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API2TOHENOT APMONlRA'

^TOIXEIA

THE HARMONICS OFARISTOXENUS

EDITED WITH TRANSLATION NOTES

INTRODUCTION AND INDEX OF WORDS; BY

HENRY S. MACRAN, M.A.,FELLOW OF TRINITY COLLEGE, DUBLIN

AND PROFESSOR OF MORAL PHILOSOPHY IN THE UNIVERSITY OF DUBLIN

OXFORD

AT THE CLARENDON PRESS190:2

HENRY FROWfiE, M.A.

PUBLISHER TO THE UNIVERSITY OF OXFORD

LONDON, EDINBURGH • ... .

NEW YORK

' & « : . • / • • • ••

PREFACE

THE main object of this book is to introduce, to suchEnglish readers as "may be curious in the matter of music,the writings of the foremost musical theorist of AncientGreece; and with this object in view I have endeavoured tosupply a sound text and a clear translation of his great work,and to illustrate its more obscure passages by citations fromother exponents of the same science. But further, since themind of the modern reader is apt to be beset by prejudicesin respect of this subject—some of which arise from hisnatural but false assumption that all music must follow thesame laws that govern the only music that he knows, whileothers are due to the erroneous theories of specialists whichhave been accepted as certain truths by a public not inpossession of the evidence—I have thought it necessary todeal at some length with those prejudices; and this is thechief aim of the Introduction.

The critical apparatus differs from that of Marquard inincluding the readings of H as given by Westphal, and cor-recting from my own collation of the Selden MS. manyincorrect reports of its readings.

I wish to express my thanks to the Provost of OrielCollege, Oxford, Mr. Mahaffy, and Mr. L. C. Purser, forreading the proofs, and for many useful suggestions; toMr. Bury for advice on many difficult passages of the text;and above all to another Fellow of Trinity College, Dublin,Mr. Goligher, for most generous and valuable aid in thepreparation of the English Translation.

HENRY S. MACRAN.TRINITY COLLEGE, DUBLIN.

Sept. 1902. .-,.. •__• < • •_.' " i l

bawa from Crerar Library

98922

CONTENTS

INTRODUCTION-PAGE

A.—ON THE DEVELOPMENT OF GREEK MUSIC . i

B.—ON ARISTOXENUS AND HIS EXTANT WORKS . 86

TEXT-r-

BOOK I 95

„ II 122

„ III 149

TRANSLATION—

BOOK I 165

187

209

. . . . . . . . 2 2 3

. . . . . . . . 295

»

NOTES

INDEX

IIIII

INTRODUCTION

A.—ON THE DEVELOPMENT OF GREEK MUSIC.

I . Music is in no sense a universal language. Like itssister, speech, it is determined in every case to a specialform by the physical and mental character of the peopleamong whom it has arisen, and the circumstances of theirenvironment. The particular nature of music is no moredisproved by the fact that a melody of Wagner speaks toGerman, French, and English ears alike, than is the particularnature of speech by the fact that the Latin tongue was atone time the recognized vehicle of cultivated thoughtthroughout the civilized world.

Further, this limitation which is common to music andspeech leads to a more complete isolation in the case ofthe former. The primary function of language is to giveus representations, whether of the facts of the world andthe soul, or of the ideals of thought, or of the fancies ofthe imagination: and to appeal to our emotions throughthe representation of such facts, ideals, or fancies. Thisservice, so far as we are capable of perception and feeling,any strange language may be made to rerlder us at the costof some study. But we are aware that our own languagehas another power for us ; that of waking immediately in usemotions in which are fused beyond all analysis the effectsof its very sounds and the feelings that are linked to thosesounds by indissoluble association. It is here that beginsthe real isolation of language, the incommunicable charmof poetry that defies translation. But the whole meaningof music depends upon this immediate appeal to ouremotions through the association of feeling with sensation;

INTRODUCTION

' and so the strangeness of the foreign music of to-day, andof the dead music of the past is insuperable, for they are theexpressions of emotions which their possessors could notanalyse, and we can never experience.

2. The same contrast appears when we consider musicin relation to painting and the other arts of imagery. Theselatter appeal to the emotions no less than music, but theydo so in the first instance mediately, through the representa-tion of certain objects. It is quite true that here, as in thecase of the emotions indirectly raised by language, the culti-vation of a certain mental habit is a necessary condition ofour receiving the proper impression from any work of art.But in painting and sculpture the mental habit consistsprimarily in our attitude not to the manner of the repre-sentation but to the object represented, whereas in music itconsists in our attitude towards the expression itself.

The incommunicable character of music finds a strikingillustration in the effect which the remnants of ancient Greekmelody produce on the modern hearer. Some years ago,for example, Sir Robert Stewart delivered a lecture inTrinity College, Dublin, on the Music of Distant Timesand Places; and illustrated it by specimens from variousnationalities and periods, an ancient Greek hymn beingincluded in the number. It was the unanimous verdictof all the musicians present that, while the music of theless civilized nations was often crude, barbarous, andmonotonous in the highest degree, the Greek hymn stoodquite alone in its absolute lack of meaning and itsunredeemed ugliness; and much surprise was expressedthat a nation which had delighted all succeeding genera-tions by its achievements in the other arts should havefailed so completely in the art which it prized and practisedmost. Yet all this criticism is an absurdity based on thefallacy that music is a universal language. It presupposes

THE DEVELOPMENT OF GREEK MUSIC

absurdly that a melody is meaningless if it means nothingto us, and it forgets with equal absurdity that the beauty ofanything for us is conditioned by our power to appreciate it,and our power to appreciate it by our familiarity with it.

3. But though it is impossible for us now to recover themeaning of this dead music of ancient Greece, and well-nighimpossible to accustom our ears to appreciate its-form, wecan at least study as a matter of speculative interest the lawsof its accidence and syntax as they have been handed downto us by its grammarians. To this end our first step mustbe to make our conceptions clear as to the formal natureof music in general. We have already seen that the functionof music is to evoke certain moods in us by the associationof feelings with sensations. But the material of thesesensations it does not find in nature, but provides for itself,by creating out of the chaos of infinite sounds a world ofsound-relations, a system in which each member has itsrelation to every other determined through the commonrelation of all to a fixed centre. The idea of such a systemimplies two facts. In the first place, no sound is a musicalsound except as perceived in its relation to another sound;in the second place, there is a direction in this relation inthat one of the two related sounds must be perceived to bethe inner, or nearer to the centre'. Thus in the chord

or in the progressionZX2Z.

the sounds f and c become musical through their relationto one another, and through the perception in any particularcase that one of them is more central than the other; inthe key of C for example that the c, in the key of VB thatthe / i s nearer the musical centre or tonic.

1 Nearer, that is, in respect of similarity, not of contiguity.' Inthis sense, the nearest note to any given note is its octave.

B 2 3

INTRODUCTION

But just as the arithmetical intuition cannot apprehend allrelations with equal ease, but finds for example the relationf more intelligible than -£&; and as the sight apprehendsthe relation of a line to its perpendicular more readily thanthe relation between two lines at an angle of 87 degrees,so there stand out from among the infinite possible sound-relations a limited class, commonly called concords, whichthe ear grasps and recognizes without effort and immediately,and these form the elements of every musical system. Notindeed that all musical systems are founded on the sameelementary relations. Universally recognized as belongingto this class are the relations between any sound and itsoctave above or below, either being regarded as tonic; therelation between a sound and its Fourth above, the latterbeing regarded as tonic; the relation between a note andits Fifth above, the former being regarded as tonic. Butthe relation of the Major Third which plays such a pro-minent part in modern music has no place as an elementaryrelation in the system of Ancient Greece.

4. But evidently these few relations would go but a littleway in the constitution of a system, and music to extend itssphere has recourse to the mediate perception of relations.Thus there are sound-relations, which the ear, unable tograsp them immediately, can apprehend by resolving theminto the elementary concords. In our diatonic scale of cfor example, the relation of d to c is resolved into therelation of d to g, and of g to c. Thus there enter intoa musical system, besides the elementary concords, all thosesound-relations which result from their composition; andto the complexity of such compound relations there seemsto be no limit either in theory or in practice. There is nochord, no progression however complex, however unpleasantat first hearing, of which we can assert that it is musicallyimpossible. The one thing needful to make it musical is

4


that the relation of its parts to one another and to thepreceding and succeeding sounds be comprehensible.

It is also possible, though perhaps a sign of imperfectdevelopment, that a note may enter into a musical systemthrough being related indeterminately to a member of thatsystem. Thus we might admit a passing note as leadingto or from a fixed note, without the position of the formerbeing exactly determined.

Sound-relations can be perceived between simultaneousand successive sounds alike. In the former case we haveharmony in the modern sense of the word, in the lattermelody; the difference between these phases of musicbeing accidental, not essential.

The development of a system such as we have beenconsidering will proceed upon two lines. On the one handthe craving for diversity will lead to new combinations ofrelations, and so to the widening of the system and themultiplication of its members; while on the other handthe growing sense of unity will press for a closer determina-tion of the relations, and result in the banishment of thosenotes whose relations cannot be exactly determined.

5. In the music of Ancient Greece we are able to trace,though unfortunately with some gaps, the first steps of sucha development. The earliest students of the science, inendeavouring to establish a scale or system of related notes,started as was natural from the smallest interval, the boundingnotes of which afforded an elementary relation. This theyfound in the interval of the Fourth, in which the higher noteis tonic; and this melodic interval, essentially identical withour concord of the Fifth, may be regarded as the funda-mental sound-relation of Greek music. When they had thussecured a definite interval on the indefinite line of pitch, theirnext concern was to ascertain at what points the voice mightlegitimately break its journey between the boundaries of this

5

INTRODUCTION

interval. But how were these points to be ascertained?Plainly, not by the exact determination of their relation tothe bounding notes; for the Fourth was the smallest intervalthe relation of whose bounding notes the Greek ear couldimmediately apprehend; and for mediate perception themusical idea was as yet immature. Consequently, the in-termediate notes, whatever they might be, could only beapprehended as passing notes, indeterminately related tothe boundaries of the scale. Evidently then the numberof such notes must be limited. The sense of unity whichsuffers by any inadequate determination of relations wouldbe completely lost if the indeterminate relations were un-duly multiplied. From these considerations resulted one ofthe first laws of Greek melody. The scale that begins withany note, and ends with its Fourth above is at most atetrachord or scale of four notes—two bounding or con-taining notes, two intermediate or contained.

6. Again; although for the theorist a minimum of musicalinterval is as absurd as a minimum of space or time, yet,for the purposes of art, it was impossible that any two ofthese four points of the scale should lie so close togetherthat the voice could not produce, or the ear distinguish theinterval between them. Was it then possible to determinefor practical purposes the smallest musical interval? Tothis question the Greek theorists gave the unanimous reply,supporting it by a direct appeal to facts, that the voice cansing, and the ear perceive a quarter-tonea; but that anysmaller interval lies beyond the power of ear and voice alike.

Disregarding then the order of the intervals, and con-sidering only their magnitudes, we can see that one possiblerdivision of the tetrachord was into two quarter-tones and

1 The tone is musically (not mathematically) determined as thedifference between the concord of the Fourth and the concord ofthe Fifth. These latter again are musically determined by the directevidence of the ear.

6


a ditone, or space of two tones; the employment of theseintervals characterized a scale as of the Enharmonic genus.

Or again, employing larger intervals one might divide thetetrachord into, say, two-thirds of a tone, and the space ofa tone and five-sixths : or into two semitones, and the spaceof a tone and a half. The employment of these divisionsor any lying between them marked a scale as Chromatic.Or finally, by the employment of two tones one mightproceed to the familiar Diatonic genus, which divided thetetrachord into two tones and a semitone.

Much wonder and admiration has been wasted on theEnharmonic scale by persons who have missed the truereason for the disappearance of the quarter-tone from ourmodern musical system. Its disappearance is due not tothe dullness or coarseness of modern e»r or voice, but to thefact that the more highly developed unity of our sptemdemands the accurate determination of all sound-relationsby direct or indirect resolution into concords; and sucha determination of quarter-tones is manifestly impossible \

7. But the constitution of our tetrachord scale is not yetcompleted. We have ascertained the maximum numberand the Various possible magnitudes of the intervals; buttheir order has yet to be determined. In the Enharmonicgenus, for example, when we are passing to the tonic fromthe Fourth below, shall we sing quarter-tone, quarter-tone,ditone; or ditone, quarter-tone, quarter-tone; or quarter-tone,ditone, quarter-tone; or are all these progressions equallylegitimate? To these questions the Greek theorists givethe unqualified and unanimous answer, not defending it byany argument, that in all divisions of a tetrachord in whichthe highest note is tonic, and the lowest a Fourth below, thelowest interval must be less than or equal to the middle,and less than the highest.

1 See below, note on p. 115,1. 3.7

INTRODUCTION

Thus the schemes of the tetrachord scales in the three generaare finally determined as they appear in the following table:—

TABLE 1.SCHEME OF THE ENHARMONIC TETRACHORD SCALE

OF THE TONIC A.

SCHEME OF THE CHROMATIC TETRACHORD SCALE

OF THE TONIC A.

! SCHEME OF THE DIATONIC TETRACHORD SCALEI. OF THE TONIC A.

In this table the following points are to be noted:—(1) The sign x is used to signify that the note before

which it is placed is sharpened a quarter-tone.(2) The distinction between the definitely determined

bounding notes, and the indeterminate passing notes isbrought out by exhibiting the former as minims, the latteras crotchets.

(3) Several divisions are possible in the Chromatic andDiatonic genera (see below, p. 116): those taken in thistable are merely typical.

8. The importance of this tetrachord scale can hardly beoverrated, for it is the original unit from the multiplicationof which in various positions arose all the later Greekscales: and it is to be observed that the tonality of thisscale is most distinctly conceived and enunciated by thetheorists. Aristoxenus is never weary of reminding us thatthe mere perception of intervals cannot enable us to under-

8


stand a succession of notes; that we must also apprehendthe Swa/ur or function of each individual in the series.Thus the highest note of the tetrachord, which at a laterperiod when the scale was enlarged, obtained from itsposition the name of Mese, or middle note, holds in relationto the lowest note the function of an apx?) or foundation, inother words of a tonic. For just as cause and effect, thoughthey exist only in their relation to one another, do notdischarge like functions in that relation inasmuch as theeffect leans upon the cause, but not the cause upon theeffect; so though the highest and lowest notes of the tetra-chord are musical notes only through their relation to oneanother, yet that relation is conceived as implying thedependence of the lower upon the higher, but not of thehigher upon the lower. The intermediate notes again areregarded as mere stopping places of approximately deter-mined position in the passage between the boundaries.According to the Greek terminology they are xivovpcvoi ormovable notes as distinguished from the «nwes or fixednotes, between which they stand. For since the essenceof a note is not its place in a group, but its function ina system, an Enharmonic, a Chromatic, and a Diatonicpassing note are not to be regarded as three notes, but asone variable note in three positions.

Even if we disregard the Enharmonic and Chromaticgenera, and confine our attention to the Diatonic, we shallseek in vain for a parallel to this tetrachord scale in theclassical system of modern music. We can descend fromthe tonic a to the e below it by the progression

fcJ -J—3t~ 5 but the progression | (fo J J

to the tonic a, though of frequent occurrence in local music,has passed completely out of classical use.

9

INTRODUCTION

9. When this meagre group of four notes was felt to beinadequate to the expression of human emotion, a readymethod for the production of a more ample scale wassought in the addition to the original tetrachord of a secondexactly similar to it. But immediately the question arose,How was the position of the second tetrachord to be deter-mined in relation to the first ? Or, to put it more generally,Supposing a scale of indefinite length to be constituted bya series of similar tetrachords, how was the position of thesetetrachords to be relatively defined ?

To this question it seems that there were three possibleanswers for the theorist, each of which no doubt foundsupport in the art product of some tribe or other of theHellenic world. The method of determination proposedin each answer constituted (as I shall here assume, post-poning my arguments for the present) a distinct apfiovLa orHarmonyx; which term I believe to have meant primarilyan ' adjustment' not of notes (for these are not the units ofmusic) but of tetrachords.• 10. According to the first of these answers, the tetra-chords might be so arranged that the highest note of anyone would coincide with the lowest note of the next aboveit. This method of conjunction, or the coincidence ofextremities I believe to have been called the Ionic Har-mony ; and it resulted in a scale of this character:—

TABLE 2.SCALES OF THE IONIC HARMONY IN THE THREE GENERA

INDEFINITELY EXTENDED.ENHARMONIC I

1 When I use the word Harmony as an equivalent of the GreekI shall employ a capital H.


CHROMATIC I

DIATONIC J J

If in the Ionic scale of any genus we take any con-secutive pair of tetrachords, we obtain the Heptachord scaleof the seven-stringed lyre.

TABLE 3.

HEPTACHORD SCALES IN THE THREE GENERA WITH

THE NAMES OF THE INDIVIDUAL NOTES

ENHARMONIC2

J 1 J r J J-*3 *m •

CHROMATIC8s

DIATONIC

a IJ J ,)

u . These names were derived not from the pitch of theii

INTRODUCTION

respective notes, but from the place on the instrument ofthe strings which sounded them. Thus a as the noteof the middle string was called Mese or 'middle'; e wascalled Hypate or highest because sounded by the top string;d which was sounded by the bottom string was in likemanner called Nete or lowest. The note below the Mesewas called Lichanus or 'forefinger,' because the stringthat sounded it was played by that finger. The namesParhypate, ' next the highest,' Paranete, ' next the lowest,'and Trite, 'third,' require no explanation.

It is important to observe exactly what these names do,and do not denote. They do not denote the membersof a scale as points of pitch determined absolutely or inrelation to any other scale. Let us take the scale

IJ A bJ J

and transpose it, say, a tone higher

" 2 § S

£ S I £• l J J

the individual notes of the resulting scale will bear thesame names as the corresponding members of the originalscale.

Again, these names do denote the points of a scale theorder of whose intervals is determined. Thus, if we takethe enharmonic scale

12


or the diatonic scale

consisting not of two complete tetrachords, but of onetetrachord and a fragment at each end, the notes of thesescales will take their names from their place not in their ownscales, but in the typical systems given in Table 3.

Once again, it is not implied by these names that theintervals between the designated notes are exactly deter-mined in magnitude; for they are applied to the membersof Enharmonic, Chromatic, and Diatonic scales.alike.

12. The second method of forming a scale of tetrachordsleft the interval of a tone, called the disjunctive tone, be-tween each pair of them. This Harmony by disjunction, orthe separation of extremities, I shall assume to have beencalled Doric. It substituted for the Heptachord the Octa-chord, or scale of the eight-stringed lyre.

TABLE 4.OCTACHORD SCALES IN THE THREE GENERA WITH

THE NAMES OF THE INDIVIDUAL NOTES.

ENHARMONIC ia

CHROMATIC

DIATONIC

INTRODUCTION

•813

s

Sr

IJ i-

The scale of this Harmony, when indefinitely prolonged,resulted in the following succession :—

TABLE 5.

SCALES OF THE DORIC HARMONY IN THE THREE

GENERA INDEFINITELY EXTENDED.

ENHARMONIC . I ,L I ,L I J -£2_

I 1 l-j-nW1^ d ^ ^

CHROMATIC

JSg^i J « J ^

The .appearance of the octachord scale necessitated analteration in the nomenclature. The old names were em-ployed to represent the four lowest and the three highest

H


members of the new system, and the title Paramese, or' next the middle,' was given to the note above the Mese.'

13. The third method of adjustment employing conjunc-tion and disjunction alternately interposed a tone betweenevery second pair of tetrachords, while every other pairwere conjunct. This Harmony I shall assume to have beencalled Aeolian; it resulted in the following scales :—

TABLE 6.

SCALES OF THE AEOLIAN HARMONY IN THE THREE

GENERA INDEFINITELY EXTENDED.

ENHARMONIC

The alternation of conjunction and disjunction which isthe characteristic of this Harmony is exemplified in thefollowing eight-note scales:—

TABLE 7.OCTAVE SCALES IN THE THREE GENERA WHICH

EXEMPLIFY THE AEOLIAN HARMONY.

ENHARMONIC

A J

INTRODUCTIONCHROMATIC

-9— —r-

DIATONIC

14. If we employ modern nomenclature we may distin-guish the first two Harmonies from the last by sayingthat the. former give rise to modulating scales, the onepassing over into the flat, the other into the sharp keys,while the latter maintains the same key throughout. Butwe must examine more closely into the nature of thisdifference. In the scale of the first Harmony we have aseries of lesser tonics B, E, A, d, g1; that is, each of thesenotes serves as tonic to the notes that immediately precedeit. What then is the relation of these tonics to one an-other ? Each serves as a tonic of higher rank to the lessertonic immediately below it and mediately through this toall below, so that we are necessarily driven upwards in oursearch for the supreme tonic, and are unable at any pointto reverse the process; for no note can serve as immediatetonic to the Fourth above it. Consequently our progresstowards the supreme or absolute tonic becomes a processad infinitum.

When we pass to the second Harmony we find an oppositecondition of things. Here the series of lesser tonics isD, A, e, b. Any one of these serves as tonic of higherrank immediately to the lesser tonic next above it, andthrough this mediately to all above, but cannot dischargea like function to those that are below it. Here then thenecessary order is the descending one, but the progression

1 When any scale contains the same note in two different octaves,we shall represent the higher by small, the lower by capital letters.

16


is equally ad infinitum; and our search for an absolute tonicis again fruitless. But when we arrive at the third Harmonywe find for the first time the object of our search. In theseries E, A, e, a, A is tonic to the e above through themediation of a1, and directly to the E below, and throughthem to all the lesser tonics of the scale.

15. The distinction, then, that holds between these threeHarmonies corresponds in no wise to the distinction betweenour Major and Minor modes. All three of them alike recog-nize no fundamental relations outside that of a note to itsFourth above or Fifth below, and that of a note to its octave;and all three alike place their passing notes in the sameposition. But our distinction of Major and Minor hasarisen through the recognition of two fresh elementarysound-relations unknown to the Greeks, those of theGreater and Lesser Third; and according as a scaleembodies one or other of them, it is denominated Majoror Minor. Thus the essential characteristic of the majorscale of A is the immediate relation of % C to A, and of $ Gto E; and of the minor scale of A, in so far as we havea minor scale at all, the immediate relation of C to A, andof G to E; and these relations are not present in the scalesof any of the three Harmonies. One might illustrate thecontrast by representing the modern minor scale of A asfollows:—

J J

_ ... |. CJ- A J1 The relation of a note to its octave above or below approximates

to identity.HACXAK Q 1J

INTRODUCTION

and the diatonic scale of the third Harmony as follows :—t ] • - • •

> I 1 0 •

*& ,J j—\

r—r—

in each case supplying the most fundamental relations ofthe scale in the form of a bass.

16. From the comparison above instituted between thethree early Harmonies of Greek music, it was clear thatthe third possessed a consistency and unity which werewanting in its rivals. Accordingly we are not surprised tofind that they fell into disuse, while the Aeolian won itsway to predominance, and finally to exclusive possessionof the field of melody. But the process was a gradualone, and there were many attempts at combination andcompromise before it was accomplished. Of such attemptswe have an example in the so-called Phrygian scale, theearliest form of which is given us by Aristides Quintilianus(Meibom, 21. 19).

TABLE 8.

(a) ENHARMONIC PHRYGIAN SCALE OF ARISTIDESQUINTILIANUS.

r-0-OLD DIATONIC

J

PHRYGIAN SCALE ON THE ANALOGY OF (a).

—1 j j ^ m • G*

Here we have a scale which, though containing two dis-junctions (between D and E, and between A and B\ yetproduces an octave by combining conjunction with dis-junction at A> and in so doing embodies the distinctive

18 .


feature of the first Harmony, the relation of the tonic A tod, its Fourth above.

17. The perverse artificiality which is conspicuous in thisscale is a common feature in the musical science of theperiod. It does not by any means follow that the musicof the time suffered from the same vice. For the sakeof brevity, we have regarded the theorists as graduallyevolving the system of Greek music; but of course theirprovince as a matter of fact extended only to the analysisand explanation of what the artist created. As the theoristof metrical science arranges in feet the rhythm to whichthe instinct of the poet has given birth, so the theorist ofscales offers an analysis of the series of notes in which thepassion of the singer has found expression. Now, the artwhich in the beginning had created the tetrachord and thenpassed on to the various combinations of tetrachords cameto require for some song or chorus the following diatonicseries of notes:—

IV- IZ2I

This scale the theorist applied himself to read, and thescheme of Table 8 is the fruit of his first attempt. Whenthe distracting claims of the First and Second Harmonieshad become silent, and the Third had come to be recog-nized as the normal method of combining tetrachords, thetrue reading of the scale became apparent

18. Aristides Quintilianus has preserved for us severalother examples of these perverse scale-readings. Composersfound room for variety within the Aeolian Harmony byemploying now one, now another segment of the indefinite

c 2 19

INTRODUCTION

Aeolian scale, not of course with any change of tonality ormodality, but simply as the melody required this or thatnumber of notes above or below the tonic. Thus there,arose a series of scales which offered material for the analysisof the theorist—an analysis that was not by any means soeasy and obvious as we might at first suppose. We seemimmediately to recognize \that they are not essentially in^dependent of one another, but differ merely as variousportions of one scale; and we are disposed to wonder thatthe Greeks should have deemed each of them worthy ofa separate analysis and a name to itself. But there are twoimportant considerations which are apt to escape us. Inthe first place, at the period -of musical science which weare now considering, the contending claims of the threeHarmonie6, and the possibility of combining them producedan uncertainty in the analysis of scales, of which music,through the simplifying tendency ever present in its develop-ment, has since cleared itself. In the second place, we areaccustomed to instruments of great actual or potentialcompass, in which the relation of such scales' to one anotheras segments of a common whole is immediately and palpablyevident. But for any performer on a limited instrument,say, one of eight notes, it would be impossible to pass fromone of these scales to another except by a fresh tuning, orin some cases by a change of instrument; and from thesepractical necessities the scales would derive a character ofindependence which does not belong to them in the natureof things. We should never think of differentiating anddistinguishing by name the octave scales in which arerespectively contained the opening phrases of Handel's' I know that my Redeemer liveth/ and his ' But thou did'stnot leave his soul in hell' But it would be natural enoughfor a player on the pipe to do so when he found that thetvyo themes could not be rendered by the same instrument,


19. Again, these scales that had to be analysed were incommon vogue, and so belonged to the Diatonic Genus.For here it is to be observed that the Enharmonic andChromatic scales seem to have been esoteric or academicalin use, and the pre-eminently natural' character of theDiatonic was recognized even by those tKeorists whodefended the other genera (see below, p. I I I J 1'. 9). Weappend a table of the scales to be analysed.

TABLE 9. .

VARIOUS SEGMENTS OF THE DIATONIC SCALE. OF. THE

AEOLIAN HARMONY.

pXT

i Q

2 1

INTRODUCTION

It is most carefully to be noted that, in order to conceive'•,-> of these scales as did the Greeks, we must entirely abstract

from the pitch relation which is necessarily introduced into. • . , them by representing them according to modern notation.

Any one of the above scales may lie higher, or lower than,or in the same compass as any other of them.

20. To guide them in their analysis the theorists werenot without certain clues. No note, they knew, could bethe tonic or Mese of the scale unless the fourth note belowit stood to it in the fundamental relation of a note to itsFourth above. And the increasing influence of the ThirdHarmony made it necessary to find the tonic in a notenext above which lay the disjunctive tone. But even withthese clues the scales often baffled their analysis. Authori-ties differed, and in one case at least a historianl recordsthe discovery in later times of the true reading of a scalewhich had formerly been misinterpreted. Nothing, perhaps,contributed more to these doubts and failures than theendeavour to find a distinctive plan of formation in eachscale. In accordance with this principle {d) in the abovetable was construed as two complete tetrachords of theDorian Harmony, and was augmented by a tone so as torepresent adequately the nature of that adjustment by dis-'

1 See Plutarch, de Musica, 1136 D \iois Si hajxTrponkia rbv 'MrpnuavavmS6vra STI OVK ivravBa i)((i (1) MifoAvStorQ ri)v 8tA£iv(iv, oirov ffx«8oi>avavTfs fyovro, dAA' liA TO ofi, rmovrov airrijp direpyaaaaOai TO a\Vlxa °^ov

TO dird napaniotjs M inaTtjv vvarSn>. ' But according to Lysis Lampro-qles the Athenian saw that the Mixolydian scale had its point of dis-junction, not where it was commonly supposed to be, but at the top ;and accordingly established its figure to be such a series of notes asfrom the Paramese to the Hypate-Hypat6n.'

22


junction only. According as this tone was added at thebottom or at the top, the scale would seem to have beencalled Dorian or Hypodorian (that is, Lower Dorian). Theappropriateness of this latter name will appear in thesequel. ^

TABLE 10.

OLD DORIAN SCALE.

— , I I J J J — J ^

OLD HYPODORIAN SCALE.

The reading of (c) resulted in the Phrygian scale, thescheme which we gave in Table 8 ; (6) and (e) were iden-tified as illustrating alternate conjunction and disjunction,and, as typical of the Aeolian Harmony, were called Lydian1.

TABLE 11.

OLD LYDIAN SCALES.

£l> .J. J 4 ;

J •>j J <

Again, ( / ) was read as in the following table, and, asessentially similar to the Phrygian scale, was called Hypo-phrygian. . • ---.

1 For the relation between the terms Aeolian and Lydian see

t

INTRODUCTION

TABLE 12.OLD HYPOPHRYGIAN SCALE.

{g) does not appear in the oldest lists of scales. Perhapsthe extreme position of the tonic made such a segment ofrare occurrence. The same fact may have helped to obscurethe analysis of (a). Certain it is at any rate that not onlythe true plan, but even the position of the tonic of thisscale remained for a long time undiscovered (see noteon p. 22). Aristides Quintilianus (Meibom, 21. 26) haspreserved for us the old reading which is curiously in-teresting.

TABLE 13.ENHARMONIC MIXOLYDIAN SCALE OF ARISTIDES

QUINTILIANUS.

IV-r

OLD DIATONIC MIXOLYDIAN SCALE ON THE ANALOGY OFTHE PRECEDING.

^ F r r J i° J: r=

In fact it was conceived as a scale constituted by theelection of certain parts of two overlapping scales of theAeolian Harmony; namely,

Q !• . — i

and


We have already seen that the term Lydian was appliedto the scale that was typical of the Aeolian Harmony; andconsistently with this, (a), as a mixture of two such scales,was called Mixolydian or Mixed Lydian. It was an exampleof what Aristoxenus calls a double scale; that is, it hadtwo Mesae or tonics, d and e.

21. Each of these scales might, at any rate theoretically,appear in Enharmonic and Chromatic as well as in Diatonicform. The following is a complete table of them in everygenus.

TABLE 14.SIX ANCIENT SCALES IN THE THREE GENERA.

{a) MIXOLYDIAN.ENHARMONIC

up I j

CHROMATIC

fDIATONIC

ENHARMONIC(b) LYDIAN.

CHROMATIC

DIATONIC

INTRODUCTION

ENHARMONIC to

CHROMATIC

DIATONIC

ENHARMONIC

CHROMATIC

—~XJ s

DIATONIC

^ * 2 e

*

\-

(d) DORIAN.

-,—«J q1 ^ —.

J • J . )

p

ENHARMONIC

CHROMATIC

—si «—|*

to

1

HYPODORIAN.

I J j J t-J


DIATONIC

\& JJ J rl

(/) HYPOPHRYGIAN.

ENHARMONIC,. ^ r

fJ J

CHROMATIC ^

DIATONIC

J -I

It is to be noted that in the Enharmonic and Chromaticscales it often appears that more notes occur than in thecorresponding Diatonic. The reason is this. If a diatonicscale exhibits, say, the combination of the conjunction e-aalong with the disjunction e-$f-b, the fixed note a of theconjunction will coincide in pitch1 with the second passingnote a of the disjunct tetrachord 4/j g, a, b; and so willnot be a different note from it according to our notation.But in the corresponding Enharmonic and Chromatic scalesthere will not be such a coincidence, and consequently ournotation is able to distinguish such notes in these genera.

22. As soon as the formal essence of these scales hadbeen established we find the Greek theorists exercised withthe question of their proper keys, in other words of theirpitch. At first sight the question seems an absurd one.In the nature of things no scale, regarded as a mere order

1 Not in function. l~ \27

\

4

\ a

INTRODUCTION

of intervals can be determined to any particular pitch; andthough practical necessities reduce the possible pitch of allscales within certain limits, they do not define the relativeposition of different scales within those limits. Let us takefor example the Lydian and Phrygian scales ; and, that ourconceptions of them may be wholly free from any admixtureof pitch relation suggested by our modern notation, let usassume as scheme of the Lydian:—

tone tone £ tone tone tone tone tone

and of the Phrygian :—

tone i tone tone tone tone \ tone tone

1 2 3 4 5 6 7 8

If then we suppose the limit of practically possible soundsto be two octaves, from

-s>-1 — ^

to

one might take as Lydian scale

and as Phrygian

in which case the Lydian is higher than the Phrygian : oragain, one might take as Lydian


and as Phrygian

—4 I

in which case the Phrygian is higher than the Lydian: or:again, one might take as Lydian

-9- - • , i - —

and as Phrygian

in which case the scales coincide in pitch.23. An explanation of the question that would naturally

suggest itself to any modern reader is that the Greek theoristsdesired to reduce these scales to segments of one universalscale, and establish thereby a theoretical relation of pitchbetween them; just as we, finding types of most of thescales of Table 14 inside the series of the white notes ofa piano, theoretically regard (c) for example as a tone above(i5). But this explanation is immediately confronted by twoobjections, each of which is fatal to it. In the first place,the Greek theorists attributed to each scale in virtue of itsformal essence an absolute ethical character, and they con-,ceived that character as dependent on its pitch. Its pitch,then, must have been something more than a mere theo-retical relation. And in the second place the answeractually given to the question is precisely the reverse ofwhat it must have been if the above explanation of thequestion were true. For the Greek theorists state that thePhrygian scale whose scheme is (c) in Table 14 is one tonenot above but below the Lydian, whose scheme is (6).

We must conceive, then, this question of the pitch of thescales as implying the possibility of determining each of

INTRODUCTION

them to a particular pitch, not arbitrary, but arising ne-cessarily from the order of its intervals; not theoretical, orrelative, but serving as the ground of an absolute ethical

. ( . character; not leading to such an order of the scales as, / would arise from the reduction of them to segments of one

1! series, but to precisely the reverse order.| i 24. To understand the possibility of such a determination

j we must take into account an important distinction between(,) ancient Greek melody, and the melody of modern music.(l We have seen that the essential feature of music is the

relation of all the notes of a scale or system to its centralpoint or tonic. To maintain the sense of this relation, it isnecessary in every musical composition, that the tonic shouldbe expressed with due frequency; and all the more neces-sary when the musical consciousness is immature. Modernmusic indeed can fulfil this requirement by means of har-mony ; and so it is not unusual to have a melody of anylength in which the tonic seldom or never occurs. But themusic of Ancient Greece, lacking the assistance of harmony,could not thus dispense with its tonic; and accordinglywe find Aristotle* enunciating the law that melody shouldconstantly recur to the Mese, as to the connecting notefrom which the scale derives its unity. Now, let us supposea singer, boy or man, or a performer on lyre or flute tohave at his disposal only eight serviceable notes; and let usimagine him to sing or play a melody in the Lydian scale.Here the Mese is third note from the top, and sixth notefrom the bottom. Consequently it lies in the higher part ofhis register, or among the higher notes of his instrument;and the melody necessarily gathering itself around this note,

i and constantly repeating it, will assume a high-pitched tone.* But now let us imagine him to pass to a melody in the

Hypophrygian scale. Here the Mese is second note from1 Problems, xix_ao.


the bottom, and seventh from the top. Therefore it lies inthe under part of his register or among the lower notes ofhis instrument; and the melody gravitating towards thisnote necessarily assumes a low-pitched character. Thusthe pitch of a Greek scale is determined not by the absoluteposition of its tonic, nor by the pitch relation between itstonic and the tonic of any other scale, but by the positionof its tonic in relation to its other notes. When for example,it is asserted that the Lydian scale is a tone higher than thePhrygian, the meaning is that, while the Phrygian tonic liestwo and a half tones from the top, and three and a halftones from the bottom of the Phrygian scale, the Lydiantonic lies one and a half tones from the top, and four anda half tones from the bottom of the Lydian scale. Thus itis seen that the relative determination of the pitch of thesescales is only made possible by the fact that each has anintrinsic pitch character of its own, consisting in a pitchrelation between its own members.

25. The relative pitch of the six scales of Table 14 maybe presented to the eye by placing them as in the followingtable between the same limiting notes, except that the Dorianand Hypodorian will extend a tone lower inasmuch as theyexceed the others by a tone.

TABLE 15.

SIX ANCIENT SCALES IN PITCH RELATION.

HYPOPHRYGIANTonic J Jr

HYPODORIANTonic

I I INTRODUCTION

MIXOLYDIAN

)

>\ I

Tonic Tonic

DORIANTonic

PHRYGIANTonic

-A—ALYDIAN Tonic

-A

I have omitted the Enharmonic and Chromatic scales inthis table, as the Diatonic are sufficient to illustrate theprinciple before us.

If we assume the pitch of the Mixolydian tonic to be $ Gwhich lies intermediate between the two Mesae G and A;the tonics of these scales taken in the above order are $ F,G,\G, A, B, 111 C. We naturally conclude that the lowestscale is the Hypophrygian, and the Hypodorian, Mixolydian,Dorian, Phrygian and Lydian follow it at intervals re-spectively of a semitone, a semitone, a semitone, a tone,a tone, a tone. When at a later time the true constructionof the Mixolydian was discovered, and its Mese was seen tobe D, its position in the pitch series was changed, and itbecame the highest of the scales. (See below, p. 128.)

26. Besides these scales, all of which are complete orcontinuous in the sense that they employ all the notesmelodically possible between their extremities, Greek artmade use at this time of certain deficient scales whichwere called transilient, because they skipped some of thepossible stopping places in their progression. The following

32


transilient scales in the Enharmonic genus are recordedby Aristides Quintilianus (Meibom, p. 21).

(a) IONIAN

0 1 J J

(b) HIGH LYDIAN

Another example is the well-known scale of Terpander[see Aristotle Probl. xix. 32 and Nicomachus (Meibom,

P- 7)]-

'$= , , 1 1 J—ri=

In the passage in which Aristides quotes these defectivescales he promises to supply on a later occasion the reasonsfor the omission of the wanting notes. Unfortunately thepromised explanation is not to be found in his extantwritings, and it is impossible for us to supply the loss. Butwe may conjecture that one cause of transilient scales wasthe adaptation of an instrument to a scale larger than thatfor which it was originally intended. Thus the scale ofTerpander would naturally find a partial explanation at anyrate in the attempt to get as much as possible of theoctachord scale

1 l

out of a seven-stringed lyre originally constructed to meetthe heptachord

J =t

33

INTRODUCTION

The Ionian scale of Aristides Quintilianus would seem tohave been obtained from the scale of two conjunct tetra-chords by the omission of the two passing notes of theupper tetrachord, and the introduction of one of the passingnotes of the disjunct tetrachord

f rIt is thus an example at the same time of deficiency and ofthe mixture of conjunction and disjunction; and the compari-son of it with the Phrygian scale supports us in our view thatthe characteristic feature of Phrygian and Ionian music alikewas the retention of the Fourth above the tonic.

27. From this point the development of the Greek musicalsystem proceeded upon lines which are easy to trace. Themost prominent moments in that development were thegrowing importance of the Diatonic genus in comparisonwith the Enharmonic and Chromatic, and the disappearanceof the Dorian and Ionian Harmonies. Thus the develop-ment was a process of simplification in which the artificialscale-readings which we have been considering were graduallyeliminated. It was seen that the section of the diatonicscale of the Aeolian Harmony from D to d (see Table 9)contains all the same characteristic features as the so-calledPhrygian scale in the same genus. Similarly the Hypophry-gian scale was seen to be the segment from G tog. Similarly,as we have already said, the Mixolydian scale was seen tobe that portion in which the Mese stands second note fromthe top. The Dorian and Hypodorian scales were deprivedof the second disjunctive tone which was their distinctivefeature, and were merged by coincidence in the one scalecalled Dorian which was the segment between E and e.Thus finally all distinctions of Harmonies perished; hence-forth all scales were but the rponoi or modes of one note-

34


series. To complete the number, the modes from Ftofand from A to a were called respectively Hypolydian andHypodorian on the analogy of the Hypophrygian. Theresults of this process of simplification are given in thefollowing table:—

TABLE 16.

THE SEVEN MODES IN THE THREE GENERA.

MlXOLYDIAN.ENHARMONIC

CHROMATIC

DIATONIC

ENHARMONIC

CHROMATIC

DIATONIC

Tonic

?=£J .i =d

Tonic

Tonic

LYDIAN.

Tonic

Tome

Tonic

J ^D 2 35

ENHARMONIC

r-9—

INTRODUCTION

PHRYGIAN.

Tonic

J J. -JCHROMATIC

Tonic

^=1=

DIATONIC

ft:Tonic

*F

ENHARMONICDORIAN.

Tonic

CHROMATICTonic

DIATONIC

ENHARMONICHYPOLYDIAN.

Tonic

Tonic . i |

^


HYPOPHRYGIAN.

J-ENHARMONIC

Tonic

HYPODORIAN.ENHARMONIC

Tome

p=i£CHROMATIC

Tonic J J |J

DIATONICTonic ,1 J J

The pitch relations of the seven modes are exhibited inthe next Table. •ti

TABLE 17.

THE SEVEN MODES (iN THE DIATONIC GENUS) REPRESENTED

IN THEIR RELATIONS OF PITCH.

MlXOLYDIAN Tonic I

INTRODUCTION

LYDIAN Tonic

PHRYGIAN Tonic

DORIAN Tonic 4-J-W—<3 'v^ m

HYPOLYDIAN Tonic-j-4-

-j f>

HYPOPHRYGIANTonic

^ = ^J

HYPODORIAN

Tonic

w^ J bJ

From this table it appears that the Hypodorian with itstonic F is the lowest of the modes, and the Hypophrygian,Hypolydian, Dorian, Phrygian, Lydian, and Mixolydianfollow at intervals respectively of a tone, a tone, a semitone,a tone, a tone, a semitone.

28. At the risk of falling into vain repetition, let us againconsider the essence of the distinction between these modes.It is not a distinction of modality such as exists betweenour major and minor scales. The_ development of GreekMusic preserved, amidst all its changes, the original tetra-chord as the permanent unit of composition. And eventhe differences that came into being through the variousHarmonies had not survived, so that the principle of con-struction remained identical in the change of mode.

38


Again, it is a distinction in the order of intervals, but onlyin so far as the several modes are different sections of onecommon whole.

Again, it is a distinction of pitch, jjut^jnot such as existsbetween our keys, for it arises immediajtejyjrqm the orderof intervals. The Mixolydian is a high mode because anymelody composed in it, whatever be the absolute pitch ofits total compass, must necessarily lie for the most part inthe upper region of that compass.

Finally, because it is such a distinction of pitch, it is alsoa distinction of ethos or mood. To understand this, let usassume that high tension of the voice is the natural expres-sion of poignant grief, an easy relaxation of it the naturalexpression of sentimentalism; let us suppose, too, that torepresent these emotions respectively a musician desires towrite two songs, neither of which is to exceed the compassof an octave. How, then, shall he bestow the requiredcharacter on each of these melodies? Evidently not bychoosing a low key for one and a high key for the other, inthe modern sense of the terms ' high' and ' low' key; forthis would imply that all first treble songs must be tragic,and all bass songs sentimental. He must, instead, leavethe general pitch of the songs undetermined, so that eitherof them may suit any voice; but he must so compose themthat the one will lie chiefly in the upper, the other in thelower region of the undetermined eight-note compass. Andthis a Greek musician could only effect by choosing, for hispathetic song, a scale in which the tonic lay near its upperextremity, and for his sentimental, one in which its positionwas the reverse \

1 Cp. Ptolemaeus, lib. ii, cap. 7 oiSi y&p iveictv rav fiapvripav tj

o(vripaiv <pojvav evpot/tev hv T^V avaraaiv TJJS leard. rbv T6VOV /MTa/9o\i}s767tvr)iiivT)V, 6ir6r( irpbs rijv Toiavrtjv 8ta<popcLv ij TUV Spyivav oKaivlirlraois ij iraXiv aveots anrapKU, iir/Sepias ye irapaMayijs irtpl ri fii\os

39

INTRODUCTION

29. At this stage the compass of the Greek scale, whosegrowth from tetrachord to heptachord, and from hepta-chord to octachord we have already witnessed, underwenta further extension. To the typical scale

« I s 1 1P s £ s I s i s

I-Jwere added at its upper extremity a conjunct tetrachord

and at its lower extremity a conjunct tetrachord and an,additional note below (called the Trpoo-Aa^avo/tevos) at theinterval of a tone

E c

The resulting scale was called the Greater Complete System.

\ dnoT€\ovp:€vr;s, orav o\ov d/iolais inrb T£>V fiapvipuvoripaiv ^ rwv i m ,\i Ttpmr dyaviGTwy Stanepaivr]Taf a\\' iveica rod xari. ri)v fiiav <psavi)v rd

• y a\nb n&\os irori fliv &irb TWV ogvripaiv rSncw &p\6ix€vov, ITOTJ Si farbTWV fiapvrlpaiv, rpmrfjv Tiva TOV qBovs ivoTe\eiv. ' N o r should w e findthat modulation of key was introduced for the sake of higher or lowervoices ; for this difference can be met by the raising or lowering of thewhole instrument, as the melody remains unaffected whether it isperformed consistently throughout by artists with high or by artistswith low voices. The object of modulation is rather that the oneunbroken melody sung by the one voice may produce a change offeeling by having its tonic (lit. ' having its beginning') now in thehigher, now in the lower, regions of that one voice.'

I 40

• \ •

• \


TABLE 18.THE GREATER COMPLETE SYSTEM WITH THE NAMES OF

ITS NOTES.Diezeug- Hyper-

HypatSn MesSn men6n bolaeSn

As will be seen from this table, all the notes of the GreaterComplete System with the exception of the Proslambano-menos were distinguished by the same names which hadbeen employed for the eight-note scale with the addition ofa term to mark the particular tetrachord to which eachbelongs. The tetrachords were named in order Hypaton i.e".'of the lowest1,'Meson i.e. 'of the middle,' Diezeugmenon2 i.e.' of the disjunct,' Hyperbolaeon i.e. ' of the highest' notes.

Side by side with the Greater Complete System therestood another scale called the Lesser Complete System, inwhich was preserved the tradition of the Ionian Harmonyand the heptachord scale. The following table exhibits itsscheme and nomenclature:—

TABLE 19.THE LESSER COMPLETE SYSTEM WITH THE NAMES OF ITS NOTES.

Hypatftn • Meson SynemmenSn

• f i I I" I l - s - I s .•§ §

1 Literally ' of the highest.' The highest or top string of the lyre

gave the lowest note. * Also called Netfln.,.

41

INTRODUCTION

30. The following table exhibits the seven modes withthe names of their notes according to the nomenclature ofTable 18:—

t

TABLE 20.

THE SEVEN MODES WITH THE NAMES OF THEIR NOTES.

Hypaton Mes8n

MlXOLYDIAN

Hy

pat

e

Par

hypa

Hy

pat

e

Mes

e

r r r f-

LYDIAN

B

Hypat8n

V

I JMesSn

13

PHRYGIAN

Mes6nDiezeug-men6n

3 B

m a^3 a I

Meson Diezeugmenon

DORIAN

i3

r r rr


Mesfln Diezeugmen8n

HYPOLYDIANI

J J JDiezeugmenSn

Hyper-bolaedn

3HYPOPHRYGIAN

HYPODORIAN

Diezeugmenon Hyperbolae6n

v|

r JThe nature of each mode as merely a segment of the

typical scale of Table 18 is here apparent; and the theoristsshowed their full recognition of this fact by extending, as isdone in the following table, each of the modes to the typicalcompass of two octaves. The result is a series of sevenscales identical in figure or order of intervals, but deter-minately distinguished from one another by the relation oftheir pitch. In other words, the modes or Tpmrot havebecome rovot or keys.

43

y •

f

INTRODUCTION

TABLE 21.

THE SEVEN KEYS.

The modes are marked off by bars.

MlXQLYDIAN

jiiLYDIAN

PHRYGIAN

DORIAN

HYPOLYDIAN

HYPOPHRYGIAN

This is a very striking change of conception. It meansthat the sense of the independent and distinct character ofthe modes was almost extinct. But this was an inevitableconsequence of musical development; for that sense pre-supposed the limitation of the scale to an octave, and this

44


limitation necessarily vanished before the widening demandsof a growing art, and the larger possibilities of more elaborateinstruments.

31. The number of the keys was afterwards, apparentlyby Aristoxenus, raised to thirteen by the addition of(1) a key at a semitone below the Phrygian, called theSecond Phrygian or Ionian; (2) a key at a semitone belowthe Lydian, called the Second Lydian or Aeolian; (3) a keyat a semitone below the Hypophrygian, called the SecondHypophrygian or Hypoionian; (4) a key at a semitone belowthe Hypolydian, called the Second Hypolydian or Hypo-aeolian; (5) a key at a semitone above the Mixolydian, calledthe Hyperionian; (6) a key at a semitone above the Hyper-ionian, called the Hyperphrygian. In this scheme theMixolydian key took the name of Hyperdorian on theanalogy of Hyperionian and Hyperphrygian. At a stilllater date two higher keys were added at intervals of a semi-tone and tone above the Hyperphrygian, and were calledrespectively the Hyperaeolian and Hyperlydian. Thus weobtain the full number of fifteen keys which we find withtheir notation in the fragment of Alypius.

In the following table for the sake of completeness andconvenience of reference, we present these fifteen keys withtheir notation1, and in the three Genera, including thetetrachord Synemmenon of the Lesser Complete System.

1 On the question of the Greek notation, the reader is referred toWestphal, Harntonik und Melopdie der Griechen (c. viii); Gevaert,Musique de VAntiquite (t. I. pp. 244 ff); Monro, Modes of AncientGreek Music (§ 27). Each sound was denoted by two characters,one for the voice, and one for instruments. The vocal characters areplainly derived from the ordinary alphabet; but both the forms andthe order of the instrumental characters raise great difficulties.

VA W

INTRODUCTION

TABLE 22.Hypat8n MesSn

§1

. E N H A R M O N I Cffi fit 1-1

Il

^ L "

CHROMATIC

(j> c P n i © H uF C u D < v > Z

3PS Awa

<t> c p n i © H uF C U D < v > Z

DIATONIC

c P M i © r uc u n < v N z

ENHARMONIC

T c n1 C D A

H A> \

CHROMATIC

o =t

DIATONIC

X T C n K I H Av\ =1 C o A < > \

X T C O K I Z AH = I C K A < C \


TABLE 22.Synemmenon Diezeugmen6n Hyperbolaedn

Pi 2

2 « I 1 Ifc 6 fi i5

A * M' © ± I' 0' H' U'\ <' V>' Z'

M' 0 A J. I' ©' H' U'H' M /> \ <' V > ' Z'

* ± M' © A M' r ©' r u-A \ T ^ / . H' < ' V N' T

^

U 5f O' X & ± K' I' H' A'Z X K' X M \ A' < ' > ' \ '

=t

U 5P O' 5K © J. K' I' H' A'Z X K' X M \ A' < ' > ' \ '

U.© O' * © O' K' I' Z' A'Z M K' X M K' A' < ' C V

47

Vi t .

INTRODUCTION

:i- I

E a

ENHARMONIC

Hypatdn

v

ft §

Mesdn

.a

/ t

25

3Pi

n <|> T T M A K Ty^ F u . = ? n - < A N

CHROMATIC

r m.n <|> r TH F IL =i n

A K^ A

rN

DIATONIC

n * Y n - M A H T

v i,

• * • { •

ENHARMONIC

rj, fS>

X (}) T O H N ZH F =1 K ^ » C

CHROMATIC

n x cj> T or *\ F =i K

H N Z

DIATONIC

n x C 0 = I Z

THE DEVELOPMENT OF GREEK MUSICSynemmenSn Diezeugmen8n Hyperbolae8n

H B<

S

« I I £ B . * IZJ y.t

B A 1 U U M ' A ' K T/ \ \ Z X X T -<'A' N'

B A X U rK ^ M' A'K' r/ \ \ Z X X T ^i'A' N'

B ^ J. U A j . M' A'H' r/ X X Z X \ T •<'>' N'

*

E A e A U * O' H 'N ' TU 1 M \ z X K' ^ ' >' C

E A O A U l O' H ' N ' Z 'U 1 M \ Z X K' ^ ' X' C

jt

E U e A U ( D O' H ' I' Z'U Z M \ Z M K' * ' < ' C

INTRODUCTION

Hypaton Mesfin

E S

ENHARMONIC•s

-*#-

O N H

^ = ^

n x n O'N HK > >

1 -1—-r -&-

n y T n o K nf t =1 3 K A >

ENHARMONIC

7 R v cL t c

P n iu D <

CHROMATIC

7 1 P V Ct- r L t c

p n iu D <

DIATONIC

7 1 R 4> C P Mi- r L F c u n


SynemmenSn Diezeugmen3n Hyperbolaeon

s «A I ft H-

zc

zc

A3

A3

— J —

— i —

X

— I -

X

—d_

rN

N

= ^ =B/

B/

— » -

A\

A\

—*—

-L\

1\

0 'K'

0 'K'

—V—

N'

N'>'

— 1 —

H'>

H'>'

—T"5—

Z A >K T B X ± O' K' H'C \ X N 7 X A K' A' > '

© H U Z E A O A ± I'V > Z C U 3 v 1 / ^ \ < '

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INTRODUCTION

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INTRODUCTION

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INTRODUCTION

32. At this stage then the musical science of Greecefound the material of all musical composition in a cer-

i tain number of two-octave scales, uniform in construc-tion, in the order of intervals, in the relation of the other

j notes to the tonic, but constituting in pitch a regular seriesI spaced by equal intervals, admitting also theoretically the1 three genera of Enharmonic, Chromatic, and Diatonic,

though the two former would seem to have fallen intopractical disuse. And these scales may be resolved intothe following elementary relations :—

(a) The relation between a note and its octave aboveor below;

;; {b) the relation of a note to its Fourth above;,', (c) the relation of a note to its Fifth below;

/[ (d) the relation of two passing notes to the extremities' ; of a tetrachord determined in so far that of the resulting

!: intervals the lowest must be less than or equal to themiddle, and less than the highest.

I The scheme of these scales, as has been already said,j; must not be identified with either our major or our minor

mode. In the Greek scale of the Diatonic genus the notesfollow one another, it is true, at the same distance as inour descending minor scale, but the 8u'ra/us or function of

[ the notes is different, and the essence of a note is itsfunction. The essential feature of our minor scale is the

1 concord of the Minor Third which makes part of its\ ! common chord; and this was to the Greek ear a discord,J that is, a sound-relation not to be immediately recognized\. or permanently acquiesced in, but demanding resolutionI and change.! 33. We have seen that in this conception of the keysj the distinction of modes is virtually ignored. But it was

destined to be revived by the revolution in musical sciencewhich was effected by Ptolemy, the celebrated mathema-tician of Alexandria. This theorist observing that, by the

! extension of the modes illustrated in Table 21, their distinc-62


tive feature of supplying certain segments of the commonscale for the use of composers and performers had beensacrificed, reduced them again to their original compass;and, to emphasize the fact that their very nature forbadetheir extension, he introduced (or made popular) a newnomenclature by which the several notes of any mode weredesignated in relation to that mode only, and not in relationto the common scale of which they were all segments.Thus the terms Hypate, Parhypate, Lichanus, Mese, Para-mese, Trite, Paranete, and Nete were employed to signifythe First, Second, Third, Fourth, Fifth, Sixth, Seventh, andEighth notes of all the modes alike. These names were dis-tinguished from those of the old system by the addition tothe former of the term Kara Oecnv 'in respect of position,' andto the latter of the term Kara Swafuv ' in respect of function.'

TABLE 23.

SEVEN MODES WITH THEIR OLD NOMENCLATURE AND

THE NOMENCLATURE OF PTQLEMY.

/card Oioiv

MIXOLYDIAN

feHard Svva/uv S

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But even in this innovation we are not justified in tracingany new sense of the possibility of different modalities.For Ptolemy himself asserts that the object of passing fromone mode to another is merely to bring the melody withina new compass of notes.

At this point we may close our investigation, as thefurther development of musical science belongs to thehistory of Modern Europe'.

34. For the sake of conciseness I have adopted in thepreceding paragraphs the somewhat misleading method ofpresenting, in the form of an historical statement, what isin reality a mere hypothesis. For the same reason I haveomitted details, and restricted myself to the most generalfeatures of the development. The latter of these deficiencieswill to some extent be made good in the notes on the textof Aristoxenus; the former demands our immediate atten-tion. Strict demonstration of the truth of our hypothesis isin the nature of the case impossible; but we must at leastexamine the rival hypotheses and satisfy ourselves that thefacts which tell fatally against them leave it unassailed.At the same time we must not be disappointed if many factsremain unexplained. In the development of any branch ofhuman activity there is much that is accidental; accidental,in the sense that the explanation of it is not to be foundinside the sphere of that activity. We shall be satisfied

MACRAN F 65

INTRODUCTION

' then if we find that our hypothesis accounts for many of therecorded facts, and is not irrefragably refuted by any ofthem ; while the other intrinsically possible hypotheses—there are but two—are put out of court by the weight ofunanswerable argument and evidence.

35. Of one of these hypotheses the essential thesis is thatthe seven modes of Table 16 differ from one another as doour major and minor scales, that is in modality, or in therelations which the other notes of the scale bear to thetonic. The tonic of each scale it finds in the fourth notefrom its lower extremity, the picrr) Kara Oimv of Ptolemy.

According to this view the seven modes and their tonicsmay be represented in the following Table. In (a) thescales are given in the Greek form, with the tonic in theFourth place from the bottom; in (b) they are given inmodern form, and start from the tonic.

TABLE 24.THE SEVEN MODES ACCORDING TO THE MODALITY

THEORY.MlXOLYDIAN

(«) Mese (b) Tonic

PHRYGIAN

Tonic J J

DORIAN

66

THE DEVELOPMENT OF GREEK MUSICHYPOLYDIAN

(a) Mese • j J (6) Tonic

J J iHYPOPHRYGIAN

{a) Mese

HYPODORIAN(a) M e s e j J J

36. We cannot deny that at first sight this theory hasmuch to recommend it. It affords an adequate explanationof the striking names bestowed upon the seven modes; forif these differed in modality, they certainly deserved distinc-tive titles. It enables us too, on the analogy of our majorand minor scales, to conceive how the Greeks might havefound in each mode a distinctive Ethos or emotional char-acter. Doubtless the objection at once presents itself thatthe ancient nomenclature of the notes recognizes no suchvariety of modality, that the note before the disjunctive toneis the Mese in every scale, no matter what its place thereinmay be. But this objection the theory finds little difficultyin answering. For it is quite permissible to suppose thatone mode, because it was most common or most ancient,or for some other reason, was regarded by the theorists astypical, and that the nomenclature of the notes, originallyapplicable to that scale only, came to be applied at a laterdate to scales of different modality. Besides we have

•seen that, in the time of Ptolemy, if not earlier, there wasa second system of nomenclature by which notes derivedtheir names from their positions in their respective scales,

F 2 67

INTRODUCTION

and according to this system the fourth note of every scalewas its Mese.

37. Nevertheless this plausible hypothesis is absolutelyuntenable, as the following considerations will show.

In the first place we must note that the modes are notthe invention of theorists, but scales in practical use. Now,it is hardly conceivable, and in the absence of evidence orparallel wholly incredible, that an early and undevelopedartistic impulse should have produced such a variety ofmodalities, so many distinct languages, as one might say,of musical expression, not distributed through differentregions and races, but all intelligible and enjoyable alike toa Hellene of Hellas proper.

In the second place, the distinction which is here sup-posed between the modes is essential not accidental, and assuch, it is wholly impossible that it should have been over-looked by the Greek theorists, who have proved themselvesin other respects the most subtle of analysts. Yet in all theextant authorities there is not one hint of such a distinction.Nay, we might go further and say that we cannot admit thishypothesis without convicting these theorists of a radicallyfalse analysis. If the tonic of the scale

i rsz:

is C, the scale must divide itself into the tetrachords

fk 1 1 1

in which G, c, d, and g are the fixed, and a, b, e, and /the passing notes. But the theorists recognize no tetra-chord of either of these forms; but insist that in all tetra-chords of which the extreme points are the fixed notes, and

68


the inner the passing notes, the lowest interval must be lessthan the highest, and equal to or less than the middle. Totake one from the countless instances we read in theJsagoge (Meibom, 3. 4) :

Tevrj 8e COTI rpta, Sidrovov, xpfijua, ap/xovia, Kai ^teXaiSeiTai TO

ixev SidVovov hrl fnev TO /3apv Kara TOVOV KCU TOVOV Kai fj/uToviov,

iirl Se TO o£t> cvavruas Kara y\[X.iToviov KO.1 TOVOV Kai TOVOV. TO

Se xpuf*a « T ' fx.€V TO fiapv Kara TpuqiUToviov Kai fjfUToviov Kai

•fj/xtToviov, 6JT* Se TO o^v cvavTtcos Kara, ^/JLITOVIOV Kai fj/jUTOViov

Kai Tpirj/xiToviov. tj 8e apfiovia eirt fiiv TO /Sapu Kara SCTOVOV Kai

StWiv Kai St'eaiv, £7rl Se TO 6£V evavrtcDS KaTa. Stecrtv Kai StWiv

Kai SLTOVOV.

Here we find a certain order of the intervals of the tetra-chord affirmed without qualification. This affirmationimplies that all diatonic scales can be reduced to com-positions of tetrachords of the form

But the scale

# jF= ° "

if C be its tonic could not be so reduced except by ananalysis extending to the superficial qualities only, andleaving the essential nature untouched.

Take again the following passage from the Isagoge(Meibom, 19^ l ) a m Se TTJS ixio~q<s Kai TS>V XOLITUIV cj>66yyo>v a i

yvoipi^ovTai, TO yap 7rais e^ei eKao"Tos a^Twv 7rpos TTJV

cpavepws ycyvtTai. ' It is from the Mese that we startto discern the functions of the other notes; for plainly it isin relation to the Mese that each of them is thus or thus;'

Or this still more striking passage from Aristotle(Problems, xix. 20):

69

INTRODUCTION

Ata TL, iav jj.lv Tts Tt]v p.ia~qv Kivrjo-y ^fnwv, dpyuocras r a s

aAAas xopSas, (cat xprJTai. TU> opyavw, ov fnovov orav Kara, TOV riys

/j.to~r]S yevrjTai <p66yyov, AVTTEI xat <£atverat dvdp/jLooTOv, dAAa.

Kai Kara rrjv aAAijv /J.e\(p8lav' eav 8e T771' Xiâvbv TJ Ttva aAAov

(j>66yyov, Tore <$>a.ivera.i Staêpctv p.6vov, orav KaKeivrj Tts

—-*H evAoy<us roBro orv//./3a£vei; TraiTa yap r a xprjora

iroAAaKts rrj jJ-io-g xprjrai, Kal iravres ol ayaOol iroirjTal

Trpos Tt]V fiea-qv aTravrwcn, KOV aireXdwo-i, Tayy

irpos Be aXXrjv ourcos oiSc/xiav. Ka.6a.irtp IK TS>V Aoycov evtaiv

eâiptOivTiov o~vv$£o~i/.<i>v OVK eariv 6 Aoyos 'EAArji'tKos, olov TO

T£ Kat TO Kai. evioi 8e ovOev Xvirovcri, Sia, TO rots //.ev dvayKarov

ctvat xpfjo-Oai TroAAaKts, «t cara t Atfyos, rots 8e [irj. OVTW KO.1 TS>V

<p66yy<ov 7] /xfcrr] aicnrep (ruvSca/ios ecrrt, Kat yoiaAtoTa TS>V Ka\S>v,

8ta TO 7rXetcrTaKis cviwapêiv TOV <f>66yyov avr^s-

[Translated by Mr. Monro, Modes of Ancient Greek Music,p. 43: ' Why is it that if the Mese is altered, after theother chords have been tuned, the instrument is felt to beout of tune not only when the Mese is sounded, but throughthe whole of the music—whereas if the Lichanus or anyother note is out of tune, it seems to be perceived onlywhen that note is struck? Is it to be explained on theground that all good melodies often use the Mese, and allgood composers resort to it frequently, and if they leave itsoon return again, but do not make the same use of anyother note? Just as language cannot be Greek if certainconjunctions are omitted, such as re and Kal, while othersmay be dispensed with, because the one class is necessaryfor language, but not the other; so with musical sounds theMese is a kind of "conjunction," especially of beautifulsounds, since it is most often heard among these.']

It is hard to imagine how the nature of a tonic could bemore clearly and truly indicated than it has been by theauthor of this passage in his description of the Mese. Andas he expressly states that the Mese is the centre of unity

70


in all good music, he must have recognized only onemodality. An attempt has, indeed, been made to evadethis conclusion by supposing Aristotle to refer not to thepear) Kara Swa/uv, but to the fj,eo~i] KOTO. Oea-iv. But thissupposition is quite untenable, not only because the nomen-clature Kara Ocaiv in all probability was the invention ofPtolemy, but also for this much more convincing reason thatthe terms Kara. Bvvafuv and Kara Oicnv seem framed with thedirect intention of precluding such a supposition. Thefiia-rj Kara Bktnv is merely the note which is located in thecentre of a group; the p-ecrq KOTO. Swa/«v is the note whichdischarges the function of a centre of unity to a system.The first is a mathematical, the second a dynamical centre.When, therefore, the whole train of Aristotle's reasoning isbased on his conception of the Mese as the connectingbond of musical sounds, can there be any manner of doubtto which Mese he refers ?

38. Again, we have seen that one attractive feature of thishypothesis is that it offers a plausible explanation of the factthat the Greeks attributed a distinct Ethos or emotionalcharacter to each of the modes. It now remains to showthat this plausible explanation is refuted by the express state-ment of the authorities as to the conditions of this Ethos.

Consider the following passages:—(a) Plato, Republic, iii. 398 E:

Ttves ovv 6pr)vdi)8eis ap/xoviai; . . . MI^OAUSIOTI, i<pi], KOI

Ti Kai ToiavTai Tivis-—TiVes ovv /xaXaKai re Kal

ai Totv ap/jLovimv; ' l ao r i , rj 8' os, t a t AVSIOTI, ainves

oj. KaAovvTac.

' What then are the scales of mourning ? ' ' Mixolydian,'said he, ' and High Lydian, and some others of thesame character.' 'Which of the scales then are soft andconvivial?' 'The Ionian,' he replied, 'and Lydian, suchas are called slack' (i.e. low-pitched).

INTRODUCTION

(b) Aristotle, Politics, vi (iv). 3. 1290 a 20:'OfjLO&os 8' e^ei K<XL irepl TOLS apfxxivia's, <5s <f>ao~l rives' Kat yap

e/cei TLOCVTCLL eiSr] 8vo, rr/v Awpicrri /ecu r^v Qpvyiari, TO. 8e aAAa

a~vvrd.yiJ.aTa TOL //.ev Acopia r a Se <frpvyia KaXovmv. fiLaXurra /xev

ovv eiwOaa'iv ovrais viroXa/jL^dveiv irepl ra>v iroXiTeiav a.\r)6ecrTepov

8e Kal /34\TLOV OJS ^/iets SieiAo/AEv Snorv 17 /U.ias ovcnys rijs KaXais

avveanrjKVLa's r a s aAAas cu/at TrapeKfidcreis, r a s ju,ev -ri}s ev K£-

KpafjLevrjS ap/xovias, Tas 8e r^s apt'crnys 7roXtT€tas, oXiyap^iKas juev

ra s arvvTovunipa'i Kal SeairoTiKoiripa';, r as 8' dveiyiicVas /cai

/xaAa/cas Sr/fioriKas.

' Some would have it that it is the same in the case ofscales; there too they posit two species, Dorian andPhrygian, and all other systems they class as either one orthe other of these. Such is the common view of forms ofgovernment. But our analysis was truer and more satis-factory, according to which of perfect systems there are butone, or two, while the rest are deviations, in the one casefrom the scale of proper composition, in the other from thebest possible government; those that incline to high pitchand masterfulness, being of the nature of oligarchy, thosethat are low in pitch and slack being of the nature ofdemocracy.'

(c) Aristotle, Politics, v (viii). 5. 1340 a 38 :Ei#vis yap rj TG>V apfjioviSiv 8teo"Ti//ce <£wis wore aKovovras

aXX(os 8taTt#ecr#ai Kal firj rbv avrov ^x€LV Tpovov irpos

avrtov, dAAci 7rpos fiikv ivias o8vpTiK(DT€p<os Kal

fi.a.Wov, olov Trpos TTJV MI£OA.DS(.<XTI Ka\ovji£vr)V, 7rpos 8e r a s

j«.aXaK(0T6pa)S "rqv SidVoiav, olov irpbs r a s dvet/tevas.

' To begin with there is such a distinction in the natureof scales that each of them produces a different dispositionin the listener. By some of them, as for example theMixolydian, we are disposed to grief and depression; byothers, as for example the low-pitched ones, we are dis-posed to tenderness of sentiment.'

72


(d) Aristotle, Politics, v (viii). 7. 1342 b 20 :Oiov rots d.Tr€iprjKo<Ti Sia xpovov 011 paSiov aSeiv r a s OVVTOVOVS

apixovias, dAAa r a s dvet/AEvas ^ caucus virofiaWzt. TOIS T^AIKOUTOIS.

' Thus for those whose powers have failed through yearsit is not easy to sing the high scales, and their time of lifenaturally suggests the use of the low.'

From these passages it is clear in the first place that theEthos of the modes was dependent on their pitch, and inthe second place that the pitch on which the Ethos dependedmade them severally suitable for voices of a certain class orcondition. But, if the distinction between the modes isone of modality in our sense of the word there is no reasonin the nature of things why they should differ in pitch at all.And though we might assume for them a conventional dis-tinction in pitch by regarding them theoretically as fragmentsof one typical scale shifted from one point of pitch toanother, the assumption would not help us to meet the facts.A conventional distinction of pitch cannot be the basis ofan absolute distinction of Ethos, nor can it account forthe practical suitability of certain scales to certain voices.

39. The weight of these arguments is so irresistible thatwe are not surprised to find Mr. Monro substituting a newhypothesis in his Modes of A?uient Greek Music. Un-fortunately this substitute, though it embodies one mostimportant truth, is open itself to objections no less grave.The fundamental principle from which Mr. Monro's theorystarts is that the Greeks knew but one modality, that is oneset of relations between the notes of a scale and its tonic;and the establishment of this principle by argument andevidence is the great contribution of Mr. Monro to the studyof Greek Music. Proceeding from this principle, he main-tains that the terms Dorian, Lydian, Phrygian originallydesignated merely so many keys, that is so many scalesidentical in their intervals and in the order of them, but

73

INTRODUCTION

differing in pitch. The connexion of these names withcertain modes or scales of different figures arose in hisopinion at a later period from the fact that practical limita-tions restricted composers and performers to a certaincompass, and the name of the key was transferred to theparticular order of notes which it afforded within that com-pass. Thus the term Mixolydian and Dorian originallydenoted the two keysMIXOLYDIAN

r PandDORIAN

Now suppose that a composer orperformer was restricted to the par-ticular compass 2SE

Within that compass the Mixolydian key would give theseries

which is of the form

-3±L

and the Dorian the series

74


which is of the form

f rand in this way the terms might come to be applied tocertain orders of intervals.

40. The objections to this theory are many and fatal. Atthe very outset, we are repelled by the supposition that sucha striking nomenclature should have been adopted to denotesuch a superficial difference. Again, how are we to explainthe distinct ethical character of the scales ? If the pitch ofthe Dorian, Phrygian, and other keys be only determinedby their relation to one another, their emotional charactermust also be only relatively determined; if, for example,high pitch is the natural expression of pathos, we can say ofthe higher of two keys that it is more pathetic than thelower, not that it is absolutely pathetic; yet the Greeksalways attribute an absolute character to each of the scales.It would follow that the pitch of the keys must have beenabsolutely determined. But of such absolute determinationthere is not a word in our authorities. Even if we assumeit, in spite of their silence, surely it cannot have been exact.Absolute and exact determination would presuppose theuniversal recognition of a conventional standard embodiedin some authorized instrument, or expressed in a mathe-matical formula; the first alternative is precluded by itsabsurdity, and there is no evidence for the second. Butif the determination, though absolute, was not exact, whilewe might admit an absolute difference of Ethos betweena scale of extreme height and one of extreme depth, therecould have been no such absolute difference between scalesseparated only by a. tone or semitone ; for let there be buta slight variation between the tuning of one day and another,and the Phrygian of to-day will be the Lydian of to-

75

INTRODUCTION

morrow. And even if we make Mr. Monro a present of allthese objections, and grant the existence in ancient Greeceof an absolute and exact determination of pitch, will anyone venture to affirm that the difference of a tone orsemitone in the pitch of two keys could result in such anantagonism in their moral effects, that Plato should haveretained one of them as a valuable aid to ethical training,while he banished the other relentlessly from his idealrepublic ?

Again, it is not uncommon1 to find the names of musiciansrecorded as inventors of certain scales. Would Mr. Monrohave us believe that the only claim of these musicians tothe regard of posterity is that they stretched the strings oftheir lyre a little more loosely or a little tighter than didtheir predecessors ?

41. Returning now to the hypothesis which we have aboveproposed we shall consider a few passages which seem tooffer striking confirmation of its truth.

(a) Heraclides Ponticus apud Athenaeum, xiv. 624 c :'HpaxAetS^s 8' 6 TIOVTLKOS iv TpiVa> Trepi Mouca/ojs oi8'

ap/xoviav <f>rjo~l Seiv KaXcIo"0ai TT/V ^pvywv, KaOairep ov$e TTJV

A.v8iov, dp/Aoytas yap elyai rpeTs" rpia. yap KCU yevecrOax 'EXXiJi/tov

yiv-q, Awptets, AioXeis, "Itovas . . . (625 d) Ka.Ta<f>povrpiov ovv TWV

Tas fjLev KO.T cTSos Sta<£opa.s ov 8vva/j.evmv Oecopelv, eiraKokovdovvrtov

1 For example see Plutarch, de Musica, 1136C-D 'ApuiT6£evos S«

fpTJGl 1S,aTT(p(tJ TTpWTTjy ilipatjQai TTjV MifoXuSiffTt . . . tV S^TOtV ^(TTOptKOlS

Tfjs'ApixovucijsIIv6oK\ei57]v (prjal rdv avXrjrfiv evpeTTjv avrijs yeyovivcu . . .

dXAi ixty Kal TZ)V 'ETravet^ivrjv AvSiori, Tfnep havria rj) MifoKvSiari, tmpa-

Tr\T]ffiav ovaav TTI 'Id5i virb Aafiwvos £vpT}G&ai <f>a(Ti TOV 'AOrjvaiov.

^ 'EiravetficvT] AvSteri, or low-pitched Lydian, is probably the same

as the later Hypolydian. By the Ionian is probably meant the Hypo-phrygian. The Hypolydian in its schema, that is in the position ofits tonic in relation to the other notes, is very similar to the Hypo-phrygian and most unlike the Mixolydian.

76


8e Trj T5>V <f>66yy<i>v O^VTYJTI (cat f3apvTr]Ti /cat Ti#e/i.ev<ov "Yirep-

[JLI£O\V$LOV apjxoviav Kal ITOXLV virtp ravrq^ aXXrjV . . . Set Se

TTJV apfioviav eTSos %Xeiv %@ovs V iraOovs.

' Heraclides Ponticus in the third book of the de Musicaasserts that the term apfiovia should not be applied to thePhrygian or Lydian scales ; that there are three Harmonies,as there are three tribes of Hellenes—Dorians, Aeolians,Ionians . . . We must conceive a very low opinion of the'theorists who fail to detect difference of species, while theykeep pace with every variation of pitch and establish aHypermixolydian Harmony and again another above that.. . . But every Harmony should possess an ethical oremotional character peculiar to itself.'

Mr. Monro, by a curious misapprehension, as I think, ofthis passage, has accused Heraclides of carrying Hellenicexclusiveness to the extreme of refusing the title of apix.ovl.aito the oriental* scales of Lydia and Phrygia. But themeaning of Heraclides' statement is that the seven scales'of Table 16, inasmuch as they are only so many segmentsof the one scale, are all instances of the one apiiovia ormethod of formation, and so cannot properly be termed somany ap/wviai. It was a different matter, he says, with thethree ancient Harmonies, the Dorian, Ionian, and Aeolian.These were really distinct adjustments; they were scales,the principles of whose construction were essentially dis-similar. Difference of pitch, he proceeds to say, does notconstitute a new apuovia.

(P) Aristides Quintilianus (Meibom, 21. 11) :To JU.€V ovv AxJSiov Siacrr^ytia o~wtTiQeo~av IK Sictrecos, Kal

SITOVOU, Kal rovov, Kal Siecrews, /cat SieVeais, Kal SITOVOU, Kal St€-

crecus' Kal TOVTO f/ikv rjv TeXeiov <xvo"rqfna, TO 8e Awptov £K TOVOU,

Kal 8i«rea)S, Kal Sieo-EM?, /cat SITOVOV, /cat TOVOU, Kal Si«r£<os, Kal

8i«raos, /cat SITOVOV rjv Se /cat TOOTO rovai TO 8ta iraoStv uTrepe^ov.

TO 8e Qpvyiov £/c TOVOU, /cat Sito-ews, /cat Stecreos, /cat SITOVOU, /cat

77

INTRODUCTION

TOVOV, Kai 8teo-£cos, /cat Siccrecos, /cat TWOV ^V 8e icat TOVTO TeXeiov

Sta w a o w .

'TheLydian scale they'[i.e. ancient musicians] 'composedof diesis, ditone, tone, diesis, diesis, ditone, diesis; thiswas a complete scale. The Dorian was composed of tone,diesis, diesis, ditone, tone, diesis, diesis, ditone; this scaleagain exceeded the octave by a tone. The Phrygian wascomposed of tone, diesis, diesis, ditone, tone, diesis, diesis,tone ; this too was a complete octave.'

(c) The Isagoge, (Meibom, 20. 1)*:SI Svo, 6£vTepos KOU /Sapirrepos, os Kai AtoAtos KaAetTar

Svo, 6 [lev fiapvs, os Kai 'iao-rtos* 6 8' ofvs. A<opi09

cts. 'YTTOXVSLOI 8VO' ofurepos KaX ySapvTtpos os Kai "YTroatoXios

'YTro(j>pvyioi Svo, wv 6 ySapurepos Kat 'Y'7rotao"Ttos

'Two Lydian keys, a higher, and a lower, also calledAeolian; two Phrygian, one low also called Ionian, andone high; one Dorian; two Hypolydian, a higher and alower, also called Hypoaeolian; two Hypophrygian, ofwhich the lower is also called Hypoionian.'

It appears from passage (a) that there was a period inthe development of the Greek musical system when thereexisted three distinct Harmonies, i. e. three scales dis-tinguished by the different methods in which their unitswere put together; and that these three Harmonies weretermed Dorian, Aeolian, and Ionian. Now the units ofGreek music are the tetrachords; and we cannot conceivehow tetrachords could have been put together except bythe method of conjunction, the method of disjunction, themethod of alternate conjunction and disjunction, or a com-bination of two or more of these methods. It is probablethen that the three Harmonies were the products of thesethree methods. But the characteristic feature of theDorian scale of Aristides Quintilianus (see passage (?>)) is

78


that it contains two disjunctive tones in succession; fromwhich we may reasonably conclude that the Dorian Harmonywas the method of disjunction.

Again in passage (c) we find that when the number ofthe keys was raised from seven to thirteen, the terms Ionianand Aeolian were employed to denote respectively theduplicate Phrygian and Lydian keys. This implies a con-nexion for purposes of music between the terms Ionianand Phrygian, and between the terms Aeolian and Lydian.But the Lydian scale of Aristides is plainly a scale ofalternate conjunction and disjunction; and the characteristicfeature of the Phrygian1 is that it introduces the Fourthabove as well as the Fourth below the tonic; in otherwords, that it retains the essence of conjunction. It seemsa fair inference then that the Ionian and, Aeolian Har-monies are identical respectively with the method ofconjunction, and the method of alternate conjunction anddisjunction.

(d) Plutarch, de Musica, 1137 D : BrjXov 8e mi TO wept rwvVTrarusv o n ov $1 ayvouxv airu^ovTO iv TOTS Acopiois TOS Terpa-

1 The mistake has commonly been made of explaining the upper

tetrachord of the Phrygian scale pro—i-3 f "T T F"

as a mixture of enharmonic and diatonic notes, d being the second

passing note of the diatonic tetrachord M) f

But this interpretation ignores the distinction between fixed andvariable notes, a distinction which Aristoxenus and other theoristsare never weary of repeating. If d in the Phrygian scale weremerely a passing note of the diatonic tetrachord, its position wouldnot be exactly determined ; and as the lowest interval of the scaleis exactly determine i as a tone, the compass of the whole could notbe definitely estimated as an octave. Besides, we should then havethree passing notes in succession, and two Aixaroi; the impossibilityof which will be obvious to any one who has grasped the Greekconception of a note as a Svvafus, not a point of pitch (see § 8).

79

INTRODUCTION

)(6pSov TOVTOV' avTLKa km TSV XonrSv TOVIHV i)(pu>vro, StjXovoTt

ctSoVes" Sta Se TTJV TOV r)6ovs <f>v\a.Kr)v a<f>rjpow iirl rov Acoptov

TOVOV, TLfurnvre^ TO KOXOV avrov. ' Wi th regard, too, to t he

tetrachord Hypaton, it is plain that it was not throughignorance that they' (ol iraXaioi, the ancients) 'abstainedfrom this tetrachord in the Dorian Scale. The fact thatthey employed it in the other keys is proof that they wereacquainted with it. But they dispensed with it in theDorian because they respected the beauty of that key, andwere determined to preserve its character.'

We saw above (§ 29) that to the early scale of the form

fit

was added at «a later period a conjunct tetrachord at its

(3 —. i l l and that thislower extremity

addition was called the tetrachord Hypaton. In the pas-sage before us Plutarch informs us that for some time anexception was made in the case of the Dorian scale becauseit was felt that such an alteration would imperil its Ethos.Mr. Monro endeavours to reconcile this statement with hishypothesis of the keys by pleading that the character ofmoderation inherent in a key of middle pitch would besacrificed by the addition to it of a series of lower notes.To which we may reply ' Would not the pathetic character ofa high pitched scale suffer equally from such an extension?'But on our hypothesis Plutarch's statement is quite in-telligible. Obviously the distinctive character of a disjunctscale would perish on the addition to it of a conjuncttetrachord.

(e) See again the passage from the Politics of Aristotle,v (viii). 7. 1342 b, quoted in § 38.

80


Aristotle here recommends the use of certain scales tovoices that are impaired by age. What then must hayebeen the special property of these scales, that justified thisrecommendation? Evidently not a particular modality,for one order of intervals does not involve a greater strainon the voice than another. Nor can it have been a meredifference of key or general pitch. How should the samekeys suit the failing tenor, and the failing bass ? The pro-perty of these ' old men's scales' must have been such thatthe melody composed in them, whatever the pitch limits ofits compass might be, made but a slight demand on thephysical powers. And this is the essential property whichour hypothesis attributes to the Hypolydian mode forexample. For whether that mode occur as the scale

~ T°™ i i I ikJ J

mfor a treble voice; or as the scale

. Tonic

J

for a tenor voice; or as the scaleTonic

for a bass voice; it necessarily results from the position ofits tonic that any melody composed in it must gravitatetowards its lower notes.

42. Many persons are under the delusion that to solvethe problem of ancient Greek music means to bring to lightsome hitherto overlooked factor, the recognition of which

HACRAN Q 8 l

INTRODUCTION

will have the effect of making the old Greek hymns as clearand convincing to our ears as the songs of Handel andMozart. Very curious is this delusion, though not astonishingto any one who has reflected on the extraordinary ignoranceof mankind about the most spontaneous and universallybeloved of the arts, and their no less extraordinary in-difference to its potent effects on the mental and moralcharacter. Who would take up a book on Egyptian orChinese painting in the expectation of learning from it somenew knack of placing or viewing an Egyptian or Chinesepicture, by which it will come to please the eye as much asa Titian or a Turner ? Who would demand from metricalscience that it should supply us with some long-lost spell bythe magic of which we shall discern in

fil) tpvvai rbv awavra vucq \6yov rb 8', In-ei <pavfi,

fiijvai KITO' 6ir60iv irep ijisei no\v Seirepov iis Tax'"™

the movement of'We are such stuff

As dreams are made on, and our little lifeIs rounded with a sleep.'

Yet no less absurd is the supposition that any, even themost perfect, knowledge of facts could lead us to the loveof these unfamiliar old-world melodies.

To some cold appreciation of their form we may perhapsattain if we are willing—sacrilege and destruction as it mayseem—to strip them of those external accidents which arepeculiar to the music of their age, and invest them insteadwith the habits of modern fashion. Otherwise the noveltyof the unfamiliar features will engross our ear to theexclusion of the essential form. To render an ancientmelody note for note is to render it unfaithfully to earsunaccustomed to its dialect; just as to translate an ancientpoet word for word is to misrepresent him, inasmuch as theattention is thereby misdirected -away from the sense to

82


the strange idiom. Nay, further, as a literal translationmay often give a directly false impression of the meaning,so strict adhesion to the notes of a foreign melody willoften lead us astray as to its essential form. As Aristoxenuswould say, in attempting to preserve the pitch, we aresacrificing the all important SiW/xt?. If, for instance, weexpress the Greek enharmonic progression to the tonicthrough Hypate, Lichanus, Mese, by

0 i

not only are our ears revolted by the unwonted progression,but we are even distorting the real form of the melody.For, to take one point only, the Lichanus being the highestof the passing notes to the tonic from the Fourth below isfor the Greek ear the next note to the tonic ; while we feelthat in passing from F to A we are skipping several notes,which the melody might have employed.

Let us apply, then, this method of paraphrase to thefamiliar Hymn to the Muse, one of the compositions ofMesomedes, a Cretan musician who lived in the reign ofthe Emperor Hadrian. The words and ancient notation(as far as it is extant) of the hymn are as follows :—

C Z Z <D <D <D C C"A-u-fic MoO-ffo noi <pi-\i]

I (DM M(io\-nqs b" i/iijs Ka • rip-xov,

Z Z Z E Z HH Iav -pt] Si aSiv dn i\-a(-a>y

M Z H I (DC PMcDCe - p d s <ppt - vas So- vt - I - T « I

C PKoA-Ai

M-6-

Pvet

c- a

G

CD Cao-<pa,

2

INTRODUCTION

y

OHpov a

RKal

MAa-

M(V-

C C C C C "- aiv vpo -Ka-6a-yi -

(b C(TO - <pi

1 E Zrows y6 - ve,

1 Z MV € f S

1jrap

P M 1wa - TO-&6

r M

1Tl

M

P

C/10t

R cbre pir - vSi'

C MIlat - av,

We shall (a) substitute for the Greek modality our majorscale; (l>) substitute Diatonic notes for those of othergenera; (<r) add simple harmonies1; (d) make slight altera-tions in the melody so as to preserve as easy a progressionin our major scale, as is the original progression in theGreek scale.

HYMN TO THE MUSE.Slow

"A - €i - 8e liov - aa

J 1 J Ji9—r

A J«•*/£-

SI c£n> d7r' d \ - ai -

1 Professor Prout has supplied the harmonies ; but he is not other-wise responsible for this well-intended mutilation.

84


e - pels <ppi-vas So - vfi - rot KaA-At - 6 -

S^S^ r r r r r i ir r7T€t - a co - <£><£, /iou - tfaJv irpo'icaO - a - y4 • TI T€p - WUJV

«

Jl-'P I

cro - 0 j /«/ - (TT0-8<i - ra, Ao - rofe y6-ve,

Jj J. i AA ^> - At • e

Ua -1 - <iv, (i - fifv - us nap - ta - T& /tot.

X"

INTRODUCTION

B.—ON ARISTOXENUS AND HIS EXTANT WORKS.

I . Our knowledge of the musical theory of AncientGreece we owe almost entirely to Aristoxenus, or the Musi-cian (such is his regular title in ancient writers). This philo-sopher was born1 in Tarentum, and received his earliestinstruction from his father Spintharus (alsq called Mnesias),a well-known musician of that town, who had travelledmuch, and come into contact with many of the great menof the day, and, among others, with Socrates, Epaminondas,and Archytas. Some part of the youth's life was spent inMantinea, the inhabitants of which city were remarkablyconservative in their musical tastes; and it was probablyfrom this sojourn, as well as from the teaching of Lamprusof Erythrae, that he derived his intense love for the severityand dignity of ancient art. On his return to Italy hebecame the pupil and friend of the Pythagorean, Xeno-philus of Chalcis. Something of the austerity of this schoolseems to have clung to him to the last; he bore, forexample, the reputation of having a violent antipathy tolaughter ! We next find him in Corinth, where he wasintimate with the exiled Dionysius. From the lips of thetyrant he took down the story of Damon and Phintias,which he incorporated in his treatise on the Pythagoreans.Lastly we hear of him as Peripatetic and pupil of Aristotle.His position in this school must have been one of import-ance ; for he entertained hopes of succeeding the master,and his disappointment and disgust at the selection ofTheophrastus betrayed him into disrespectful languagetowards the mighty dead. Indeed, if report speaks truly,want of reverence must have been his besetting sin; he

1 For everything that is known about the life of Aristoxenus, andfor the references to the ancient authorities, see the excellent articlein Westphal's Aristoxenus, vol. ii, pp. i-xii.

86

ON ARISTOXENUS AND HIS EXTANT WORKS

would seem to have consistently undervalued Plato, and tohave maliciously propagated scandalous stories, which hehad gleaned from his father, about the domestic life ofSocrates. Besides his works on musical theory he wrotephilosophy and biography.

2. The signal merits of this philosopher do not flash uponus at the first reading of him. The faults of his style are soglaring—his endless repetitions, his pompous reiterations of' Alone I did it,' his petty parade of logical thoroughness,his triumphant vindication of the obvious by chains ofsyllogisms—that we are apt to overlook the services whichsuch an irritating writer rendered to the cause of musicalscience. And yet these services were of great importance ;for they consisted in no mere improvement of exposition,in no mere discovery of isolated facts, or deeper analysisof particular phenomena, but, firstly, in the accurate deter-mination of the scope of Musical Science, lest on the onehand it should degenerate into empiricism, or on the otherhand lose itself in Mathematical Physics; and secondly, inthe application to all the questions and problems of Musicof a deeper and truer conception of the ultimate nature ofMusic_ itself. And by these two discoveries it is not toomuch to say that he accomplished a revolution in thephilosophy of the art.

Until Aristoxenus appeared upon the scene the limits ofMusical Science had been wholly misconceived. Thereexisted, indeed, a flourishing school of Musical Art; therewas conscious preference of this style of composition tothat; of this method of performance to that; of this con-struction of instruments to that; and the habits formed bythese preferences were transmitted by instruction. Tofacilitate this instruction, and as an aid to memory, recoursewas had to diagrams and superficial generalizations; butwith principles for their own sake the artist, empiricist as he

INTRODUCTION

was, did not concern himself, and it is with principles fortheir own sake that science begins.

Over against these empiricists there stood a school ofmathematicians and physicists, professing to be studentsof music, and claiming Pythagoras as their master, who werebusied in reducing sounds to air vibrations, and ascertainingthe numerical relations which replace for the mathematicalintellect the sense-distinctions of high and low pitch. Herewe have a genuine school of science, the soundness ofwhose hypotheses and the accuracy of whose computationshave been established by the light of modern discovery.Nevertheless, musical science was still to seek. For if theartists were musicians without science, the physicists andmathematicians were men of science without music. Underthe microscope of their analysis all musical preferences arelevelled, all musical worth is sacrificed ; noble and beautifulsounds and melodies dissolve, equally with the ugly and base,into arithmetical relations and relations of relations, any oneof which is precisely as valuable and as valueless as any other.True musical science, on the contrary, accepts as elementsrequiring no further explanation such conceptions as voice,interval, high, low, concord, discord; and seeks to reducethe more complex phenomena of music to these simpleforms, and to ascertain the general laws of their connexion.Yet, while it will not be enticed to transgress the limits ofthe sensible, within those limits it will aim at thoroughnessof analysis, and completeness of deduction. Such is thescience which Aristoxenus claimed to have founded.

And with this clearer perception of the scope of musicalscience there came also a deeper conception of music itself.So busy were the Pythagoreans in establishing the merephysical and mathematical antecedents of sounds in general,that they never saw. that the essence of musical sounds liesin their dynamical relation to one another. Thus they

88


missed the true formal notion of music, which is everpresent to Aristoxenus, that of a system or organic wholeof sounds, each member of which is essentially what it does, ;

and in which a sound cannot become a member becausemerely there is room for it, but only if there is a functionwhich it can discharge. ___

The conception, then, of a science of music which will âccept its materials from the ear, and carry its analysis no \further than the ear can follow; and the conception of '<a system of sound-functions, such and so many as the jmusical understanding may determine them to be, are the twogreat contributions of Aristoxenus to the philosophy of Music.

3. Suidas credits Aristoxenus with the authorship of 453volumes. Of these nothing considerable has survived savean incomplete treatise on Rhythm, and the so-called 'ThreeBooks of the Harmonic Elements.' That the last title is anerroneous one has been established by Marquard andWestphal, who appeal to the following facts among others.

(a) Porphyry cites the first of these books as TrpcSros ireplap^wv, and the second as 7rpa>Tr>s TO>V a.pfj.oviKS>v oroijfeuav.

(£) Though the usual titles of these three books aresupported by most of the MSS., there are some importantexceptions. The Codex Venetus (M) has for initial titleof the first book 'Apiaroîvov Trpb TSIV apjjjoviKwv aroiêimv

(though a later hand has crossed out irpb T5>V and addedTTpS>Tov), and similarly the Codex Barberinus reads irpb TS>VapfwvLKwv TrpSyrov. The concluding inscription of this bookin M is 'Apurroêvov TO Trpwrov aroixeiov, but the third handhas written Trpb T5>V over irpwrov, and o> over the latter o oforoixeiov. In the same MS. the title of the second book is'Apurro£evov apfuovitdav orotêtW (the u> in the latter wordsis a correction of the second hand for o) /?, but an a hasbeen written through the /J by a later hand; the concludinginscription of the same book is 'ApLorog&ov <m>ix«W apfwvt-

89

INTRODUCTION

KU>V a, but the a is crossed out, and j3 written beside i t ; theheading of the third book is 'Apiorofevov crroi^Cmv apfx.oviK£>v/3, with the /3 crossed out and y written beside it.

(c) The text of the ' Three Books' contains matter ofthree distinct classes ; firstly, introductory matter or exposi;tion of the scope and divisions of the subject; secondly,general principles or expositions of primary laws and facts;thirdly, propositions of details, following one another inlogical order like the o-Toixeia or Elements of Euclid.

(d) We find in several cases more than one treatment ofthe same subject.

(e) We find certain inconsistencies. Thus jj.zkoiroi.ia., ormusical composition, is sometimes included in, and some-times omitted from, the list of objects with which Harmonicscience is concerned.

Westphal, not content with negative criticism, has en-deavoured to reconstitute from the extant fragments thescheme of three works of Aristoxenus on the Theory ofMusic; each containing a Trpoot/xtov or introduction, a state-ment of dpxa' or principles, and a system of a-Toi eTa orelementary propositions. His idea may well be correct;but the result is so unsatisfactory from the utterly frag-mentary nature of the data, that we need not enter into thedetails of his attempt.

4. The most important MSS. of the ' Harmonic Elements'are the following :

The Codex Venetus (in the Library of St. Mark), writtenby one Zosimus in Constantinople in the twelfth century.It has been corrected by many hands; but two of especial im-portance have been identified, one older than the fourteenthcentury (denoted in the Critical Apparatus by Mb) and oneof that century or later (Me). Ma denotes the first hand;Mx a hand not identified; (a later manuscript in the samelibrary is denoted by m):

90


The Codex Vaticanus of the thirteenth and fourteenthcenturies, which appears to have been directly copied fromM. In the Critical Apparatus the first hand of this MS.is denoted by Va, a corrector by Vb :

The Codex Seldenianus (in the Bodleian Library), datingfrom the beginning of the sixteenth century. It is denotedby S in the Critical Apparatus. Mr. H. S. Jones hasdemonstrated (Classical Review, VII. io), that thisMS. depends closely on V throughout, though its exactrelationship is hard to determine, since in some places itadheres to the original reading (Va), and in others adoptsthe corrections and additions of Vb. I have collated thisMS. afresh:

The Codex Riccardianus (in Florence) of the sixteenthcentury (collated by van Herwerden), which shows relation*ship with Me :

The Codex Barberinus (in the Bibliotheca Barberina inRome) of the first half of the sixteenth century. Frompage 95 to 121 of the text this MS. shows agreement withMe and R ; but from page 121 on, it appears to have beencopied from V after the corrections of Vb. This MS. hasnumerous corrections in the margin, which, however, are inthe same hand as the original:

A Codex of great value which belonged to the Library ofthe Protestant Seminary at Strassburg, and perished whenthat building was burned down by the German- troops onthe night of August 24,1870. It was collated by M. Ruelle,who published the results with his translation of Aristo-xenus. It seems to have been independent of all the otherMSS. that we possess, none of which can be regarded eitheras its ancestor or its descendant. M. Ruelle attributes itto the fifteenth century. It is denoted by H in the CriticalApparatus. \

The 'Harmonic Elements' were first published at Venice-;91

MI T ' - - • •

4/ '"

INTRODUCTION

in 1542, in a Latin translation by Antonius Gogavinus,a worthless work crowded with errors. The first editionof the Greek was printed in Leyden in 1616 by Elzevir,with the corrections and commentary of Johannes Meursius,who displays gross ignorance of the general theory of Greekmusic, and of the doctrine of Aristoxenus in particular..Meibom's well-known edition with the Greek text, Latintranslation, and commentary, was published in 1652 atAmsterdam by Elzevir. The text of this work is poor andthe translation often obscure, but the commentary is valuable,and shows a thorough acquaintance with the system ofAristoxenus. Paul Marquard's edition with a German trans-lation (so literal and servile as to be wholly useless) wasissued at Berlin in 1868. The chief value of this work liesin the new light thrown on the text by the author's collationof the Codex Venetus. Westphal's exhaustive but diffuseand garrulous book on Aristoxenus was published at Leipzigin two volumes, the first in 1883, and the second in 1893,after the author's death. It is most valuable as a storehouseof facts. M. Ruelle's French translation of Aristoxenus,to which I have referred above, was published in Paris in1870.

The following authors and works are referred to in thepresent volume:

The TZlaaywyr) d.pfwviKrj (referred to in this volume asIsagoge) formerly attributed erroneously to Euclid (and soinscribed in Meibom), but probably the work of one Cleon-ides, of whom nothing else is known. It exhibits a strongresemblance to the doctrine and arrangement of the ' Har-monic Elements' of Aristoxenus :

Nicomachus of Gerasa, who flourished in the secondcentury, A. D. J a Pythagorean mathematician, and musician;author of a manual of Harmonic : ,?

Bacchius Senex, a musician of the time of the Emperor9a


Constantine. The so-called ' Introduction of Bacchius' isa mass of excerpts of unequal value, some showing agree-ment with the doctrine of Aristoxenus, and some directlycontradicting it:

Gaudentius the Philosopher, a musician of uncertaindate, though he certainly was not earlier than the secondcentury, A. D. His ' Introduction to Harmonic' is an eclecticwork combining views of the Aristoxenean, Peripatetic, andPythagorean schools :

Alypius, of uncertain date, whose ' Introduction' exhibitsthe complete scales of the three genera in all the modes,with their notation:

Aristides Quintilianus, a musician of the first century, A.D.,author of a treatise in three books on Music, in which thetheory of the Aristoxenean school is presented in detail:

Anonymi Scriptio de Musica (referred to in this volume asAnonymus) a cento of the works of Aristpxenus, AristidesQuintilianus, Alypius, Ptolemy, &c, probably of very latedate.

The works of Nicomachus, Bacchius, Gaudentius, Aly-pius, and Aristides Quintilianus, and the Isagoge arecomprised in the Antiquae musicac auctores septem ofMeibom. The same works, with the exception of AristidesQuintilianus, have been edited by Karl v. Jan in the Teubneredition of the classics under the title Musid ScriptoresGraeci. The Anonymi Scriptio was edited by Bellermann,and published at Berlin in 184 r.

93

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96

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