian and the Dorian. Taking the view of its tonality expressed in
+the last chapter (p. 93), we should describe it as the Dorian scale
+of Aristides with the two highest notes omitted. The omission, in so
+short a fragment, is of little weight; and the agreement in the use
+of an additional lower note (Hyper-hypatê) is certainly worth notice.
+On the other hand, the Dorian is precisely the mode, of those given
+in the list of Aristides, which least needs defence, as it is the
+most faithful copy of the Perfect System. Hence the fact that it is
+verified by an actual piece of music does not go far in support of
+the other scales in the same list.
+
+If our suspicions are well-founded, it is evident that they seriously
+affect the genuineness of all the antiquarian learning which
+Aristides sets before his readers, and in particular of his account
+of the Platonic modes. I venture to think that they go far to deprive
+that account of the value which it has been supposed to have for the
+history of the earliest Greek music.
+
+For the later period, however, to which Aristides himself belongs,
+these apocryphal scales are a document of some importance. The fact
+that they do not agree entirely with the species of the Octave as
+given by the pseudo-Euclid leads us to think that they may be
+influenced by scales used in actual music. This applies especially to
+the Phrygian, which (as has been shown) is really diatonic. The
+Ionian, again, is perhaps merely an imperfect form of the same scale,
+viz. the octave _d-d_ with lower _d_ omitted. And the Syntono-lydian
+may be the Lydian diatonic octave _c-c_ with a similar omission of
+the lower _c_. § 35. _Evidence for Scales of different species._
+
+The object of the foregoing discussion has been to show, in the first
+place, that there was no such distinction in ancient Greek music as
+that which scholars have drawn between Modes ([Greek: harmoniai]) and
+Keys ([Greek: tonoi] or [Greek: tropoi]): and, in the second place,
+that the musical scales denoted by these terms were primarily
+distinguished by difference of _pitch_,--that in fact they were so
+many keys of the standard scale known in its final form as the
+Perfect System. The evidence now brought forward in support of these
+two propositions is surely as complete as that which has been allowed
+to determine any question of ancient learning.
+
+It does not, however, follow that the Greeks knew of no musical forms
+analogous to our Major and Minor modes, or to the mediaeval Tones. On
+the contrary, the course of the discussion has led us to recognise
+distinctions of this kind in more than one instance. The doctrine
+against which the argument has been mainly directed is not that
+ancient scales were of more than one species or 'mode' (as it is now
+called), but that difference of species was the basis of the ancient
+Greek Modes. This will become clear if we bring together all the
+indications which we have observed of scales differing from each
+other in species, that is, in the _order_ of the intervals in the
+octave. In doing so it will be especially important to be guided by
+the principle which we laid down at the outset, of arranging our
+materials according to chronology, and judging of each piece of
+evidence strictly with reference to the period to which it belongs.
+It is only thus that we can hope to gain a conception of Greek music
+as the living and changing thing that we know it must have been.
+
+1. The principal scale of Greek music is undoubtedly of the
+Hypo-dorian or common species. This is sufficiently proved by the
+facts (1) that two octaves of this species (_a-a_) constitute the
+scale known as the Greater Perfect System, and (2) that the central
+_a_ of this system, called the Mesê, is said to have been the
+key-note, or at least to have had the kind of importance in the scale
+which we connect with the key-note (Arist. _Probl._ xix. 20). This
+mode, it is obvious, is based on the scale which is the descending
+scale of the modern Minor mode. It may therefore be identified with
+the Minor, except that it does not admit the leading note.
+
+It should be observed that this mode is to be recognised not merely
+in the Perfect System but equally in the primitive octave, of the
+form _e - e_, out of which the Perfect System grew. The important
+point is the tonic character of the Mesê (_a_), and this, as it
+happens, rests upon the testimony of an author who knows the
+primitive octave only. The fact that that octave is of the so-called
+Dorian species does not alter the _mode_ (as we are now using that
+term), but only the compass of the notes employed.
+
+The Hypo-dorian octave is seen in two of the scales of the cithara
+given by Ptolemy (p. 85), viz. those called [Greek: tritai] and
+[Greek: tropoi], and the Dorian octave (_e - e_) in two scales,
+[Greek: parupatai] and [Greek: ludia]. It is very possible (as was
+observed in commenting on them) that the two latter scales were in
+the key of _a_, and therefore Hypo-dorian in respect of mode. The
+Hypo-dorian mode is also exemplified by three at least of the
+instrumental passages given by the _Anonymus_ (_supra_, p. 89).
+
+2. The earliest trace of a difference of species appears to be found
+in the passage on the subject of the Mixo-lydian mode quoted above
+(p. 24) from Plutarch's _Dialogue on Music_. In that mode, according
+to Plutarch, it was discovered by a certain Lamprocles of Athens that
+the Disjunctive Tone was the highest interval, that is to say, that
+the octave in reality consisted of two conjunct tetrachords and a
+tone:
+
+[Music: Mesê Disj. Tone]
+
+As the note which is the meeting-point of the two tetrachords is
+doubtless the key-note, we shall not be wrong in making it the Mesê,
+and thus finding the octave in question in the Perfect System and in
+the oldest part of it, viz. the tetrachords Mesôn and Synêmmenôn,
+with the Nêtê Diezeugmenôn. How then did this octave come to be
+recognised by Lamprocles as distinctively Mixo-lydian? We cannot tell
+with certainty, because we do not know what the Mixo-lydian scale was
+before his treatment of it. Probably, however, the answer is to be
+sought in the relation in respect of pitch between the Dorian and
+Mixo-lydian keys. These, as we have seen (p. 23), were the keys
+chiefly employed in tragedy, and the Mixo-lydian was a Fourth higher
+than the other. Now when a scale consisting of white notes is
+transposed to a key a Fourth higher, it becomes a scale with one
+[Symbol: Flat]. In ancient language, the tetrachord Synêmmenôn
+(_a-b[Symbol: Flat]-c-d_) takes the place of the tetrachord
+Diezeugmenôn. In some such way as this the octave of this form may
+have come to be associated in a special way with the use of the
+Mixo-lydian key.
+
+However this may be, the change from the tetrachord Diezeugmenôn to
+the tetrachord Synêmmenôn, or the reverse, is a change of mode in the
+modern sense, for it is what the ancients classified as a change of
+System ([Greek: metabolê kata systêma])[1]. Nor is it hard to
+determine the two 'modes' concerned, if we may trust to the authority
+of the Aristotelian _Problems_ (_l. c._) and regard the Mesê as
+always the key-note. For if _a_ is kept as the key-note, the octave
+_a-a_ with one [Symbol: b] is the so-called Dorian (_e - e_ on the
+white notes). In this way we arrive at the somewhat confusing result
+that the ancient Dorian species (_e - e_ but with _a_ as key-note)
+yields the Hypo-dorian or modern Minor mode: while the Dorian mode of
+modern scientific theory[2] has its ancient prototype in the
+Mixo-lydian species, viz. the octave first brought to light by
+Lamprocles. The difficulty of course arises from the species of the
+Octave being classified according to their compass, without reference
+to the tonic character of the Mesê.
+
+The Dorian mode is amply represented in the extant remains of Greek
+music. It is the mode of the two compositions of Dionysius, the Hymn
+to Calliope and the Hymn to Apollo (p. 88), perhaps also of Mr.
+Ramsay's musical inscription (p. 90). It would have been satisfactory
+if we could have found it in the much more important fragment of the
+_Orestes_. Such indications as that fragment presents seem to me to
+point to the Dorian mode (Mixo-lydian of Lamprocles).
+
+3. The scales of the cithara furnish one example of the Phrygian
+species (_d-d_), and one of the Hypo-phrygian (_g-g_): but we have no
+means of determining which note of the scale is to be treated as the
+key-note.
+
+[Footnote 1: Ps. Eucl. _Introd._ p. 20 Meib. [Greek: kata systêma de
+hotan ek synaphês eis diazeuxin ê anapalin metabolê ginêtai]. Anonym.
+
+
+
+
+§ 65 [Greek: systêmatikai de] (sc. [Greek: metabolai]) [Greek:
+hopotan ek diazeuxeôs eis synaphên ê empalin metelthê to melos].]
+
+[Footnote 2: As represented primarily by the analysis of Helmholtz,
+_Die Tonempfindungen_, p. 467, ed. 1863.]
+
+In the Hymn to Nemesis, however, in spite of the incomplete form in
+which it has reached us, there is a sufficiently clear example of the
+Hypo-phrygian mode. It has been suggested as possible that the melody
+of Mr. Ramsay's inscription is also Hypo-phrygian, and if so the
+evidence for the mode would be carried back to the first century.
+
+The Hypo-phrygian is the nearest approach made by any specimen of
+Greek music to the modern Major mode,--the Lydian or _c_-species not
+being found even among the scales of the cithara as given by Ptolemy.
+It is therefore of peculiar interest for musical history, and we look
+with eagerness for any indication which would allow us to connect it
+with the classical period of Greek art. One or two sayings of
+Aristotle have been thought to bear upon this issue.
+
+The most interesting is a passage in the _Politics_ (iv. 3, cp. p.
+13), where Aristotle is speaking of the multiplicity of forms of
+government, and showing how a great number of varieties may
+nevertheless be brought under a few classes or types. He illustrates
+the point from the musical Modes, observing that all constitutions
+may be regarded as either oligarchical (government by a minority) or
+democratical (government by the majority), just as in the opinion of
+some musicians ([Greek: hôs phasi tines]) all modes are essentially
+either Dorian or Phrygian. What, then, is the basis of this grouping
+of certain modes together as Dorian, while the rest are Phrygian in
+character? According to Westphal it is a form of the opposition
+between the true Hellenic music, represented by Dorian, and the
+foreign music, the Phrygian and Lydian, with their varieties.
+Moreover, it is in his view virtually the same distinction as that
+which obtains in modern music between the Minor and the Major
+scales[1]. This account of the matter, however, is not supported by
+the context of the passage. Aristotle draws out the comparison
+between forms of government and musical modes in such a way as to
+make it plain that in the case of the modes the distinction was one
+of pitch ([Greek: tas suntonôteras ... tas d' aneimenas kai
+malakas]). The Dorian was the best, because the highest, of the lower
+keys,--the others being Hypo-dorian (in the earlier sense,
+immediately below Dorian), and Hypo-phrygian--while Phrygian was the
+first of the higher series which took in Lydian and Mixo-lydian. The
+division would be aided, or may even have been suggested, by the
+circumstance that it nearly coincided with the favourite contrast of
+Hellenic and 'barbarous' modes[2]. There is another passage, however,
+which can hardly be reconciled with a classification according to
+pitch alone. In the chapters dealing with the ethical character of
+music Aristotle dwells (as will be remembered) upon the exciting and
+orgiastic character of the Phrygian mode, and notices its especial
+fitness for the dithyramb. This fitness or affinity, he says, was so
+marked that a poet who tried to compose a dithyramb in another mode
+found himself passing unawares into the Phrygian (_Pol._ viii. 7). It
+is natural to understand this of the use of certain sequences of
+intervals, or of cadences, such as are characteristic of a 'mode' in
+the modern sense of the word, rather than of a change of key. If this
+is so we may venture the further hypothesis that the Phrygian music,
+in some at least of its forms, was distinguished not only by pitch,
+but also by the more or less conscious use of scales which differed
+in type from the scale of the Greek standard system.
+
+[Footnote 1: _Harmonik und Melopöie_, p. 356 (ed. 1863): 'Die älteste
+griechische Tonart ist demnach eine Molltonart.... Aus Kleinasien
+wurden zunächst zwei Durtonarten nach Griechenland eingeführt, die
+lydische und phrygische.' In the 1886 edition of the same book (p.
+189) Westphal discovers a similar classification of modes implied in
+the words of Plato, _Rep._ p. 400 a [Greek: tri' atta estin eidê ex
+hôn hai baseis plekontai, hôsper en tois phthongois tettara hothen
+hai pasai harmoniai]. But Plato is evidently referring to some matter
+of common knowledge. The three forms or elements of which all rhythms
+are made up are of course the ratios 1: 1, 2: 1 and 3: 2, which yield
+the three kinds of rhythm, dactylic, iambic and cretic (answering to
+common, triple, and quintuple time). Surely the four elements of all
+musical scales of which Plato speaks are not four kinds of scale
+(_Harmonien-Klassen_), but the four ratios which give the primary
+musical intervals--viz. the ratios 2: 1, 3: 2, 4: 3 and 9: 8, which
+give the Octave, Fifth, Fourth and Tone.]
+
+[Footnote 2: If Hypo-phrygian is the same as the older Ionian (p.
+11), the coincidence is complete for the time of Aristotle. Plato
+treats the claim of Ionian to rank among the Hellenic modes as
+somewhat doubtful (_Laches_, p. 188).]
+
+It may be urged that this hypothesis is inconsistent with our
+interpretation of the passage of the _Problems_ about the tonic
+character of the Mesê. If _a_ is key-note, it was argued, the mode is
+that of the _a_-species (Hypo-dorian, our Minor), or at most--by
+admitting the tetrachord Synêmmenôn--it includes the _e_-species
+(Dorian of Helmholtz). The answer may be that the statement of the
+_Problems_ is not of this absolute kind. It is not the statement of a
+technical writer, laying down definite rules, but is a general
+observation, or at best a canon of taste. We are not told how the
+predominance of the Mesê is shown in the form of the melody. Moreover
+this predominance is not said to be exercised in music generally, but
+in all _good_ music ([Greek: panta gar ta chrêsta melê pollakis tê
+mesê chrêtai]). This may mean either that tonality in Greek music was
+of an imperfect kind, a question of style and taste rather than of
+fixed rule, or that they occasionally employed modes of a less
+approved stamp, unrecognised in the earlier musical theory. § 36.
+_Conclusion._
+
+The considerations set forth in the last chapter seem to show that if
+difference of mode or species cannot be entirely denied of the
+classical period of Greek music, it occupied a subordinate and almost
+unrecognised place.
+
+The main elements of the art were, (1) difference of _genus_,--the
+sub-divisions of the tetrachord which Aristoxenus and Ptolemy alike
+recognise, though with important discrepancies in detail; (2)
+difference of pitch or _key_; and (3) _rhythm_. Passing over the
+last, as not belonging to the subject of _Harmonics_, we may now say
+that genus and key are the only grounds of distinction which are
+evidently of practical importance. No others were associated with the
+early history of the art, with particular composers or periods, with
+particular instruments, or with the ethos of music. This, however, is
+only true in the fullest sense of Greek music before the time of
+Ptolemy. The main object of Ptolemy's reform of the keys was to
+provide a new set of scales, each characterised by a particular
+succession of intervals, while the pitch was left to take care of
+itself. And it is clear, especially from the specimens which Ptolemy
+gives of the scales in use in his time, that he was only endeavouring
+to systematise what already existed, and bring theory into harmony
+with the developments of practice. We must suppose, therefore, that
+the musical feeling which sought variety in differences of key came
+to have less influence on the practical art, and that musicians began
+to discover, or to appreciate more than they had done, the use of
+different 'modes' or forms of the octave scale. Along with this
+change we have to note the comparative disuse of the Enharmonic and
+Chromatic divisions of the tetrachord. The Enharmonic, according to
+Ptolemy, had ceased to be employed. Of the three varieties of
+Chromatic given by Aristoxenus only one remains on Ptolemy's list,
+and that the one which in the scheme of Aristoxenus involved no
+interval less than a semitone. And although Ptolemy distinguished at
+least three varieties of Diatonic, it is worth notice that only one
+of these was admitted in the tuning of the lyre,--the others being
+confined to the more elaborate cithara. In Ptolemy's time, therefore,
+music was rapidly approaching the stage in which all its forms are
+based upon a single scale--the natural diatonic scale of modern
+Europe.
+
+In the light of these facts it must occur to us that Westphal's
+theory of seven modes or species of the Octave is really open to an
+_a priori_ objection as decisive in its nature as any of the
+testimony which has been brought against it. Is it possible, we may
+ask, that a system of modes analogous to the ecclesiastical Tones can
+have subsisted along with a system of scales such as the genera and
+'colours' of early Greek music? The reply may be that Ptolemy himself
+combines the two systems. He supposes five divisions of the
+tetrachord, and seven modes based upon so many species of the
+Octave--in all thirty-five different scales (or seventy, if we bring
+in the distinction of octaves [Greek: apo nêtês] and [Greek: apo
+mesês]). But when we come to the scales actually used on the chief
+Greek instrument, the cithara, the number falls at once to six.
+Evidently the others, or most of them, only existed on paper, as the
+mathematical results of certain assumptions which Ptolemy had made.
+And if this can be said of Ptolemy's theory, what would be the value
+of a similar scheme combining the modes with the Enharmonic and the
+different varieties of the Chromatic genus? The truth is, surely,
+that such a scheme tries to unite elements which belong to different
+times, which in fact are the fundamental ideas of different stages of
+art.
+
+The most striking characteristic of Greek music, especially in its
+earlier periods, is the multiplicity and delicacy of the intervals
+into which the scale was divided. A sort of frame-work was formed by
+the division of the octave into tetrachords, completed by the
+so-called disjunctive tone; and so far all Greek music was alike. But
+within the tetrachord the reign of diversity was unchecked. Not only
+were there recognised divisions containing intervals of a fourth, a
+third, and even three-eighths of a tone, but we gather from several
+things said by Aristoxenus that the number of possible divisions was
+regarded as theoretically unlimited. Thus he tells us that there was
+a constant tendency to flatten the 'moveable' notes of the Chromatic
+genus, and thus diminish the small intervals, for the sake of
+'sweetness' or in order to obtain a plaintive tone[1];--that the
+Lichanos of a tetrachord may in theory be any note between the
+Enharmonic Lichanos (_f_ in the scale _e-e*-f-a_) and the Diatonic
+(_g_ in the scale _e-f-g-a_)[2];--and that the magnitude of the
+smaller intervals and division of the tetrachord generally belongs to
+the indefinite or indeterminate element in music[3]. Moreover, in
+spite of the disuse of several of the older scales, much of this
+holds good for the time of Ptolemy. The modern diatonic scale is
+fully recognised by him, but only as one of several different
+divisions. And the division which he treats as the ordinary or
+standard form of the octave is not the modern diatonic scale, but one
+of the so-called 'soft' or flattened varieties. It is clear that in
+the best periods of Greek music these refinements of melody, which
+modern musicians find scarcely conceivable, were far from being
+accidental or subordinate features. Rather, they were as much bound
+up with the fundamental nature of that music as complex harmony is
+with the music of modern Europe.
+
+[Footnote 1: Aristox. _Harm._ p. 23 Meib. [Greek: hoi men gar tê nun
+katechousê melopoiia ounêtheis monon ontes eiktôs tên ditonon
+lichanon] (_f_ in the scale _e-a_) [Greek: exorizousi; suntonôterais
+gar chrôntai schedon hoi pleistoi tôn nun. toutou d' aition to
+boulesthai glukainein aei. sêmeion de hoti toutou stochazontai,
+malista men gar kai pleiston chronon en tô chrômati diatribousin.
+hotan d' aphikôntai pote eis tên harmonian engus tou chromatos
+prosagousi, sunepismômenou tou êthous.]]
+
+[Footnote 2: Ibid. p. 26 [Greek: noêteon gar apeirous ton arithmon
+tas lichanous. hou gar an stêsês tên phônên apodedeigmenon lichanô
+topou lichanos estai; diakenon de ouden esti tou lichanoeidous topou,
+oude toiouton hôste mê dechisthai lichanon]. And p. 48 [Greek: epeidê
+per ho tês lichanou topos eis apeirous temnetai tomas].]
+
+[Footnote 3: Aristox. _Harm._ p. 69 Meib. [Greek: kata men oun ta
+megethê tôn diastêmatôn kai tas tôn phthongôn taseis apeira pôs
+phainetai einai ta peri to melos, kata de tas dynameis kai kata ta
+eidê kai kata tas theseis peperasmena te kai tetagmena.]]
+
+The mediaeval modes or Tones, on the other hand, are essentially
+based on the diatonic scale,--the scale that knows only of tones and
+semitones. To suppose that they held in the earliest Greek music the
+prominent place which we find assigned to the ancient Modes or
+[Greek: harmoniai] is to suppose that the art of music was developed
+in Greece in two different directions, under the influence of
+different and almost opposite ideas. Yet nothing is more remarkable
+in all departments of Greek art than the strictness with which it
+confines itself within the limits given once for all in the leading
+types, and the consequent harmony and consistency of all the forms
+which it takes in the course of its growth.
+
+The dependence of artistic forms in their manifold developments upon
+a central governing idea or principle has never been more luminously
+stated than by the illustrious physicist Helmholtz, in the thirteenth
+chapter of his _Tonempfindungen_. I venture to think that in applying
+that truth to the facts of Greek music he was materially hindered by
+the accepted theory of the Greek modes. The scales which he analyses
+under that name were certainly the basis of all music in the Middle
+Ages, and are much more intelligible as such than in relation to the
+primitive Greek forms of the art[1].
+
+[Footnote 1: The ecclesiastical Modes received their final shape in
+the _Dodecachordon_ of Glareanus (Bâle, 1547). They are substantially
+the Greek modes of Westphal's theory, although the Greek names which
+Glareanus adopted seem to have been chosen at haphazard. But the
+ecclesiastical Modes, as Helmholtz points out, were developed under
+the influence of polyphonic music from the earlier stages represented
+by the Ambrosian and Gregorian scales. It would be a singular chance
+if they were also, as Greek modes, the source from which the
+Ambrosian and Gregorian scales were themselves derived.
+
+Some further hints on this part of the subject may possibly be
+derived from the musical scales in use among nations that have not
+attained to any form of harmony, such as the Arabians, the Indians,
+or the Chinese. A valuable collection of these scales is given by Mr.
+A. J. Ellis at the end of his translation of Helmholtz (Appendix XX.
+Sect. K, _Non-harmonic Scales_). Among the most interesting for our
+purpose are the eight mediaeval Arabian scales given on the authority
+of Professor Land (nos. 54-61). The first three of these--called
+'Ochaq, Nawa and Boas[=i]li--follow the Pythagorean intonation, and
+answer respectively to the Hypo-phrygian, Phrygian, and Mixo-lydian
+species of the octave. The next two--Rast and Zenkouleh--are also
+Hypo-phrygian in species, but the Third and Sixth are flatter by
+about an eighth of a tone (the Pythagorean comma). In Zenkouleh the
+Fifth also is similarly flattened. The last two scales--Hhosa[=i]ni
+and Hhidjazi--are Phrygian: but the Second and Fifth, and in the case
+of Hhidjazi also the Sixth, are flatter by the interval of a comma.
+The remaining scale, called Rahawi, does not fall under any species,
+since the semitones are between the Third and Fourth, and again
+between the Fifth and Sixth. It will be seen that in general
+character--though by no means in details--this series of scales bears
+a considerable resemblance to the 'scales of the cithara' as given by
+Ptolemy (_supra_, p. 85). In both cases the several scales are
+distinguished from each other partly by the order of the intervals
+(_species_), partly by the intonation, or magnitude of the intervals
+employed (_genus_). This latter element is conspicuously absent from
+the ecclesiastical Modes.]
+
+
+
+
+§ 37. _Epilogue--Speech and Song._
+
+Several indications combine to make it probable that singing and
+speaking were not so widely separated from each other in Greek as in
+the modern languages with which we are most familiar.
+
+(1) The teaching of the grammarians on the subject of accent points
+to this conclusion. Our habit of using Latin translations of the
+terms of Greek grammar has tended to obscure the fact that they
+belong in almost every case to the ordinary vocabulary of music. The
+word for 'accent' ([Greek: tonos]) is simply the musical term for
+'pitch' or 'key.' The words 'acute' ([Greek: oxys]) and 'grave'
+([Greek: barys]) mean nothing more than 'high' and 'low' in pitch. A
+syllable may have two accents, just as in music a syllable may be
+sung with more than one note. Similarly the 'quantity' of each
+syllable answers to the time of a musical note, and the rule that a
+long syllable is equal to two short ones is no doubt approximately
+correct. Consequently every Greek word (enclitics being reckoned as
+parts of a word) is a sort of musical phrase, and every sentence is a
+more or less definite melody--[Greek: logôdes ti melos], as it is
+called by Aristoxenus (p. 18 Meib.). Moreover the accent in the
+modern sense, the _ictus_ or stress of the voice, appears to be quite
+independent of the pitch or 'tonic' accent: for in Greek poetry the
+_ictus_ ([Greek: arsis]) is determined by the metre, with which the
+tonic accent evidently has nothing to do. In singing, accordingly,
+the tonic accents disappear; for the melody takes their place, and
+gives each syllable a new pitch, on which (as we shall presently see)
+the spoken pitch has no influence. The rise and fall of the voice in
+ordinary speaking is perceptible enough in English, though it is more
+marked in other European languages. Helmholtz tells us--with tacit
+reference to the speech of North Germany--that an affirmative
+sentence generally ends with a drop in the tone of about a Fourth,
+while an interrogative is marked by a rise which is often as much as
+a Fifth[1]. In Italian the interrogative form is regularly given, not
+by a particle or a change in the order of the words, but by a rise of
+pitch. The Gregorian church music, according to a series of rules
+quoted by Helmholtz (_l. c._), marked a comma by a rise of a Tone, a
+colon by a fall of a Semitone; a full stop by a Tone above, followed
+by a Fourth below, the 'reciting note'; and an interrogation by a
+phrase of the form _d b c d_ (_c_ being the reciting note).
+
+These examples, however, do little towards enabling modern scholars
+to form a notion of the Greek system of accentuation. In these and
+similar cases it is the _sentence as a whole_ which is modified by
+the tonic accent, whereas in Greek it is the individual _word_. It is
+true that the accent of a word may be affected by its place in the
+sentence: as is seen in the loss of the accent of oxytone words when
+not followed by a pause, in the anastrophe of prepositions, and in
+the treatment of the different classes of enclitics. But in all these
+instances it is the intonation of the word as such, not of the
+sentence, which is primarily concerned. What they really prove is
+that the musical accent is not so invariable as the stress accent in
+English or German, but may depend upon the collocation of the word,
+or upon the degree of emphasis which it has in a particular use.
+
+[Footnote 1: _Tonempfindungen_, p. 364 (ed. 1863).]
+
+(2) The same conclusion may be drawn from the terms in which the
+ancient writers on music endeavour to distinguish musical and
+ordinary utterance.
+
+Aristoxenus begins his _Harmonics_ by observing that there are two
+movements of the voice, not properly discriminated by any previous
+writer; namely, the _continuous_, which is the movement
+characteristic of speaking, and the _discrete_ or that which proceeds
+by _intervals_, the movement of singing. In the latter the voice
+remains for a certain time on one note, and then passes by a definite
+interval to another. In the former it is continually gliding by
+imperceptible degrees from higher to lower or the reverse[1]. In this
+kind of movement the rise and fall of the voice is marked by the
+_accents_ ([Greek: prosôdiai]), which accordingly form the melody, as
+it may be called, of spoken utterance[2]. Later writers state the
+distinction in much the same language. Nicomachus tells us that the
+two movements were first discriminated by the Pythagoreans. He dwells
+especially on the ease with which we pass from one to the other. If
+the notes and intervals of the speaking voice are allowed to be
+separate and distinct, the form of utterance becomes singing[3].
+Similarly Aristoxenus says that we do not rest upon a note, unless we
+are led to do so by the influence of feeling ([Greek: an mê dia
+pathos pote eis toiautên kinêsin anankasthômen elthein]).
+
+[Footnote 1: Aristox., _Harm._ p. 3 Meib. [Greek: kineitai men gar
+kai dialegomenôn hêmôn kai melôdountôn tên eirêmenên kinêsin; oxy gar
+kai bary dêlon hôs en amphoterois toutois enestin.] Also p. 8 [Greek:
+dyo tines eisin ideai kinêseôs, hê te synechês kai hê diastêmatikê;
+kata men oun tên synechê topon tina diexienai phainetai hê phônê tê
+aisthêsei houtôs hôs an mêdamou histamenê, k.t.l.] And p. 9 [Greek:
+tên oun synechê logikên einai phanen, k.t.l.]]
+
+[Footnote 2: Ibid. p. 18 Meib. [Greek: tou ge logôdous kechôristai
+tautê to mousikon melos; legetai gar dê kai logôdes ti melos, to
+synkeimenon ek tôn prosôdiôn tôn en tois onomasin; physikon gar to
+epiteinein kai anienai en tô dialegesthai.]]
+
+[Footnote 3: Nicomachus, _Enchiridion_, p. 4 [Greek: ei gar tis ê
+dialegomenos ê apologoumenos tini ê anaginôskôn ge ekdêla metaxy
+kath' hekaston phthongon poiei ta megethê, diistanôn kai metaballôn
+tên phônên ap' allou eis allon, ouketi legein ho toioutos oude
+anaginôskein alla meleazein legetai.]]
+
+According to the rhetorician Dionysius of Halicarnassus the interval
+used in the melody of spoken utterance is approximately a Fifth, or
+three tones and a half ([Greek: dialektou men oun melos heni
+metreitai diastêmati tô legomenô dia pente, hôs engista; kai oute
+epiteinetai pera tôn triôn tonôn kai hêmitoniou epi to oxy oute
+anietai tou chôriou toutou pleion epi to bary][1]). He gives an
+interesting example (quoted above on p. 91) from the _Orestes_ of
+Euripides, to show that when words are set to music no account is
+taken of the accents, or spoken melody. Not merely are the intervals
+varied (instead of being nearly uniform), but the rise and fall of
+the notes does not answer to the rise and fall of the syllables in
+ordinary speech. This statement is rendered the more interesting from
+the circumstance that the inscription discovered by Mr. Ramsay
+(_supra_, p. 89), which is about a century later, does exhibit
+precisely this correspondence. Apparently, then, the melody of the
+inscription represents a new idea in music,--an attempt to bring it
+into a more direct connexion with the tones of the speaking voice.
+The fact of such an attempt being made seems to indicate that the
+divergence between the two kinds of utterance was becoming more
+marked than had formerly been the case. It may be compared with the
+invention of recitative in the beginning of the seventeenth century.
+
+Aristides Quintilianus (p. 7 Meib.) recognises a third or
+intermediate movement of the voice, viz. that which is employed in
+the recitation of poetry. It is probable that Aristides is one of the
+latest writers on the subject, and we may conjecture that in his time
+the Greek
+
+[Footnote 1: _De Compositione Verborum_, c. 11, p. 58 Reisk.]
+
+language had in great measure lost the original tonic accents, and
+with them the quasi-melodious character which they gave to prose
+utterance.
+
+In the view which these notices suggest the difference between
+speaking and singing is reduced to one of degree. It is analysed in
+language such as we might use to express the difference between a
+monotonous and a varied manner of speaking, or between the sounds of
+an Aeolian harp and those of a musical instrument.
+
+(3) What has been said of melody in the two spheres of speech and
+song applies also _mutatis mutandis_ to rhythm. In English the time
+or quantity of syllables is as little attended to as the pitch. But
+in Greek the distinction of long and short furnished a prose rhythm
+which was a serious element in their rhetoric. In the rhythm of
+music, according to Dionysius, the quantity of syllables could be
+neglected, just as the accent was neglected in the melody[1]. This,
+however, does not mean that the natural time of the syllables could
+be treated with the freedom which we see in a modern composition. The
+regularity of lyric metres is sufficient to prove that the increase
+or diminution of natural quantity referred to by Dionysius was kept
+within narrow limits, the nature of which is to be gathered from the
+remains of the ancient system of Rhythmic. From these sources we
+learn with something like certainty that the rhythm of ordinary
+speech, as determined by the succession of long or short syllables,
+was the basis not only of metres intended for recitation, such as the
+hexameter and the iambic trimeter, but also of lyrical rhythm of
+every kind.
+
+[Footnote 1: _De Comp._ c. 11, p. 64 [Greek: to de auto ginetai kai
+peri tous rhythmous; hê men gar pezê lexis oudenos oute onomatos oute
+rhêmatos biazetai tous chronous oude metatithêsin, all' oias
+pareilêphe tê physei tas syllabas, tas te makras kai tas bracheias,
+toiautas phylattei; hê de mousikê te kai rhythmikê metaballousin
+autas meiousai kai parauxousai, ôite pollakis eis tanantia
+metachôrein; ou gar tais syllabais apeuthynousi tous chronous, alla
+tois chronois tas syllabas.]]
+
+(4) As to the use of the stress accent in Greek prose we are without
+direct information. In verse it appears as the metrical _ictus_ or
+_arsis_ of each foot, which answers to what English musicians call
+the 'strong beat' or accented part of the bar[1]. In the Homeric
+hexameter the ictus is confined to long syllables, and appears to
+have some power of lengthening a short or doubtful syllable. In the
+Attic poetry which was written in direct imitation of colloquial
+speech, viz. the tragic and comic trimeter, there is no necessary
+connexion between the ictus and syllabic length: but on the other
+hand a naturally long syllable which is without the ictus may be
+rhythmically short. In lyrical versification the ictus does not seem
+to have any connexion with quantity: and on the whole we may gather
+that it was not until the Byzantine period of Greek that it came to
+be recognised as a distinct factor in pronunciation. The chief
+elements of utterance--pitch, time and stress--were independent in
+ancient Greek speech, just as they are in music. And the fact that
+they were independent goes a long way to prove our main contention,
+viz. that ancient Greek speech had a peculiar quasi-musical
+character, consequently that the difficulty which modern scholars
+feel in understanding the ancient statements on such matters as
+accent and quantity is simply the difficulty of conceiving a form of
+utterance of which no examples can now be observed.
+
+[Footnote 1: The metrical accent or ictus was marked in ancient
+notation by points placed over the accented syllable. These points
+have been preserved in Mr. Ramsay's musical inscription (see the
+Appendix, p. 133) and in one or two places of the fragment of the
+_Orestes_ (p. 130). Hence Dr. Crusius has been able to restore the
+rhythm with tolerable certainty, and has made the interesting
+discovery that in both pieces the ictus falls as a rule on a short
+syllable. The only exceptions in the inscription are circumflexed
+syllables, where the long vowel or diphthong is set to two notes, the
+first of which is short and accented. The accents on the short first
+syllables of the dochmiacs of Euripides are a still more unexpected
+evidence of the same rhythmical tendency.]
+
+       *       *       *       *       *
+
+The conception which we have thus been led to form of ancient Greek
+as it was spoken is not without bearing on the main subject of these
+pages. For if the language even in its colloquial form had qualities
+of rhythm and intonation which gave it this peculiar half musical
+character, so that singing and speaking were more closely akin than
+they ever are in our experience, we may expect to find that music was
+influenced in some measure by this state of things. What is there,
+then, in the special characteristics of Greek music which can be
+connected with the exceptional relation in which it stood to
+language?
+
+Greek music was primarily and chiefly vocal. Instrumental music was
+looked upon as essentially subordinate,--an accompaniment or at best
+an imitation of singing. For in the view of the Greeks the words
+([Greek: lexis]) were an integral part of the whole composition. They
+contained the ideas, while the music with its variations of time
+([Greek: rhythmos]) and pitch ([Greek: harmonia]) furnished a natural
+vehicle for the appropriate feelings. Purely instrumental music could
+not do this, because it could not convey the ideas or impressions
+fitted to be the object of feeling. Hence we find Plato complaining
+on this ground of the separation of poetry and music which was
+beginning to be allowed in his time. The poets, he says, rend asunder
+the elements of music; they separate rhythm and dance movements from
+melody, putting unmusical language into metre, and again make melody
+and rhythm without words, employing the lyre and the flute without
+the voice: so that it is most difficult, when rhythm and melody is
+produced without language, to know what it means, or what subject
+worthy of the name it represents ([Greek: kai hotô eoike tôn
+axiologôn mimêmatôn]). It is utterly false taste, in Plato's opinion,
+to use the flute or the lyre otherwise than as an accompaniment to
+dance and song[1]. Similarly in the Aristotelian _Problems_ (xix. 10)
+it is asked why, although the human voice is the most pleasing,
+singing without words, as in humming or whistling, is not more
+agreeable than the flute or the lyre. Shall we say, the writer
+answers, 'that the human voice too is comparatively without charm if
+it does not _represent_ something? ([Greek: ê oud' ekei, ean mê
+mimêtai, homoiôs hêdy?]) That is to say, music is expressive of
+_feeling_, which may range from acute passion to calm and lofty
+sentiment, but feeling must have an object, and this can only be
+adequately given by language. Thus language is, in the first instance
+at least, the matter to which musical treatment gives artistic form.
+In modern times the tendency is to regard instrumental music as the
+highest form of the art, because in instrumental music the artist
+creates his work, not by taking ideas and feelings as he finds them
+already expressed in language, but directly, by forming an
+independent vehicle of feeling,--a new language, as it were, of
+passion and sentiment,--out of the absolute relations of movement and
+sound.
+
+The intimate connexion in Greek music between words and melody may be
+shown in various particulars. The modern practice of basing a musical
+composition--a long and elaborate chorus, for example--upon a few
+words, which are repeated again and again as the music is developed,
+would have been impossible in Greece.
+
+[Footnote 1: Plato, _Legg._ p. 669.]
+
+It becomes natural when the words are not an integral part of the
+work, but only serve to announce the idea on which it is based, and
+which the music brings out under successive aspects. The same may be
+said of the use of a melody with many different sets of words. Greek
+writers regard even the repetition of the melody in a strophe and
+antistrophe as a concession to the comparative weakness of a chorus.
+With the Greeks, moreover, the union in one artist of the functions
+of poet and musician must have tended to a more exquisite adaptation
+of language and music than can be expected when the work of art is
+the product of divided labour. In Greece the principle of the
+interdependence of language, metre, and musical sound was carried
+very far. The different recognised styles had each certain metrical
+forms and certain musical scales or keys appropriated to them, in
+some cases also a certain dialect and vocabulary. These various
+elements were usually summed up in an ethnical type, one of those
+which played so large a part in their political history. Such a term
+as Dorian was not applied to a particular scale at random, but
+because that scale was distinctive of Dorian music: and Dorian music,
+again, was one aspect of Dorian temper and institutions, Dorian
+literature and thought.
+
+Whether the Greeks were acquainted with harmony--in the modern sense
+of the word--is a question that has been much discussed, and may now
+be regarded as settled[1]. It is clear that the Greeks were
+acquainted with the phenomena on which harmony depends, viz. the
+effect produced by sounding certain notes together. It appears also
+that they made some use of harmony,--and of dissonant as well as
+consonant intervals,--in instrumental accompaniment ([Greek:
+krousis]). On the other hand it was unknown in their vocal music,
+except in the form of bass and treble voices singing the same melody.
+In the instrumental accompaniment it was only an occasional ornament,
+not a necessary or regular part of the music. Plato speaks of it in
+the _Laws_ as something which those who learn music as a branch of
+liberal education should not attempt[1]. The silence of the technical
+writers, both as to the use of harmony and as to the tonality of the
+Greek scale, points in the same direction. Evidently there was no
+_system_ of harmony,--no notion of the effect of _successive_
+harmonies, or of two distinct _parts_ or progressions of notes
+harmonising with each other.
+
+[Footnote 1: On this point I may refer to the somewhat fuller
+treatment in Smith's _Dictionary of Antiquities_, art. MUSICA (Vol.
+II, p. 199, ed. 1890-91).]
+
+The want of harmony is to be connected not only with the defective
+tonality which was probably characteristic of Greek music,--we have
+seen (p. 42) that there is some evidence of tonality,--but still more
+with the non-harmonic quality of many of the intervals of which their
+scales were composed. We have repeatedly dwelt upon the variety and
+strangeness (to our apprehension) of these intervals. Modern writers
+are usually disposed to underrate their importance, or even to
+explain them away. The Enharmonic, they point out, was produced by
+the interpolation of a note which may have been only a passing note
+or _appoggiatura_. The Chromatic also, it is said, was regarded as
+too difficult for ordinary performers, and most of its varieties went
+out of use at a comparatively early period. Yet the accounts which we
+find in writers so remote in time and so opposed in their theoretical
+views as Aristoxenus and Ptolemy, bear the strongest testimony to the
+reality and persistence of
+
+[Footnote 1: Plato, _Legg_. p. 812 d [Greek: panta oun ta toiauta mê
+prospherein tois mellousin en trisin etesi to tês mousikês chrêsimon
+eklêpsesthai dia tachous.]]
+
+these non-diatonic scales. And we have the decisive fact that of the
+six scales of the cithara given by Ptolemy (see p. 85) not one is
+diatonic in the modern sense of the word. It may be alleged on the
+other side that the ideal scale in the _Timaeus_ of Plato is purely
+diatonic, and exhibits the strictest Pythagorean division. But that
+scale is primarily a framework of mathematical ratios, and could not
+take notice of intervals which had not yet been identified with
+ratios. It is not certain when the discovery of Pythagoras was
+extended to the non-diatonic scales. Even in the _Sectio Canonis_ of
+Euclid there is no trace of knowledge that any intervals except those
+of the Pythagorean diatonic scale had a numerical or (as we should
+say) physical basis[1].
+
+[Footnote 1: In Euclid's _Sectio Canonis_ the Pythagorean division is
+assumed, and there is no hint of any other ratio than those which
+Pythagoras discovered. Prop. xvii shows how to find the Enharmonic
+Lichanos and Paranêtê by means of the Fourth and Fifth. Prop. xviii
+proves against Aristoxenus (of course without naming him), that a
+[Greek: pyknon] cannot be divided into two equal intervals; but there
+is no attempt to explain the nature of the Enharmonic diesis. It is
+worth notice that in these propositions the Lichanos and Paranêtê of
+the Enharmonic scale are called [Greek: lichanos] and [Greek:
+paranêtê] simply, as though the Enharmonic were the only genus--a
+usage which agrees with that of the Aristotelian _Problems_ (supra,
+p. 33).
+
+According to Ptolemy (i. 13) the Pythagorean philosopher Archytas was
+the author of a new division of the tetrachord for each of the three
+genera. In it the natural Major Third (5: 4) was given for the large
+interval of the Enharmonic, in place of the Pythagorean ditone (81:
+64); and the Diatonic was the same as the Middle Soft Diatonic of
+Ptolemy. But, as Westphal long ago pointed out (_Harmonik und
+Melopöie_, p. 230, ed. 1863), this scheme is probably the work of the
+later Pythagorean school. It seems to be unknown to Plato and
+Aristoxenus,--the latter wrote a life of Archytas--and also to
+Euclid, as we have seen. The next scheme of musical ratios is that of
+Eratosthenes, who makes no use of the natural Major Third.]
+
+In Plato's time, as we can see from a well-known passage of the
+_Republic_ (quoted on p. 53), the Enharmonic and Chromatic scales
+were the object of much zealous study and experiment on the part of
+musicians of different schools,--some seeking to measure and compare
+the intervals directly by the ear, others to find numbers in the
+consonances which they heard, and both, from the Platonic point of
+view, 'setting ears above intelligence,' and therefore labouring in
+vain[1].
+
+The multiplicity of intervals, then, which surprises us in the
+doctrine of the _genera_ and 'colours' was not an accident or
+excrescence. And although some of the finer varieties, such as the
+Enharmonic, belong only to the early or classical period, there is
+enough to show that it continued to be characteristic of the Greek
+musical system, at least until the revival of Hellenism in the age of
+the Antonines. The grounds of this peculiarity may be sought partly
+in the Greek temperament. We can hardly deny the Greeks the credit of
+a fineness of sensibility upon which civilisation, to say the least,
+has made no advance. We may note further how entirely it is in
+accordance with the analogies of Greek art to find a series of
+artistic types created by subtle variations within certain
+well-defined limits. For the present purpose, however, it will be
+enough to consider how the phenomenon is connected with other known
+characteristics of Greek music,--its limited compass and probably
+imperfect tonality, the thin and passionless quality of its chief
+instrument, on the other hand the keen sense of differences of pitch,
+the finely constructed rhythm, and finally the natural adaptation, on
+which we have already dwelt, between the musical form and the
+language. The last is perhaps the feature of greatest significance,
+especially in a comparison of the ancient and modern types of the
+art. The beauty and even the persuasive effect of a voice depend, as
+we are more or less aware, in the first place upon the pitch or key
+in which it is set, and in the second place upon subtle variations of
+pitch, which give emphasis, or light and shade. Answering to the
+first of these elements ancient music, if the main contention of this
+essay is right, has its system of Modes or keys. Answering to the
+second it has a series of scales in which the delicacy and variety of
+the intervals still fill us with wonder. In both these points modern
+music shows diminished resources. We have in the Keys the same or
+even a greater command of degrees of pitch: but we seem to have lost
+the close relation which once obtained between a note as the result
+of physical facts and the same note as an index of temper or emotion.
+A change of key affects us, generally speaking, like a change of
+colour or of movement--not as the heightening or soothing of a state
+of feeling. In respect of the second element of vocal expression, the
+rise and fall of the pitch, Greek music possessed in the multiplicity
+of its scales a range of expression to which there is no modern
+parallel. The nearest analogue may be found in the use of modulation
+from a Major to a Minor key, or the reverse. But the changes of genus
+and 'colour' at the disposal of an ancient musician must have been
+acoustically more striking, and must have come nearer to reproducing,
+in an idealised form, the tones and inflexions of the speaking voice.
+The tendency of music that is based upon harmony is to treat the
+voice as one of a number of instruments, and accordingly to curtail
+the use of it as the great source of dramatic and emotional effect.
+The consequence is twofold. On the one hand we lose sight of the
+direct influence exerted by sound of certain degrees of pitch on the
+human sensibility, and thus ultimately on character. On the other
+hand the music becomes an independent creation. It may still be a
+vehicle of the deepest feeling: but it no longer seeks the aid of
+language, or reaches its aim through the channels by which language
+influences the mind of man.
+
+[Footnote 1: The two schools distinguished by Plato seem to be those
+which were afterwards known as the [Greek: harmonikoi] or
+Aristoxeneans, and the [Greek: mathêmatikoi], who carried on the
+tradition of Pythagoras. The [Greek: harmonikoi] regarded a musical
+interval as a quantity which could be measured directly by the ear,
+without reference to the numerical ratio upon which it might be
+based. They practically adopted the system of equal temperament. The
+[Greek: mathêmatikoi] sought for ratios, but by experiment 'among the
+consonances which are heard,' as Plato says. Hence they failed
+equally with those whose method never rose above the facts of sense.]
+
+       *       *       *       *       *
+
+
+                   APPENDIX
+
+
+TABLE I.
+_Scales of the seven oldest Keys, with the species of the same name._
+[Music: Mixo-lydian. _b_-species.]
+[Music: Lydian. _c_-species.]
+[Music: Phrygian. _d_-species.]
+[Music: Dorian. _e_-species.]
+[Music: Hypo-lydian. _f_-species.]
+[Music: Hypo-phrygian. _g_-species.]
+[Music: Hypo-dorian. _a_-species.]
+
+TABLE II.
+_The fifteen Keys._
+Mesê.
+[Music: Hyper-lydian.]
+[Music: Hyper-aeolian.]
+[Music: Hyper-phrygian.]
+[Music: Hyper-ionian.]
+[Music: Mixo-lydian.]
+[Music: Lydian.]
+[Music: Aeolian.]
+[Music: Phrygian.]
+[Music: Ionian.] Mesê.
+[Music: Dorian.]
+[Music: Hypo-lydian.]
+[Music: Hypo-aeolian.]
+[Music: Hypo-phrygian.]
+[Music: Hypo-ionian.]
+[Music: Hypo-dorian.]
+
+
+The moveable notes ([Greek: phthongoi kinoumenoi]) are distinguished
+by being printed as crotchets.
+
+The two highest of these keys--the Hyper-lydian and the
+Hyper-aeolian--appear to have been added in the time of the Empire.
+The remaining thirteen are attributed to Aristoxenus in the
+pseudo-Euclidean _Introductio_ (p. 19, l. 30), and by Aristides
+Quintilianus (p. 22, l. 30): but there is no mention of them in the
+extant _Harmonics_. It may be gathered, however, from the criticism
+of Heraclides Ponticus (see the passage discussed on pp. 9-12) that
+the list of keys was being considerably enlarged in his time, and
+Aristoxenus, though not named, is doubtless aimed at there. Music of
+the 'Orestes' of Euripides (ll. 338-344).
+
+[Symbols: II P C. P? 40 n] [Greek: katoloPHYROMAIZMATEROS haima sas]
+
+[Symbols: Z (?)..1' "Z E E (?)] [Greek: ho s' anab AKCHEUEIZOMEGAS
+olbos ou]
+
+[Symbols:-ii P C. I' Z] [Greek: monimoSEMBROTOISZANA de laiphos]
+
+[Symbols: C P-A C p-i?. c,] [Greek: hôs tiSAKATOUTHOASTINAxas dai-]
+
+[Symbols:] [Greek: môn KATEKLYSEN deinôn]
+
+[Symbols: Z re. z?] [Greek: ponôN[Symbols:???]ÔÔSPONT ou]
+
+[Symbols: I C: C: Pvl(?) 40(?)] [Greek: olethrIoiSIN en kymasin]
+
+[Music: Restoration proposed by Dr. Crusius.
+
+    [Greek: kat-o-lo-phu-ro-mai ma-te-ros ai-ma sas
+    o s ana-bak-cheu-ei. o me-gas ol-bos ou
+    mon-i-mos en Bro-tois a-na de lai-phos hôs
+    tis a-ka-tou tho-as ti-na-xas dai-môn
+    kat-ek-ly-sen dei-nôn po-nôn hôs pon-tou
+    lab-rois o-leth-ri-oi-sin en ky-ma-sin]
+
+]
+
+The metre is dochmiac, each dochmius consisting of an iambus followed
+by a cretic, [Symbols: u--u-]. The points which seem to mark the
+ictus, or rhythmical accent, are found on the first syllable of each
+of these two feet. If we assume that the first syllable of the iambus
+has the chief accent, the dochmius will be correctly expressed as a
+musical bar of the form--
+
+[Music]
+
+If the first syllable of the cretic is accented, the dochmius is
+divided between two bars, and becomes--
+
+[Music]
+
+The accompaniment or [Greek: krousis], consisting of notes interposed
+between the phrases of the melody, is found by Dr. Wessely and Dr.
+Crusius in the following characters:
+
+1. The character [Symbols:] appears at the end of every dochmius
+shown by the papyrus. After the first, third and fifth it is written
+in the same line with the text. After the seventh it is written above
+that line, between two vocal notes. Dr. Crusius takes it to be the
+instrumental [Symbols: Z], explaining the difference of shape as due
+to the necessity or convenience of distinguishing it from the vocal
+[Symbols: Z]. If that were so the form [Symbols: 1.] would surely
+have been permanent, and would have been given in the schemes of
+Alypius and Aristides Quintilianus. I venture to suggest that it is a
+mark intended to show the end of the dochmius or bar.
+
+2. The group [Symbols: 21 D] occurs twice, before and after the words
+[Greek: deinôn ponôn]. There is a difficulty about the sign [Symbols:
+2], which Dr. Crusius takes to be a _Vortragszeichen_. The other two
+characters may be instrumental notes.
+
+The double [Greek: ô] of [Greek: hôs] (written [Greek: ÔÔS]) is
+interesting because it shows that when more than one note went with a
+syllable, the vowel or diphthong was repeated. This agrees with the
+well-known [Greek: hei-ei-ei-ei-ei-eilissete] of Aristophanes (_Ran._
+1314), and is amply confirmed by the newly discovered hymn to Apollo
+(p. 134). _Musical part of the Seikelos inscription._
+
+[Symbols: C Z Z KIZ I] [Greek: OSONZÊSPHAINOU]
+
+[Symbols: K I Z IK O] [Greek: MÊDENOLÔSSY]
+
+[Symbols: E., C O i; C K Z] [Greek: LYPOUPOSOLI]
+
+[Symbols: I IC I K C OZ] [Greek: GONESTITOZÊN]
+
+[Symbols: C K O i [.Z]] [Greek: TOTELOSOCHRO]
+
+[Symbols: K C [=C] C [.=X]] [Greek: NOSAPAITEI]
+
+The inscription of which these lines form part was discovered by Mr.
+W. M. Ramsay, and was first published by him in the _Bulletin de
+correspondance hellénique_ for 1883, p. 277. It professes to be the
+work of a certain [Greek: Seikelos]. The discovery that the smaller
+letters between the lines are musical notes was made by Dr. Wessely.
+
+The Seikelos inscription, as Dr. O. Crusius has shown (_Philologus_
+for 1893, LII. p. 161), is especially valuable for the light which it
+throws upon ancient rhythm. The quantity of the syllables and the
+place of the _ictus_ is marked in every case, and we are able
+therefore to divide the melody into bars, which may be represented as
+follows:
+
+[Symbols: V?--I v %.)..s 10-I? L, I/4 i v^%., L)? % i:\--%. i v1/4d]
+[Greek: hoson | zês phai-| nou; mêden | holôs sy ly-| pou; pros
+oli-|]
+
+[Symbols: " \s 10 V1/4.0,? V? V V Lo V V V L.? I/4.?] [Greek: gon
+esti to | zên; to telos | ho chronos apai-| tei.] _The hymns recently
+discovered at Delphi._
+
+Since these sheets were in type the materials for the study of
+ancient Greek music have received a notable accession. The French
+archaeologists who are now excavating on the site of Delphi have
+found several important fragments of lyrical poetry, some of them
+with the music noted over the words, as in the examples already
+known. The two largest of these fragments have been shown to belong
+to a single inscription, containing a hymn to Apollo, which dates in
+all probability from the early part of the third century B.C. Of the
+other fragments the most considerable is plausibly referred to the
+first century B.C. These inscriptions have been published in the
+_Bulletin de correspondance hellénique_ (viii-xii. pp. 569-610), with
+two valuable commentaries by M. Henri Weil and M. Théodore Reinach.
+The former scholar deals with the text, the latter chiefly with the
+music.
+
+The music of the hymn to Apollo is written in the vocal notation. The
+metre is the cretic or paeonic ([Symbols:]), and the key, as M.
+Reinach has shown, is the Phrygian--the scale of C minor, with the
+conjunct tetrachord _c--d[Symbol: flat]--d--f_.
+
+In the following transcription I have followed M. Reinach except in a
+few minor points. When two notes are sung to the same syllable the
+vowel or diphthong is repeated, as in the fragment of the Orestes (p.
+132): but I have thought it best to adhere to the modern method.
+
+[Music: A [Symbols: o r 4] [Greek: [Ton kithari]sei kly-ton pai-da
+me-ga-lou [Dios a-]]
+
+[Symbols: oruh.u4r] [Greek: eidete pa]r' a-kro-ni-phê ton-de pa-gon,
+am[broth' hos]]]
+
+[Music: [Symbols: #1? ZS A rty r M Y M] [Greek: pa-si thna-tois
+pro-phai-neis [logia, tr]i-po-da man-]
+
+[Symbols: 1M I O r O 4ruh.0] [Greek: tei-on hôs hei[les, echthros hon
+e-phr]ou-rei dra-kôn;]
+
+[Symbols: 4:I U!or 4 u] [Greek: ho-te te[oisi belesin e-tr]ê-sas
+ai-o-lon he-lik-tan[]
+
+[Symbols: I omio r 4] [Greek:] sy-rig-math' hi-eis a-thô-pe[ut' eba;]
+[Symbols: U ior.t. U]
+
+[Greek: nyn] de Ga-la-tan a-rês..n epe-ras' a-sep-t[os
+
+[Symbols:] [Greek: sal-li-ô](?) [Greek: gen-nan..n thalos phi-lon]
+
+[Symbols:] [Greek: da-moi-o lo....rôn e-phor..]
+
+[Symbols:] [Greek: te-on k.. e-nai k..]]
+
+(about 12 bars wanting.)] [Music: B [Symbols: I M G M Th I M] [Greek:
+Helik]ôna ba-thy-den-dron hai la[chete Dios eri]bro-mou]
+
+[Symbols: I M U M Th Th I M I] [Greek: thy-ga-tres eu-ô-le[noi]
+mo-le[te] syn-o-mai-mon hi-na]
+
+[Symbols: M U M U M W Th G W] [Greek: Phoi-bon ô-dai-si mel-psê-te
+chry-se-o-ko-man;]
+
+[Symbols: Th Ô Ps Ô Th Ô Th I M Th] [Greek: hos a-na di-ko-ry-ni-a
+Par-nas-si-dos tas-de pet-]
+
+[Symbols: I M U M U M I Th I Th G Ô Ps G] [Greek:-ras he-dra-na
+[me]ta kly-tais Del-phi-sin Kas-ta-li-dos]
+
+[Symbols: Ô Ps Ô Th G L M] [Greek: eu-u-drou na-mat' e-pi-ni-se-tai,
+Del-phon a-na]
+
+[Symbols: G M I Th I M Ph G] [Greek: [pr]ô-na man-tei-on e-phe-pôn
+pa-gon. [ithi] klyta]] [Music: [Symbols:] [Greek: me-ga-lo-po-lis
+Ath-this, eu-chai-si phe-ro-ploi-o nai-]
+
+[Symbols:] [Greek:-ou-sa Tri-tô-ni-dos da[ped]on a-thrauston, ha-gi-]
+
+[Symbols:] [Greek:-ois de bô-moi-sin Ha-phais-tos ai-thei ne-ôn]
+
+[Symbols:] [Greek: mê-ra tau-rôn; ho-mou de nin A-raps at-mos es Y-
+
+[Symbols:] [Greek:-lym-pon a-na-kid-na-tai; li-gy de lô-tos bre-môn]
+
+[Symbols:] [Greek: ai-o-lois [me]le-sin ô-dan kre-kei; chry-sea d']
+
+[Symbols:] [Greek: ha-dy-throu[s ki]-tha-ris hym-noi-sin
+a-na-mel-pe-tai;]
+
+[Symbols:] [Greek: ho de [the]-ô-rôn pro-pas es-mos Ath-thi-da
+lach[ôn]]] The notes employed in this piece of music cover about an
+octave and a half, viz. from Parypatê Hypatôn to the Chromatic
+Lichanos Hyperbolaiôn. In two of the tetrachords, viz. Synemmenôn and
+Hyperbolaiôn, the intervals employed are Chromatic (or possibly
+Enharmonic): in the tetrachord Diezeugmenôn they are Diatonic, while
+in the tetrachord Mesôn the Lichanos, which would distinguish the
+genus, is wanting. On the other hand there are two notes which do not
+belong to the Phrygian key as hitherto known, viz. [Symbol: O], a
+semitone below Mesê, and [Symbol: B], a semitone below Nêtê
+Diezeugmenôn. If we assume that we have before us Chromatic of the
+standard kind ([Greek: chrôma toniaion]), the complete scale is--
+
+[Music: [Symbols:]]
+
+If the intervals are Enharmonic, or Chromatic of a different variety,
+the moveable notes (in this case [Symbols: A K] and [Symbols: 4 3E])
+will be somewhat flatter.
+
+M. Reinach is particularly happy in tracing the successive changes of
+genus and key in the course of the poem. The opening passage, as he
+shows, is Diatonic. With the mention of the Gaulish invasion ([Greek:
+Galatan arês]) we come upon the group [Symbols: U 4] (_g--a[Symbol:
+b]--a_) of the Chromatic tetrachord Hyperbolaiôn. At the beginning of
+the second fragment the intervals are again Diatonic, up to the point
+where the poet turns to address the Attic procession ([Greek: ithi,
+klyta megalopolis Aththis, k.t.l.]). From this point the melody lies
+chiefly in the Chromatic tetrachord Synemmenôn [Symbols: M AK r]
+(_c--d[Symbol: o]--d--f_)--a modulation into the key of the
+sub-dominant as well as a change of genus. At the end of the fragment
+the poet returns to the Diatonic and the original key. With regard to
+the _mode_--the question which mainly concerns us at present--M.
+Reinach's exposition is clear and convincing. He appeals to three
+criteria,--(1) the impression which the music makes on a modern ear;
+(2) the endings of the several phrases and divisions; and (3) the
+note which recurs most frequently. All these criteria point to a
+Minor mode. The general impression made by the Diatonic parts of the
+melody is that of the key of _C_ minor: the rhythmical periods end on
+one or other of the notes _c-e[Symbol: flat]-g_, which form the chord
+of that key: and the note _c_ distinctly predominates. This
+conclusion, it need hardly be said, is in entire agreement with the
+main thesis of the preceding pages.
+
+The symbols [Symbol: O] and [Symbol: B], which do not belong to the
+Phrygian scale, are explained by M. Reinach in a way that is in a
+high degree plausible and suggestive. In other keys, he observes, the
+symbol [Symbol: O] stands for the note _b_ (natural). Thus it holds
+the place of 'leading-note' (_note sensible_) to the keynote, _c_. It
+has hitherto been supposed that the standard scale of Greek music,
+the octave _a-a_, differed from the modern Minor in the want of a
+leading note. Here, however, we find evidence that such a note was
+known in practice, if not as a matter of theory, to Greek musicians.
+If this is so, it strongly confirms the view that _c_ was in fact the
+key-note of the Phrygian scale. The symbol [Symbol: B], which occurs
+only once, answers to our _g_[Symbol: flat], and may be similarly
+explained as a leading note to _g_, the dominant of the key. We
+infer, with M. Reinach, that the scale employed in the hymn is not
+only like, but identical with, the scale of our Minor.
+
+The fragment marked C by M. Weil resembles the hymn to Apollo in
+subject, and also in metre, but cannot belong to the same work. The
+melody is written in the Lydian key, with the notation which we have
+hitherto known as the instrumental, but which is now shown to have
+been used, occasionally at least, for vocal music. The fragment is as
+follows:[Music: [Symbols]
+
+[Greek: t' e-pi tê-les-ko-pon tan[de] di-ko-ry-phon klei-tyn hym[in]
+Pi-erides ai ni-pho-bo-lous mel-pe-te de Py-thi-on Phoi-bon on
+e-tik-te L[a-tô]]
+
+M. Reinach connects this fragment with a shorter one, also in the
+Lydian key, but not in paeonic metre, viz.--
+
+[Music: [Symbols]
+
+[Greek:.. thon es-che ma ... thê-ra kat-ek-ta.... syrigm' a-per..]]
+
+M. Reinach thinks that the mode may be the so-called Hypo-lydian (the
+octave _f - f_). The materials are surely too scanty for any
+conclusion as to this.
+
+The fragment D, the only remaining piece which M. Reinach has found
+it worth while to transcribe, is also written in the instrumental
+notation of the Lydian key. The metre is the glyconic. The fragment
+is as follows:--
+
+[Music: [Symbols]
+
+[Greek: ton man-to-sy[na klyton] ô-leth' hy-gra ch ... despoti
+Krê-siôn.. ai nae-tas Delphôn]] [Music: [Symbols]
+
+[Greek: ...in ap-tais-tous Bak-chou [thiasous] ...te prospolois]]
+
+[Symbols] [Greek: tan te do[u]ri[klytôn ar-chan au-xet' a-gê-ra-tô
+thal ...]]
+
+This piece also is referred by M. Reinach to the Hypo-lydian mode. It
+may surely be objected that of three places in which we may fairly
+suppose that we have the end of a metrical division, viz. those which
+end with the words [Greek: Delphôn, prospolois] and [Greek: agêratô],
+two present us with cadences on the Mesê (_d_), and one on the Hypatê
+(_a_). This seems to point strongly to the Minor Mode.
+
+On the whole it would seem that the only _mode_ (in the modern sense
+of the word) of which the new discoveries tell us anything is a mode
+practically identical with the modern Minor. I venture to think this
+a confirmation, as signal as it was unexpected, of the main
+contention of this treatise.
+
+It does not seem to have been observed by M. Weil or M. Reinach that
+in all these pieces of music there is the same remarkable
+correspondence between the melody and the accentuation that has been
+pointed out in the case of the Seikelos inscription (pp. 90, 91). It
+cannot indeed be said that every acute accent coincides with a rise
+of pitch: but the note of an accented syllable is almost always
+followed by a note of lower pitch. Exceptions are, [Greek: aiolon,
+hina] (which may have practically lost its accent, cp. the Modern
+Greek [Greek: na]), and [Greek: molete] (if rightly restored). The
+fall of pitch in the two notes of a circumflexed syllable is
+exemplified in [Greek: manteion, heilen, Galatan, Phoibon, ôdaisi,
+klytais, bômoisin, homou]: the opposite case occurs only once, in
+[Greek: thnatois]. The observation holds not only of the chief hymn,
+but of all the fragments.
+
+INDEX OF PASSAGES DISCUSSED OR REFERRED TO.
+
+      AUTHOR                             PAGE
+
+_Anonymi Scriptio de Musica_, § 28 (the modes employed on different
+instruments), 27
+  §§ 63-64 ([Greek: topoi tês phônês]), 64
+
+Aristides Quintilianus (ed. Meib.):
+  p. 10 (Lichanos), 31
+  p. 13 (ethos of music), 63, 66
+  p. 15 ([Greek: kata dieseis harmonia]), 53, 98
+  p. 21 (Modes in Plato's _Republic_), 94-100
+  p. 28 ([Greek: topoi tês phônês]), 63
+
+Aristophanes, _Eq._ 985-996 (Dorian Mode), 7, 42
+
+Aristotle:
+  _Metaphysics_, iv. 11, p. 1018 _b_ 26 ([Greek: archê]), 46
+  Politics, iv. 3, p. 1290 a 20 (Dorian and Phrygian), 105
+    viii. 5-7, pp. 1340-1342 (ethos of music), 9, 12, 13, 107
+    viii. 7, p. 1342 _a_ 32 (Phrygian Mode), 12, 13, 107
+  Problems, xix. 20, p. 919 a 13 (Mesê), 43, 82, 102, 107
+      26, p. 919 _b_ 21 ([Greek: harmonia]=System), 55
+      33, p. 920 _a_ 19 (Hypatê), 44
+      36, p. 920 _b_ 7 (Mesê), 44
+      47, p. 922 _b_ 3 (heptachord scales), 33
+      48, p. 922 _b_ 10 (modes used by chorus), 14
+      49, p. 922 _b_ 31 (high and low pitch), 15
+
+  _Rhetoric_, iii. 1, p. 1403 b 27 ([Greek: tonos] and
+[Greek: harmonia]), 15
+Aristoxenus (ed. Meib.):
+  _Harm._ p. 2, l. 15 (diagrams of [Greek: harmoniai]), 49
+    p. 3 (melody of speech),  115
+    p. 6 (nomenclature by [Greek: thesis] or position), 81
+    p. 6, l. 20 (species of the Octave), 50
+    p. 8 (speaking and singing), 115
+    p. 8, l. 12 (perfect System), 36
+    p. 18 (melody of speech),  90, 115
+    p. 23 (Chromatic and Enharmonic), 110
+    p. 26, l. 14 (Lichanos indefinite), 110
+    p. 27, l. 34 (diagrams), 52
+    p. 36, l. 29 (seven [Greek: harmoniai]), 51, 54
+    p. 37 ([Greek: tonoi] or keys), 17-19
+    p. 48, l. 13 (Lichanos indefinite), 110
+    p. 69, l. 6 (nomenclature by position), 81
+    _ibid._ (indefinite element in music), 111
+
+
+Bacchius (ed. Meib.), p. 11 (topoi tês phônês), 65
+  p. 19 (theseis tetrachordôn), 82
+
+
+Dionysius Hal.:
+  c. 11, p. 58 Reisk. (accent and melody), 90, 115
+  c. 11, p. 64 Reisk. (rhythm and quantity), 115
+
+
+Euclid (ed. Meib.):
+  _Introductio_, p. 19 (ten-stringed lyre), 38
+    p. 20 (modulation), 104
+  _Sectio Canonis_, Prop. xvii, xviii, 123
+
+Euripides, _Orest._ 338-343 (musical setting), 92, 130
+
+
+Heraclides Ponticus ap. Athen. xiv. pp. 624-626 (modes), 9-11, 76
+
+
+Lasus ap. Athen. xiv. p. 624 _e_ ([Greek: Aiolis harmonia]), 6
+
+
+Nicomachus (ed. Meib), p. 4 (speaking and singing), 115
+  p. 7 (heptachord scales), 34
+
+
+Pausanias, iv. 27, 4 (Sacadas and Pronomus), 75
+
+Pherecrates ap. Plut. _de Mus._ c. 30, 38
+
+Pindar, _Nem._ iv. 45 (Lydian), 7
+
+Plato:
+  _Phileb._ p. 17 ([Greek: harmonia] = System), 55
+  _Laches_, p. 188 (Dorian, Ionian, Phrygian, Lydian), 8
+  _Repub._ p. 398 (use of modes in education), 7, 8
+    p. 399 ([Greek: aulos--poluchordia])., 39, 41
+    p. 531 A (study of music), 53, 123
+  _Laws_, p. 669 (instrumental music), 120
+    p. 812 D (harmony), 122
+Plutarch:
+  _De Musica_, c. 6 ([Greek: harmoniai]), 25
+    cc. 15-17 (Platonic modes), 21-25, 103
+    c. 19 ([Greek: tonos, harmonia]), 26
+
+    _De gener. Mundi_, p. 1029 _c_ (Proslambanomenos), 39
+
+Pollux, _Onom._ iv. 78 ([Greek: harmoniai aulêtikai]), 22, 28
+
+Pratinas ap. Athen. xiv. p. 624 _f_ ([Greek: mête syntonon k.t.l.]), 5
+
+Ptolemy:
+  Harm. i. 13 (musical ratios of Archytas), 123
+    i. 16 ([Greek: hêgemôn]=highest note), 45
+    _ibid._ (scales of the cithara), 84-86, 102, 123
+    _ibid._ (Pythagorean division), 87
+    ii. 6 (modulation), 67
+    ii. 7 (pitch of scales), 80
+    ii. 16 (scales of the cithara), 84-86, 102
+
+
+Seikelos inscription, 89, 132
+
+
+Telestes ap. Athen. xiv. p. 625 _f_ (Phrygian and Lydian), 6
+
+Theon Smyrnaeus, c. 8 (enlargement of scale), 37
+
+
+
+THE END
+
+
+_Note on the Seikilos Inscription_ (pp. 89-91, 133).
+
+
+Since the publication of this work, the Seikilos inscription has been
+examined afresh by Mr. J. A. R. Munro (of Lincoln College, Oxford).
+The result of his examination is to show that the last note of the
+melody has been misread. From a squeeze which he has kindly placed at
+my disposal it appears that the word [Greek: apaitei] is written--
+
+[Symbols: c x] [Greek: APAITEI]
+
+The line drawn under the three notes [Symbols: C X I] has caused the
+last to be read as [Symbol: 3], which has no meaning here. In fact it
+is a reversed Gamma ([Greek: g apestrammenon]), and answers to our
+_e_ natural.
+
+Hence the last line of the transcription on pp. 89-90 should be as
+follows:
+
+[Music: [Greek: to te-los ho chro-nos a-pai--tei]]
+
+The importance of this correction is obvious. The scale employed is
+now seen to be the octave--
+
+
+          _e f# g a b c# d e_
+
+
+If, as I ventured to suggest on p. 90, the mode is the Hypo-phrygian
+(the scale of our Major mode, but with a flat Seventh), the key-note
+will be _a_. The close on the Dominant _e_ will then have to be noted
+as a fact supporting the belief that in Greek music the close on the
+Dominant or Hypatê was the usual one (see p. 45).
+
+The line drawn under the three symbols [Symbols: C N1] is found in
+several other cases where the melody gives more than one note for a
+syllable. So [Symbols: 1K] (l. 2), and [Symbols: 04)] (l. 3),
+[Symbols: K1] and [Symbols: 04)] (l. 4). It does not appear however
+under [Symbols: K I Z] (l. 1).
+
+
+                                                  D. B. M.
+
+
+
+
+
+
+End of the Project Gutenberg EBook of The Modes of Ancient Greek Music, by 
+David Binning Monro
+
+*** END OF THE PROJECT GUTENBERG EBOOK 40288 ***