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diff --git a/40288.txt b/40288.txt deleted file mode 100644 index cdb87fb..0000000 --- a/40288.txt +++ /dev/null @@ -1,5568 +0,0 @@ -Project Gutenberg's The Modes of Ancient Greek Music, by David Binning Monro - -This eBook is for the use of anyone anywhere at no cost and with -almost no restrictions whatsoever. You may copy it, give it away or -re-use it under the terms of the Project Gutenberg License included -with this eBook or online at www.gutenberg.org - - -Title: The Modes of Ancient Greek Music - -Author: David Binning Monro - -Release Date: July 20, 2012 [EBook #40288] - -Language: English - -Character set encoding: ASCII - -*** START OF THIS PROJECT GUTENBERG EBOOK THE MODES OF ANCIENT GREEK MUSIC *** - - - - -Produced by Linda Cantoni, Paul Marshall, Bryan Ness and -the Online Distributed Proofreading Team at -http://www.pgdp.net (This book was produced from scanned -images of public domain material from the Google Print -project.) - - - - - - - - - - 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: xeinosynes 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 -hellenique_ 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 - - Sec. 1. _Introductory._ PAGE -Musical forms called [Greek: harmoniai] or [Greek: tropoi] 1 - - - Sec. 2. _Statement of the question._ -The terms Dorian, Phrygian, Lydian, &c. 3 - - - Sec. 3. _The Authorities._ -Aristoxenus--Plato--Aristotle--Heraclides Ponticus--the - Aristotelian _Problems_ 4 - - - Sec. 4. _The Early Poets._ -Pratinas--Telestes--Aristophanes 5 - - - Sec. 5. _Plato._ -The [Greek: harmoniai] in the _Republic_--The _Laches_ 7 - - - Sec. 6. _Heraclides Ponticus._ -The three Hellenic [Greek: harmoniai]--the Phrygian and Lydian--the - Hypo-dorian, &c. 9 - - - Sec. 7. _Aristotle--The Politics._ -The [Greek: harmoniai] in the _Politics_ 12 - - - Sec. 8. _The Aristotelian Problems._ -Hypo-dorian and Hypo-phrygian 14 - - - Sec. 9. _The Rhetoric._ -The [Greek: harmonia] of oratory 15 - - - Sec. 10. _Aristoxenus._ -The [Greek: topoi] or keys 16 - - Sec. 11. _Names of keys._ -The prefix Hypo- --the term [Greek: tonos] 19 - - - Sec. 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 - - - Sec. 13. _Modes employed on different instruments._ -Modes on wind-instruments--on the water-organ--on the - cithara--on the flute 27 - - - Sec. 14. _Recapitulation._ -Equivalence of [Greek: harmonia] and [Greek: tonos] 28 - - - Sec. 15._ The Systems of Greek music._ -The musical System ([Greek: systema emmeles]) 30 - - - Sec. 16. _The standard Octachord System._ -The scale in Aristotle and Aristoxenus 31 - - - Sec. 17. _Earlier Heptachord Scales._ -Seven-stringed scales in the _Problems_--Nicomachus 33 - - - Sec. 18. _The Perfect System._ -The Greater and Lesser Perfect Systems--Aristoxenus--enlargement - of the scale--Timotheus--Pronomus--the - Proslambanomenos--the Hyperhypate 35 - - - Sec. 19. _Relation of System and Key._ -The standard System and the 'modes'--the multiplicity of - [Greek: harmoniai] 40 - - - Sec. 20. _Tonality of the Greek musical scale._ -The Mese as a key-note--the close on the Hypate--[Greek: arche] in - the _Metaphysics_ 42 - - - Sec. 21. _The Species of a Scale._ -The seven Species ([Greek: schemata, eide]) of the Octave--connexion - with the Modes 47 - - Sec. 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 - - - Sec. 23. _The Seven Species._ -Aristoxenus--the _Introductio Harmonica_ 56 - - - Sec. 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 - - - Sec. 25. _The Ethos of Music._ -Regions of the voice--branches of lyrical poetry--kinds of - ethos 62 - - - Sec. 26. _The Ethos of the Genera and Species._ -Ethos depending on pitch--on the genus 66 - - - Sec. 27. _The Musical Notation._ -The instrumental notes--original form and date 67 - - - Sec. 28. _Traces of the Species in the Notation._ -Westphal's theory 75 - - - Sec. 29. _Ptolemy's Scheme of Modes._ -Reduction of the Modes to seven--nomenclature according - to _value_ and according to _position_ 78 - - - Sec. 30. _Nomenclature by Position._ -The term [Greek: thesis] in Aristoxenus--in the Aristotelian - _Problems_ 81 - - - Sec. 31. _Scales of the Lyre and Cithara._ -The scales on the lyre--on the cithara (viz. [Greek: tritai, tropoi, - parypatai, lydia, hypertropa, iastiaioliaia]) 83 - - - Sec. 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 - - - Sec. 33. _Modes of Aristides Quintilianus._ -The six Modes of Plato's _Republic_ 94 - - Sec. 34. _Credibility of Aristides Quintilianus._ -Date of Aristides--genuineness of his scales 95 - - - Sec. 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 - - - Sec. 36. _Conclusion._ -Early importance of genus and key only--change in - Ptolemy's time in the direction of the mediaeval Tones 108 - - - Sec. 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. - - - - -Sec. 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 mimemata ouk echo -legein]), and leaves the matter for future inquiry[1]. - -[Footnote 1: Plato, _Rep._ p. 400 _b_ [Greek: alla tauta men, en d' -ego, kai meta Damonos bouleusometha, tines te aneleutherias kai -hybreos e manias kai alles kakias prepousai baseis, kai tinas tois -enantiois leipteon rhythmous.]] - -Sec. 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 -Theorie de la Musique de l'Antiquite_ 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. - - - - -Sec. 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: harmonike]) 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. - - - - -Sec. 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: mete syntonon dioke mete tan aneimenan - Iasti mousan, alla tan messan neon - arouran aiolize to 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: aneimene]), 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 melpo Koran te Klymenoio alochon Meliboian, - hymnon anagon 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: protoi para krateras Hellenon en aulois - synopadoi Pelopos matros oreias phrygion aeison nomon; - toi d' oxyphonois pektidon 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: oxyphonos] 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 pephilemenon.] - -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' ego ge thaumazo tes hyomousias - autou phasi gar auton hoi paides hoi xynephoiton - ten Doristi monen enarmottesthai thama ten lyran, - allen d' ouk ethelein labein; kata ton kitharisten - orgisthent' apagein keleuein, hos harmonian ho pais - outos ou dynatai mathein en me Dorodokesti.] - - - - -Sec. 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: threnodeis])?' '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: atechnos Doristi, all' ouk Iasti, oiomai de oude Phrygisti -oude Lydisti, all' he per mone Hellenike 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: mete syntonon dioke mete 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_). - - - - -Sec. 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 -phesi dein kaleisthai ten Phrygion, kathaper oude ten 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: Dorion men auten ou nomizein, prosemphere de pos -ekeine]). 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 -schematos 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: te -ton phthongon exyteti kai baryteti]); 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 he 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). - - - - -Sec. 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: semeia]), acting -through association, but are an actual _copy_ or reflex of the forms -of moral temper ([Greek: en de tois melesin autois esti mimemata ton -ethon]); 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 odyrtikoteros kai -synestekotos mallon]); by others, such as those which are called the -'relaxed' ([Greek: aneimenai]), we are disposed to 'softness' of mind -([Greek: malakoteros ten dianoian]). The Dorian, again, is the only -one under whose influence men are in a middle and settled mood -([Greek: mesos kai kathestekotos 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: stasimotate]), 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 apeirekosi dia chronon ou -rhadion adein tas syntonous harmonias, alla tas aneimenas he physis -hypoballei tois telikoutois]). 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 ethika, 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: ton harmonion -parekbaseis kai ton melon ta syntona kai parakechrosmena]). - -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 syntonoteras kai -despotikonteras, tas d' aneimenas kai malakas demotikas]). This is -obviously the Platonic doctrine of two right keys, holding the mean -between high and low. - - - - -Sec. 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: ethos 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 eremaios estin, ho de oxys kinetikos, k.t.l.]: -'since a deep note is soft and calm, and a high note is exciting, -&c.' - - - - -Sec. 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 pos tois tonois, oion -oxeia kai bareia kai mese], sc. [Greek: phone]); 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 hon 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. - - - - -Sec. 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: -systemata]). By a [Greek: systema] 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' on tithemena ta systemata melodeitai]). -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 archon]. 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 Melopoeie 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 -lepteon]), 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 ten ton aulon trupesin 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: houto gar hoi men ton -harmonikon legousi barytaton men ton Hypodorion ton tonon, hemitonio -de oxyteron toutou ton Mixolydion, toutou de hemitonio ton Dorion, -tou de Doriou tono ton Phrygion: hosautos de kai tou Phrygiou ton -Lydion hetero tono.] Westphal (_Harmonik und Melopoeie_ p. 165) would -transfer the words [Greek: hemitonio ... Mixolydion] to the end of -the sentence, and insert [Greek: oxyteron] before [Greek: ton -Dorion]. 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 ten ton aulon trypesin blepontes] -and the complaint [Greek: ti d' esti pros ho blepontes ... ouden -eirekasin]. But if [Greek: pros ten ... 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: metabole]) 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. - - - - -Sec. 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 _diesis_ 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). - - - - -Sec. 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: eide tou dia] [Greek: pason]). 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 musica_ 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: epikedeion aulesai -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 tes harmonias -hypomnemata]) 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 Paramese -to Hypate Hypaton ([Greek: toiouton autes apergasasthai to schema -hoion to apo parameses epi hypaten hypaton]). Moreover, it is said -that the relaxed Lydian ([Greek: epaneimenen Lydisti]), which is the -opposite of the Mixo-lydian, being similar to the Ionian ([Greek: -paraplesian ousan te Iadi]), was invented by Damon the Athenian.' - -'These modes then, the one plaintive, the other relaxed ([Greek: -eklelymene]), 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: epaneimene 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 auletike -Doristi, Phrygisti, Lydios kai Ionike, kai syntonos Lydisti en -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 -te Doristi]). 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: he men -to megaloprepes kai axiomatikon apodidosin, he de to pathetikon, -memiktai de dia touton tragodia]). 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 ten ton aulon trypesin -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 (Hypate Hypaton to -Paramese). In Aristoxenus, as we shall see (p. 31), the primitive -octave (from Hypate to Nete) 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 Synemmenon 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: ten 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 trimeres]) on account of the change of key.' In -Westphal's _Harmonik und Melopoeie_ (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 -pason]. - -(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 Hypaton was not used in Dorian music -([Greek: en tois Doriois]), 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 -de ten tou ethous phylaken apheroun tou Doriou tonou, timontes 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 te Doristi, tauten -proutimesen]). On the other hand the usual sense of [Greek: tonos] is -supported by the consideration that the want of the tetrachord -Hypaton 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. - - - - -Sec. 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 te ton tropon, 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, -Dorion; hoi de tous hepta tinas; Mixolydion, Lydion, Phrygion, -Dorion, Hypolydion, Hypophrygion, Hypodorion, touton poios estin -oxyteros? ho Mixolydios, k.t.l.] And Gaudentius (p. 21, l. 2) [Greek: -kath' hekaston tropon he 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 auletike Doristi, -Phrygisti, Lydios kai Ionike, kai syntonos Lydisti hen 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]. - - - - -Sec. 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: doristi], [Greek: -phrygisti], &c., or the neuter [Greek: ta doria], [Greek: ta -phrygia], &c., where there is nothing to show whether 'mode' or -'key,' [Greek: harmonia] or [Greek: tonos], is intended. - - - - -Sec. 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: systema]. - -A System ([Greek: systema]) is defined by the Greek technical writers -as a group or complex of intervals ([Greek: to ek pleionon e henos -diastematon 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: -systema 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: chorde]) 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]. - - - - -Sec. 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: - - - Nete ([Greek: neate] or [Greek: nete], lit. 'lowest,' our 'highest'). - Paranete ([Greek: paranete], 'next to Nete'). - Trite ([Greek: trite], _i.e._ 'third' string). - Paramese ([Greek: paramese] or [Greek: paramesos], 'next to Mese'). - Mese ([Greek: mese], 'middle string'). - Lichanos ([Greek: lichanos], _i.e._ 'forefinger' string). - Parhypate ([Greek: parypate]). - Hypate ([Greek: hypate], lit. 'uppermost,' our 'lowest'). - - -It will be seen that the conventional sense of high and low in the -words [Greek: hypate] and [Greek: neate] 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 Hypate to Mese, the higher -of those from Paramese to Nete: the interval between Mese and -Paramese 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--Hypate, -Mese, Paramese, Nete--are the same for every genus, and accordingly -are called the 'standing' or 'immoveable' notes ([Greek: phthongoi -hestotes, akinetoi]), 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 to genei lichanoi prosegoreuthesan, homonymos to -plettonti daktylo ten echousan autas chorden onomastheisai]. But -Trite 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._ Parhypate is a -semitone above Hypate, and Lichanos a tone above Parhypate. In the -Enharmonic genus the intervals are two successive quarter-tones -([Greek: diesis]) followed by a ditone or major Third: consequently -Parhypate is only a quarter of a tone above Hypate, and Lichanos -again a quarter of a tone above Parhypate. 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 =Nete= \ e =Nete= \ - d Paranete } ( c Paranete } - c Trite } +---( b* Trite } - b =Paramese= / | ( b =Paramese= / - a =Mese= \ | a =Mese= \ - g Lichanos } | ( f Lichanos } - f Parhypate } | +-( e* Parhypate } - e =Hypate= / | | ( e =Hypate= / - | | - [Greek: pyknon] [Greek: pyknon] - - -In the Chromatic genus and its varieties the division is of an -intermediate kind. The interval between Lichanos and Mese 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 Parhypate is difficult to sing, while Hypate -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 Paramese was left out, and -consequently the Mese became the lowest note of the upper [Greek: -pyknon], _i.e._ the group of 'close' notes consisting of Mese, Trite, -and Paranete. 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 Parhypate is -only a diesis, for it is never nearer Hypate than a diesis or further -off than a semitone. - - - - -Sec. 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 ten hypaten all' ou ten neten - katelipon: he ou ten] [Greek: hypaten] (leg. [Greek: neten]), - [Greek: alla ten nyn paramesen kaloumenen apheroun kai to - toniaion diastema; echronto de te eschate mese tou epi to oxy - pyknou; did kai mesen auten proseloreusan [he] oti en tou men - ano tetrachordon teleute, tou de kato arche, kai meson eiche - logon tono ton akron?] - - 'Why did the ancient seven-stringed scales include Hypate but - not Nete? Or should we say that the note omitted was not Nete, - but the present Paramese and the interval of a tone (_i.e._ - the disjunctive tone)? The Mese, then, was the lowest note of - the upper [Greek: pyknon]: whence the name [Greek: mese], - 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 pason], not [Greek: di' -okto],--as the Fourth is [Greek: dia tessaron], the Fifth [Greek: dia -pente]. The answer suggested is that there were anciently seven -strings, and that Terpander left out the Trite and added the Nete. -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 okto] was inappropriate. - -Among later writers who confirm this account we may notice -Nicomachus, p. 7 Meib. [Greek: mese dia tessaron pros amphotera en te -heptachordo kata to palaion diestosa]: and p. 20 [Greek: te toinyn -archaiotropo lyra toutesti te heptachordo, kata synaphen ek duo -tetrachordon synestose 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 Mese. 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. - - - - -Sec. 18. _The Perfect System._ - -The term 'Perfect System' ([Greek: systema 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: systema 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 Hypate we have a new tetrachord Hypaton ([Greek: -tetrachordon hypaton]), the notes of which are accordingly called -Hypate Hypaton, Parhypate Hypaton, and Lichanos Hypaton: and -similarly above Nete we have a tetrachord Hyperbolaion. Finally the -octave downwards from Mese is completed by the addition of a note -appropriately called Proslambanomenos. - -The Lesser Perfect System ([Greek: systema teleion elasson]) is -apparently based upon the ancient heptachord which consisted of two -'conjunct' tetrachords meeting in the Mese. 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: systema teleion ametabolon]), which may be -represented in modern notation[1] as follows: - - - a Nete Hyperbolaion \ Tetrachord - g Paranete Hyperbolaion } Hyperbolaion - f Trite Hyperbolaion / - e Nete Diezeugmenon - d Paranete Diezeugmenon \ Tetrachord - c Trite Diezeugmenon } Diezeugmenon - b Paramese / - d Nete Synemmenon \ Tetrachord - c Paranete Synemmenon } Synemmenon - b flat Trite Synemmenon/ - a Mese \ - g Lichanos Meson } Tetrachord - f Parhypate Meson } Meson - e Hypate Meson / - d Lichanos Hypaton \ Tetrachord - c Parhypate Hypaton } Hypaton - b Hypate Hypaton / - 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 ton allon 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: synemmenon de eklethe to holon systema hoti to -prokeimeno teleio to mechri meses syneptai], 'the whole scale was -called conjunct because it is conjoined to the complete scale that -reaches up to Mese' (_i.e._ the octave extending from -Proslambanomenos to Mese). So p. 16 [Greek: kai ha men auton esti -teleia, ha d' ou, atele 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: kitharodoi]). 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: -epeuxemenes de tes mousikes kai polychordon kai polyphthongon -gegonoton organon to proslephthenai kai epi to bary kai epi to oxy -tois pro[:y]parchousin okto phthongois allous pleionas, homos 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: Ion]) -[Greek: en dekachordo lyra] (_i.e._ in a poem on the subject of the -ten-stringed lyre):-- - - [Greek: ten dekabamona taxin echousa - tas symphonousas harmonias triodous; - prin men s' heptatonon psallon dia tessara pantes - Hellenes, 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: cheiron] 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 e auletas paradexei eis ten polin? e 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 tes en Timaio psychogonias]) speaks of the -Proslambanomenos as having been added in comparatively recent times -(p. 1029 _c_ [Greek: hoi de neoteroi ton proslambanomenon tono -diapheronta tes hypates epi to bary taxantes to men holon diastema -dis dia pason epoiesan]). The rest of the Perfect System he ascribes -to 'the ancients' ([Greek: tous palaious ismen hypatas men dyo, treis -de netas, mian de mesen kai mian paramesen tithemenous]). An earlier -addition--perhaps the first made to the primitive octave--was a note -called Hyperhypate, which was a tone below the old Hypate, in the -place afterwards occupied on the Diatonic scale by Lichanos Hypaton. -It naturally disappeared when the tetrachord Hypaton came into use. -It is only mentioned by one author, Thrasyllus (quoted by Theon -Smyrnaeus, cc. 35-36[1]). - -[Footnote 1: The term [Greek: hyperypate] had all but disappeared -from the text of Theon Smyrnaeus in the edition of Bullialdus (Paris, -1644), having been corrupted into [Greek: hypate] or [Greek: -parypate] 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 Hypate, and in -Boethius (_Mus._ i. 20). - -It may be worth noticing also that Thrasyllus uses the words [Greek: -diezeugmene] and [Greek: hyperbolaia] in the sense of [Greek: nete -diezeugmenon] and [Greek: nete hyperbolaion] (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: eisagoge -harmonike]) 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 katatome]) 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).] - - - - -Sec. 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' hon tithemena ta systemata melodeitai]). If then we -speak of Hypate or Mese (just as when we speak of a moveable Do), we -mean as many different notes as there are keys: but the Dorian Hypate -or the Lydian Mese 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: systema] which (as we have seen) was based upon the -lyre and its primitive gamut? - -[Footnote 1: Plato, Rep. p. 399: [Greek: ouk ara, en d' ego, -polychordias ge oude panarmoniou hemin deesei en tais odais te kai -melesin. Ou moi, ephe, phainetai. Trigonon ara kai pektidon kai -panton organon hosa polychorda kai polyarmonia demiourgous ou -threpsomen. Ou phainometha. Ti de? aulopoious e auletas paradexei eis -ten polin? e ou touto polychordotaton, kai auta ta panarmonia aulou -tynchanei onta mimema? Dela de, e d' hos. Lyra de soi, en d' ego, kai -kithara leipetai, kai kata polin chresima; kai au kat' agrous tois -nomeusi syrinx an tis eie.] - -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 Hypate to Nete: 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.] - - - - -Sec. 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 ten mesen - kinese hemon, harmosas tas allas chordas, kai chretai to - organo, ou monon hotan kata ton tes meses genetai phthongon - lypei kai phainetai anarmoston, alla kai kata ten allen - melodian, ean de ten lichanon e tina allon phthongon, tote - phainetai diapherein monon hotan kakeine tis chretai? e - eulogos touto symbainei? panta gar ta chresta mele pollakis te - mese chretai, kai pantes hoi agathoi poietai pykna pros ten - mesen apantosi, kan apelthosi tachy epanerchontai, pros de - allen houtos oudemian. kathaper ek ton logon enion - exairethenton syndesmon ouk estin ho logos Hellenikos, hoion - to te kai to kai, enioi de outhen lypousi, dia to tois men - anankaion einai chresthai pollakis, ei estai logos, tois de - me, houto kai ton phthongon he mese hosper syndesmos esti, kai - malista ton kalon, dia to pleistakis enyparchein ton phthongon - autes.] - - 'Why is it that if the Mese is altered, after the other - strings have been tuned, the instrument is felt to be out of - tune, not only when the Mese 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 Mese, 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 Mese 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 Mese, which -determines them with reference to it ([Greek: he taxis he hekastes -ede di' ekeinen]): so that the loss of the Mese means the loss of the -ground and unifying element of the scale ([Greek: arthentos tou -aitiou tou hermosthai kai tou synechontos])[1]. - -These passages imply that in the scale known to Aristotle, viz. the -octave _e - e_, the Mese _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 Mese united the two conjunct -tetrachords. It was quite in accordance with this state of things -that the later enlargement completed the octaves from Mese 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 Mese 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 Mese is spoken of as -characteristic of _good_ melody ([Greek: panta ta chresta mele -pollakis te mese chretai]), 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 Hypate. The words are these -(_Probl._ xix. 33): - - - [Greek: Dia ti euarmostoteron apo tou oxeos epi to bary e apo - tou] - - -[Footnote 1: So in the Euclidean _Sectio Canonis_ the propositions -which deal with the 'movable' notes, viz. Paranete and Lichanos -(Theor. xvii) and Parhypate and Trite (Theor. xviii), begin by -postulating the Mese ([Greek: esto gar mese ho B k.t.l.]).] - - - [Greek: bareos epi to oxy; poteron hoti to apo tes arches - ginetai archesthai? he gar mese kai hegemon oxytate tou - tetrachordou; to de ouk ap' arches all' apo teleutes.] - - 'Why is a descending scale more musical than an ascending one? - Is it that in this order we begin with the beginning,--since - the Mese 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 -Hypate, or even that it began with the Mese. In what sense, then, was -the Mese a 'beginning' ([Greek: arche]), and the Hypate an 'end'? In -Aristotelian language the word [Greek: arche] has various senses. It -might be used to express the relation of the Mese 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 Mese is -the beginning ([Greek: arche]) of one of the two tetrachords which -form the ordinary octave scale (viz. the tetrachord Meson); and again -in _Probl._ xix. 47 that in the old heptachord which consisted of two -conjunct tetrachords (_e-a-d_) the Mese (_a_) was the end of the -upper tetrachord and the beginning of the lower one ([Greek: hoti en -tou men ano tetrachordou teleute, tou de kato arche]). 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: hegemon] or 'leading note' of the -tetrachord Meson, here applied to the Mese, is found in the same -sense in Plutarch, _De Mus._ c. 11, where [Greek: ho peri ton -hegemona keimenos tonos] means the disjunctive tone. Similarly -Ptolemy (_Harm._ i. 16) speaks of the tones in a diatonic scale as -being [Greek: en tois hegoumenois 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 hegoumenos tou enarmoniou -genous]).] - -Another instance of the use of [Greek: arche] 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 - horismenon diesteke kata ton logon, hoion parastates - tritostatou proteron, kai paranete netes; entha men gar ho - koryphaios, entha de he mese arche.] - - '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 Paranete to the Nete: for in the one case the coryphaeus - is the starting-point, in the other the Mese.' - - -Here the Mese is again the [Greek: arche] or beginning, but the order -is the ascending one, and consequently the Nete is the end. The -passage confirms what we have learned of the relative importance of -the Mese: but it certainly negatives any inference regarding the note -on which the melody ended. - -It appears, then, that the Mese 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 -Mese was shown--whether, for example, the melody ended on the Mese. -The supposed evidence for an ending on the Hypate has been shown to -be insufficient. But we may at least hold that as far as the Mese 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 Mese of _Probl._ xix. 20 was the note which we have -understood by the term--the Mese of the standard System. This, as we -shall presently see, is the plea to which Westphal has recourse. - - - - -Sec. 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: -schemata, eide]) of the interval which measured the compass of the -scale in question. Thus, the interval of the Octave ([Greek: dia -pason]) 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: -systemata emmele]), 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. - - - - -Sec. 22. _The Scales as treated by Aristoxenus._ - -The subject of the musical scales ([Greek: systemata]) 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 Hypate to Nete), 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 ton enarmonion] ([Greek: harmonion] MSS.) - [Greek: ekkeitai monon systematon, diatonon d' e chromatikon - oudeis popoth' heoraken; kaitoi ta diagrammata g' auton edelou - ten pasan tes melodias taxin, en hois peri systematon - oktachordon enarmonion] ([Greek: harmonion] MSS.) [Greek: - monon elegon, peri de ton allon genon te kai schematon en auto - te to genei tonto 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 hexes]), 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: ton d' allon katholou men - kathaper emprosthen eipomen oudeis heptai, henos de systematos - Eratokles epecheirese kath' hen genos exarithmesai ta schemata - tou dia pason apodeiktikos te periphora ton diastematon - deiknys; ou katamathon hoti, me prosapodeichthenton] (qu. - [Greek: proapod.]) [Greek: ton de tou dia pente schematon kai - ton tou dia tessaron pros de toutois kai tes syntheseos auton - tis pot' esti kath' hen emmelos syntithentai, pollaplasia ton - 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: ton de systematon tas diaphoras hoi -men holos ouk epecheiroun exarithmein, alla peri auton monon ton -heptachordon ha ekaloun harmonias ten episkepsin epoiounto, hoi de -epicheiresantes oudena tropon exerithmounto.] - -For [Greek: heptachordon] Meibomius and other editors read [Greek: -hepta oktachordon]--a correction strongly suggested by the parallel -words [Greek: systematon oktachordon] 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: -zeteteon de to syneches ouch hos hoi harmonikoi en tais ton -diagrammaton katapyknosesin apodidonai peirontai, toutous -apophainontes ton phthongon hexes allelon keisthai hois symbebeke to -elachiston diastema diechein aph' hauton. ou gar to me dynasthai -dieseis okto kai eikosin hexes melodeisthai tes phones estin, alla -ten triten 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 ten katapyknosin blepontas hosper -hoi harmonikoi]: p. 38, 3 [Greek: hoti de estin he katapyknosis -ekmeles kai panta tropon achrestos phaneron]: p. 53, 3 [Greek: kata -ten tou melous physin zeteteon to hexes kai ouch hos hoi eis ten -katapyknosin blepontes eiothasin apodidonai to hexes]. - -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: [=ke]] 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 symphonias kai -phthongous allelois anametrountes anenyta, hosper hoi astronomoi, -ponousin. Ne tous theous, ephe, kai geloios ge, pyknomat' atta -onomazontes kai paraballontes ta ota, hoion ek geitonon phonen -thereuomenoi, hoi men phasin eti katakouein en meso tina echen kai -smikrotaton einai touto diastema, ho metreteon, 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: pyknoma]), and the filling up of the scale in that way was -therefore a [Greek: katapyknosis 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: haute estin he para tois archaiois kata -dieseis harmonia, heos [=kd] dieseon to proteron diagousa dia pason, -to deuteron dia ton hemitonion auxesasa]: '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: he 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: eide]) 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 diastema, ho metreteon.] 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: -enarmonion] in the passage first quoted (compare the words [Greek: -peri auton monon ton hepta oktachordon ha ekaloun harmonias] with -[Greek: peri systematon oktachordon enarmonion 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', o phile, epeidan labes ta -diastemata hoposa esti ton arithmon tes phones oxytetos te peri kai -barytetos, kai hopoia, kai tous horous ton diastematon, kai ta ek -touton hosa systemata gegonen, ha katidontes hoi prosthen paredosan -hemin 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 systemata theoresai posa te esti kai poia -atta, kai pos ek te ton diastematon kai phthongon synestekota]). -Further, the use of [Greek: harmonia] for [Greek: systema], or rather -of the plural [Greek: harmoniai] for the [Greek: systemata] 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: systema]. 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 -mese kaleitai en tais harmoniais, ton de okto ouk esti meson], _i.e._ -how can we speak of the Mese 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: systema] 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: te de tes kineseos -taxei rhythmos onoma eie, te d' au tes phones, tou te oxeos hama kai -bareos synkerannymenon, harmonia onoma prosagoreuoito.]] - - - - -Sec. 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 Hypate Hypaton -(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-- - - - Hypate Hypaton to Hypate Meson _b b* c e_ (1/4 1/4 2 ) - Parhypate " " Parhypate " _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 Hypate Hypaton to Paramese -(_b-b_) this tone (_a-b_) is the highest interval; in the next -octave, from Parhypate Hypaton to Trite Diezeugmenon (_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 - - - - -Sec. 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: systemata]) 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 Hypate to Nete: 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 Mese, and that from Mese -to Nete Hyperbolaion. 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. - - - - -Sec. 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 phthongon]). 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 Parhypate or in the place of a Lichanos (p. 13 -Meib. [Greek: hetera gar ethe 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 tes phones]). There are three kinds of composition, he -tells us (p. 28), viz. that which is akin to Hypate ([Greek: -hypatoeides]), that which is akin to Mese ([Greek: mesoeides]), and -that which is akin to Nete ([Greek: netoeides]). The first part of -the art of composition is the choice ([Greek: lepsis]) which the -musician is able to make of the region of the voice to be employed -([Greek: lepsis men di' hes heuriskein to mousiko perigignetai apo -poiou tes phones to systema topou poieteon, poteron hypatoeidous e -ton loipon 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 tes 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: systaltike]), viz. -that by which we move painful feelings; another "expanding" ([Greek: -diastaltike]), that by which we arouse the spirit ([Greek: thymos]); -and another "middle" ([Greek: mese]), 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 psyches androdes]), 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: hesychastikon -ethos]) 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 (Secs. 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 Hyperbolaion ([Greek: topos hyperboloeides]). 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 Hypate Meson to the Dorian Mese; the intermediate or -mesoid region from the Phrygian Hypate Meson to the Lydian Mese; the -netoid region from the Lydian Mese to the Nete Synemmenon; 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 tes phones -posous legomen einai? treis. tinas? toutous; oxyn, meson, baryn.] The -varieties of ethos also appear (p. 14 Meib.): [Greek: he de metabole -kata ethos? hotan ek tapeinou eis megaloprepes; e ex hesychou kai -synnou eis parakekinekos.] '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. - - - - -Sec. 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 ethe -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 Parhypate in their tetrachord, viz. the notes called -Parhypate or Trite: the second are similarly the notes called -Lichanos or Paranete. 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: arrhenopon d' esti kai -austeroteron]), the Chromatic sweet and plaintive ([Greek: hediston -te kai goeron]), the Enharmonic stirring and pleasing ([Greek: -diegertikon d' esti touto kai epion]). 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]. - - - - -Sec. 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 Hypate to Nete, 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: semeia]) 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: parasemantike]) had come to be considered by some persons -identical with the science of music ([Greek: harmonike]),--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: haute de hosper ekpiptein auten] (sc. [Greek: ten -aisthesin]) [Greek: poiei tou synethous kai prosdokomenou melous, -hotan epi pleon men syneiretai to akolouthon, metabaine de pe pros -heteron eidos, etoi kata to genos e kata ten 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, Dorikous te kai Phrygious kai Lydious en -to auto asmati poiountes; kai tas melodias exellatton, 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 Melopoeie -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: e 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 Froehner in the _Revue Archeologique_, 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 Hypate to Parhypate), and -reversed to raise it by both (Hypate 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 Parhypate and Trite 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' hon tithemena ta systemata melodeitai]). - -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: e] " [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'Antiquite_, 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 (Hyperbolaion), 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 hestotes]), -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, Hypate Hypaton, Hypate Meson, Mese, Paramese, Nete -Diezeugmenon and Nete Hyperbolaion in the seven oldest keys: the two -lowest are marked as doubtful:-- - - - TABLE LEGEND: - Column A = Prosl. - Column B = Hyp. Hypaton. - Column C = Hyp. Meson. - Column D = Mese. - Column E = Par. - Column F = Nete Diez. - Column G = Nete 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 Melopoeie_, 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 mousuies alles men oudemias, aulon de -Boiotion kai Argeion; ta te Sakada kai Pronomou mele tote de -proechthe malista eis hamillan.]] - - - - -Sec. 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: e 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: e - 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. Sec. 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: systema 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 -pason tous ap' autou tou dia pason apotero parelkontos hypotithentai, -tous autous aei ginomenous tois proeilemmenois.]] - -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 Mese, for example, was two tones higher than -the Dorian Mese, 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 Mese 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, Hypate Hypaton 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: hoste med' an heteron eti doxai -to eidei ton tonon para ton proteron, all' hypodorion palin, e ton -auton hypophrygion, oxyphonoteron tinos e baryphonoteron 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 Hypate Meson -([Greek: kata thesin]) to Nete Diezeugmenon (called the octave -[Greek: apo netes]), and that from Proslambanomenos to Mese (the -octave [Greek: apo meses]). 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 ten toiauten diaphoran he ton -organon holon epitasis e 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 pason -phthasantes, hoi d' ep' auto monon, hoi de epi to meizon toutou, -prokopen tina schedon toiauten aei ton neoteron para tous -palaioterous theromenon, anoikeion tes peri to hermosmenon physeos te -kai apokatastaseos; he mone perainein anankaion esti ten ton esomenon -akron tonon diastasin]. We may compare c. 11.] - - - - -Sec. 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 schema 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 ton tetrachordon pros allela 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 megethe ton diastematon kai tas ton - phthongon taseis apeira pos phainetai einai ta peri melos, - kata de tas dynameis kai kata ta eide 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: he men gar kata tonon eis diazeuxin -agei to tou systematos eidos, he de kata thateron diastema ho ti -depot' echei megethos eis synaphen]). 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' auten ten thesin, to oxyteron haplos e -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 tetrachordon -hois to melos horizetai eisin hepta? synaphe, 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 Mese 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 Mese of the Perfect System -([Greek: mese 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 Mese of -this passage to be the [Greek: mese kata thesin], or Mese by -position. That is, Westphal is obliged by his theory of the Modes to -take the term Mese 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--Mese, -Hypate, Nete 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. - - - - -Sec. 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: chroma 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 te -lyra kaloumena sterea tonou tinos hypo ton tou toniaiou diatonou -arithmon tou autou tonou, ta de malaka hypo ton en to migmati tou -malakou chromatos apithmon 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 doriou] 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 Doriou].] - -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 Melopoeie_, 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 Doriou]. 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: chromatikon - 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: mese -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 Mese [Greek: kata thesin] (_g_), -since the interval _g-c_ is not consonant (9/8 x 9/8 x 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 -Mese [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: plen kathoson adousi men -akolouthos to dedeigmeno syntono diatoniko, kathaper exestai skopein -apo tes ton oikeion autou logon paraboles, harmozontai de heteron ti -genos] (sc. the Pythagorean), [Greek: xynengizon men ekeino, k.t.l.]] - - - - -Sec. 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 Etudes 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'Antiquite_, 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 Parhypate Hypaton to Trite Diezeugmenon (_f - f_ -with one [symbol: flat]). The first employs the same octave with a -lower note added, viz. Hypate Hypaton (_e_): the third adds the next -higher note, Paranete Diezeugmenon (_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 Hypate Meson; 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 Meson, 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 Mese (_a_) being the -key-note. (See Gevaert, i. p. 141.) A fourth (Sec. 104) also ends on the -Mese, but the key-note appears to be the Parhypate Meson (_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 zes phai-nou. - me-den hol-os sy ly-pou. - pros o-li-gon es-ti to zen. - 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: logodes 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 arbyles - tithete, me ktypeite; - apoprobat' ekeis' apopro moi koitas,] - -[Footnote 1: _Harm._ p. 18 Meib. [Greek: legetai gar de kai logodes -ti melos, to synkeimenon ek ton prosodion, to en tois onomasi; -physikon gar to epiteinein kai anienai en to 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: arbyles] 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: ephanistai]), 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: zes) 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 hos ti)s a-ka-tou tho-as ti-na(xas daimon) - kat-e-kly-sen (deinon ponon) hos 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 Hypate Meson to Trite Diezeugmenon. -But in either case the lowest note (_g_) finds no place in the -System, since it can only be the Diatonic Lichanos Hypaton. 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 -Hypate--the note, in fact, which we have already met with under the -name of Hyper-hypate (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.] - - - - -Sec. 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 Hypate. - -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_). - - - - -Sec. 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 Parhypate 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 Trite and also of the Nete 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 Trite -(_b*_) and the Nete (_e_) are wanting. But the Paramese (_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: he 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-hypate) 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_. Sec. 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 Mese, 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 Mese (_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: Mese 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 Mese, -and thus finding the octave in question in the Perfect System and in -the oldest part of it, viz. the tetrachords Meson and Synemmenon, -with the Nete Diezeugmenon. 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 Synemmenon -(_a-b[Symbol: Flat]-c-d_) takes the place of the tetrachord -Diezeugmenon. 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 Diezeugmenon to -the tetrachord Synemmenon, 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: metabole kata systema])[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 Mese 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 Mese. - -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 systema de -hotan ek synaphes eis diazeuxin e anapalin metabole ginetai]. Anonym. - - - - -Sec. 65 [Greek: systematikai de] (sc. [Greek: metabolai]) [Greek: -hopotan ek diazeuxeos eis synaphen e empalin metelthe 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: hos 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 suntonoteras ... 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 Melopoeie_, p. 356 (ed. 1863): 'Die aelteste -griechische Tonart ist demnach eine Molltonart.... Aus Kleinasien -wurden zunaechst zwei Durtonarten nach Griechenland eingefuehrt, 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 eide ex -hon hai baseis plekontai, hosper 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 Mese. 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 Synemmenon--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 Mese 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 chresta mele pollakis te -mese chretai]). 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. Sec. 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 netes] and [Greek: apo -meses]). 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 te nun -katechouse melopoiia ounetheis monon ontes eiktos ten ditonon -lichanon] (_f_ in the scale _e-a_) [Greek: exorizousi; suntonoterais -gar chrontai schedon hoi pleistoi ton nun. toutou d' aition to -boulesthai glukainein aei. semeion de hoti toutou stochazontai, -malista men gar kai pleiston chronon en to chromati diatribousin. -hotan d' aphikontai pote eis ten harmonian engus tou chromatos -prosagousi, sunepismomenou tou ethous.]] - -[Footnote 2: Ibid. p. 26 [Greek: noeteon gar apeirous ton arithmon -tas lichanous. hou gar an steses ten phonen apodedeigmenon lichano -topou lichanos estai; diakenon de ouden esti tou lichanoeidous topou, -oude toiouton hoste me dechisthai lichanon]. And p. 48 [Greek: epeide -per ho tes lichanou topos eis apeirous temnetai tomas].] - -[Footnote 3: Aristox. _Harm._ p. 69 Meib. [Greek: kata men oun ta -megethe ton diastematon kai tas ton phthongon taseis apeira pos -phainetai einai ta peri to melos, kata de tas dynameis kai kata ta -eide 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 (Bale, 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.] - - - - -Sec. 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: logodes 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: prosodiai]), 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 me dia -pathos pote eis toiauten kinesin anankasthomen elthein]). - -[Footnote 1: Aristox., _Harm._ p. 3 Meib. [Greek: kineitai men gar -kai dialegomenon hemon kai melodounton ten eiremenen kinesin; oxy gar -kai bary delon hos en amphoterois toutois enestin.] Also p. 8 [Greek: -dyo tines eisin ideai kineseos, he te syneches kai he diastematike; -kata men oun ten syneche topon tina diexienai phainetai he phone te -aisthesei houtos hos an medamou histamene, k.t.l.] And p. 9 [Greek: -ten oun syneche logiken einai phanen, k.t.l.]] - -[Footnote 2: Ibid. p. 18 Meib. [Greek: tou ge logodous kechoristai -taute to mousikon melos; legetai gar de kai logodes ti melos, to -synkeimenon ek ton prosodion ton en tois onomasin; physikon gar to -epiteinein kai anienai en to dialegesthai.]] - -[Footnote 3: Nicomachus, _Enchiridion_, p. 4 [Greek: ei gar tis e -dialegomenos e apologoumenos tini e anaginoskon ge ekdela metaxy -kath' hekaston phthongon poiei ta megethe, diistanon kai metaballon -ten phonen ap' allou eis allon, ouketi legein ho toioutos oude -anaginoskein 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 diastemati to legomeno dia pente, hos engista; kai oute -epiteinetai pera ton trion tonon kai hemitoniou epi to oxy oute -anietai tou choriou 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; he men gar peze lexis oudenos oute onomatos oute -rhematos biazetai tous chronous oude metatithesin, all' oias -pareilephe te physei tas syllabas, tas te makras kai tas bracheias, -toiautas phylattei; he de mousike te kai rhythmike metaballousin -autas meiousai kai parauxousai, oite pollakis eis tanantia -metachorein; 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 hoto eoike ton -axiologon mimematon]). 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: e oud' ekei, ean me -mimetai, homoios hedy?]) 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 me -prospherein tois mellousin en trisin etesi to tes mousikes chresimon -eklepsesthai 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 Paranete 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 Paranete of -the Enharmonic scale are called [Greek: lichanos] and [Greek: -paranete] 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 -Melopoeie_, 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: mathematikoi], 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: mathematikoi] 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._ -Mese. -[Music: Hyper-lydian.] -[Music: Hyper-aeolian.] -[Music: Hyper-phrygian.] -[Music: Hyper-ionian.] -[Music: Mixo-lydian.] -[Music: Lydian.] -[Music: Aeolian.] -[Music: Phrygian.] -[Music: Ionian.] Mese. -[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: hos tiSAKATOUTHOASTINAxas dai-] - -[Symbols:] [Greek: mon KATEKLYSEN deinon] - -[Symbols: Z re. z?] [Greek: ponoN[Symbols:???]OOSPONT 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 hos - tis a-ka-tou tho-as ti-na-xas dai-mon - kat-ek-ly-sen dei-non po-non hos 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: deinon ponon]. 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: o] of [Greek: hos] (written [Greek: OOS]) 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: OSONZESPHAINOU] - -[Symbols: K I Z IK O] [Greek: MEDENOLOSSY] - -[Symbols: E., C O i; C K Z] [Greek: LYPOUPOSOLI] - -[Symbols: I IC I K C OZ] [Greek: GONESTITOZEN] - -[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 hellenique_ 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 | zes phai-| nou; meden | holos 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 | zen; 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 hellenique_ (viii-xii. pp. 569-610), with -two valuable commentaries by M. Henri Weil and M. Theodore 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-phe 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 hos hei[les, echthros hon -e-phr]ou-rei dra-kon;] - -[Symbols: 4:I U!or 4 u] [Greek: ho-te te[oisi belesin e-tr]e-sas -ai-o-lon he-lik-tan[] - -[Symbols: I omio r 4] [Greek:] sy-rig-math' hi-eis a-tho-pe[ut' eba;] -[Symbols: U ior.t. U] - -[Greek: nyn] de Ga-la-tan a-res..n epe-ras' a-sep-t[os - -[Symbols:] [Greek: sal-li-o](?) [Greek: gen-nan..n thalos phi-lon] - -[Symbols:] [Greek: da-moi-o lo....ron 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]ona 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-o-le[noi] -mo-le[te] syn-o-mai-mon hi-na] - -[Symbols: M U M U M W Th G W] [Greek: Phoi-bon o-dai-si mel-pse-te -chry-se-o-ko-man;] - -[Symbols: Th O Ps O Th O 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 O Ps G] [Greek:-ras he-dra-na -[me]ta kly-tais Del-phi-sin Kas-ta-li-dos] - -[Symbols: O Ps O 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]o-na man-tei-on e-phe-pon -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-to-ni-dos da[ped]on a-thrauston, ha-gi-] - -[Symbols:] [Greek:-ois de bo-moi-sin Ha-phais-tos ai-thei ne-on] - -[Symbols:] [Greek: me-ra tau-ron; ho-mou de nin A-raps at-mos es Y- - -[Symbols:] [Greek:-lym-pon a-na-kid-na-tai; li-gy de lo-tos bre-mon] - -[Symbols:] [Greek: ai-o-lois [me]le-sin o-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]-o-ron pro-pas es-mos Ath-thi-da -lach[on]]] The notes employed in this piece of music cover about an -octave and a half, viz. from Parypate Hypaton to the Chromatic -Lichanos Hyperbolaion. In two of the tetrachords, viz. Synemmenon and -Hyperbolaion, the intervals employed are Chromatic (or possibly -Enharmonic): in the tetrachord Diezeugmenon they are Diatonic, while -in the tetrachord Meson 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 Mese, and [Symbol: B], a semitone below Nete -Diezeugmenon. If we assume that we have before us Chromatic of the -standard kind ([Greek: chroma 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 ares]) we come upon the group [Symbols: U 4] (_g--a[Symbol: -b]--a_) of the Chromatic tetrachord Hyperbolaion. 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 Synemmenon [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 te-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-to]] - -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 ... the-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] o-leth' hy-gra ch ... despoti -Kre-sion.. ai nae-tas Delphon]] [Music: [Symbols] - -[Greek: ...in ap-tais-tous Bak-chou [thiasous] ...te prospolois]] - -[Symbols] [Greek: tan te do[u]ri[klyton ar-chan au-xet' a-ge-ra-to -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: Delphon, prospolois] and [Greek: agerato], -two present us with cadences on the Mese (_d_), and one on the Hypate -(_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, odaisi, -klytais, bomoisin, 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_, Sec. 28 (the modes employed on different -instruments), 27 - Secs. 63-64 ([Greek: topoi tes phones]), 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 tes phones]), 63 - -Aristophanes, _Eq._ 985-996 (Dorian Mode), 7, 42 - -Aristotle: - _Metaphysics_, iv. 11, p. 1018 _b_ 26 ([Greek: arche]), 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 (Mese), 43, 82, 102, 107 - 26, p. 919 _b_ 21 ([Greek: harmonia]=System), 55 - 33, p. 920 _a_ 19 (Hypate), 44 - 36, p. 920 _b_ 7 (Mese), 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 tes phones), 65 - p. 19 (theseis tetrachordon), 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 auletikai]), 22, 28 - -Pratinas ap. Athen. xiv. p. 624 _f_ ([Greek: mete syntonon k.t.l.]), 5 - -Ptolemy: - Harm. i. 13 (musical ratios of Archytas), 123 - i. 16 ([Greek: hegemon]=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 Hypate 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. 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