What Music Really s .com

presents

PLATE i

AULETE PLAYING ON THE DOUBLE AULOIFROM ' THE THRONE OF VENUS ' 5TH CENTURY B.C.

The position of the Aulete with head bent over the Auloi, thus relaxing the muscles ofthe glottis, implies a melos with a low tessitura such as that of the Hypophrygian H

THE GREEK AULOSA STUDY OF ITS MECHANISM AND OF ITS RELATIONTO THE MODAL SYSTEM OF ANCIENT GREEK MUSIC

followed by

A SURVEY OF THE GREEK HARMONIAI IN SURVIVALOR REBIRTH IN FOLK-MUSIC

by

KATHLEEN SCHLESINGER

'

fi de a.Q/uovia . .

fisgrj avzfjg xai rd fxeyiQ-q. (paiverai re to.

xai atlaopLSTQiav'

ARIST. FR. 43 BEKKER

With an Introduction by

J. F. MOUNTFORDPROFESSOP OF LATIN IN THE UNIVERSITY OF LIVERPOOL

BOUMA'S BOEKHUIS N.V. PUBLISHER

GRONINGEN - 1970

90- 6088-027-7.

Unchanged Reprint of the EditionMethuen London 1939.

TO

ELSIE HAMILTONAND OUR LONG AND HAPPY FRIENDSHIP

and to

THE MEMORYOF THE BEST OF BROTHERS

HARRY ADRIAN BURGESS

PREFACE

FOR the last three centuries eminent scholars of many nationshave attempted to fathom the mysteries of Greek musicwithout reaching any general agreement. There would,

therefore, seem to be some justification for the introduction atthis point 1 of a new musical fact which bears directly upon thevery foundations of the Greek Musical System.

The aim of the present work is not to supersede what hasgone before, but to open out a new avenue of approach to thisdifficult subject. This study does not, moreover, attempt acomprehensive survey of the rise and development of Music inAncient Greece, but it offers a new conception of the nature ofModality based upon ascertained evidence. I have, therefore,confined myself in this study to placing before the reader thenew data with their implications, and to giving an account ofsuch experimental tests and their results as may prove useful toother investigators in the field.

The basic principle which brings the Modes to birth is foundembodied in pipes and flutes, in which the fmgerholes have beenplaced at equal distances, a proceeding which seems to be instinc-tive and universal. A new world and a new language of Musicstand revealed, in which surprising adventures and experiencesin theory and practice abound

;but, it must be confessed, the

perusal of this volume may put the enthusiasm and patience ofthe reader to a severe test.

I had for a long time been greatly attracted by the significanceand reactions of harmonic overtones, and I was carrying outcertain experiments on my long psaltery 2 when I came uponthe discovery of the basic principle of Modality, which is describedin Chapter i. That principle in operation revealed the cause of

1 The latest authoritative pronouncement on the subject by R. P. Winnington-Ingram (Camb. Univ. Press, 1936), Mode in Ancient Greek Music, concludes a lucidand reasoned survey of available evidence on a somewhat despondent note admittingthe failure of the quest, but adding the hope that one day the illuminating hypothesiswill be struck which is to fuse all unrelated parts into a coherent whole.

2 An instrument strung with eight steel strings of the same length, but of differentthickness and weight, and tuned in unisonconditions which favour a rich polyphonicharmonic development, strengthened by the phenomenon of resonance.

vii

viii THE GREEK AULOSwhat has sometimes been termed in writings on Greek music,' the movable Mese i.e. the Mese placed upon a different degreeof the octave scale in each Harmonia or Species, viz. on theseventh degree in the Mixolydian ; on the sixth in the Lydian

;

on the fifth in the Phrygian ; on the fourth in the Dorian ; onthe third in the Hypolydian ; and on the second for the Hypo-phrygian

; while in the Hypodorian, the Mese was both Alphaand Omega. This new orientation inevitably led to a protractedinvestigation, lasting many years, into the behaviour in theoryand practice of the Aulos and its mouthpieces, and later of theprimitive and medieval flutes having equidistant fingerholes. Theresults of this investigation constitute the basis of the presentwork.

At the inception of this revolutionary idea, which shed a newlight upon the Modal System of Ancient Greece, my joy wastempered by a faint realization of the immensity of the task thusimposed upon one who was so poorly equipped for the purpose.Only my intense belief in the Greek genius gave me the courageto proceed. In my eventual search through the Greek andGraeco-Roman sources, for a confirmation of this revealing modalprocess, I had the good fortune to enlist the help of Mrs. ElizabethJohnson, B.A., who translated viva voce from the Greek andLatin, as literally as possible, in order to afford scope for discus-sion of passages of vital interest but now considered in the lightof the new musical fact. These translations have been of greatassistance to me in preparing the background. For some yearswe worked together at regular intervals translating the whole ofPtolemy's Harmonics, Meibomius and numerous other treatisesand quotations. Needless to say, no such description of the basicprinciple of Modality was found in the sources, although Aristotle(in Fragment 43 Bekker) does name, in a terse statement, thefactors responsible for the Harmonia. While to the initiated hisfew words constitute illuminating evidence, scholars have passedthem by as meaningless. The passage is fully discussed at thebeginning of Chapter v, which treats of the evidence broughtforward in support of my thesis.

It is not suggested that the significance and implications ofthe Aulos Harmoniai altogether rule out the system founded uponthe ditonal scale, described by the Graeco-Roman theorists, butthat a corner of the veil, which had for centuries obscured theModal System of the Greeks, has been lifted. The fact is thereb]'revealed that these two systems, the Modal of the Harmonists,and the non-modal ditonal, were in use contemporaneously in

PREFACE ix

Greece, a fact which is emphasized by some twelve Polemicsdirected by Aristoxenus against the Harmonists (the custodiansof the Harmonia), which I have collected and discussed inChapters ii and v. These bitter, and sometimes violent, tiradescontain precious evidence of all the salient points in the systemof the Harmoniai

;they bear witness, moreover, to the great

importance and influence of the teachings promulgated in theSchools of the Harmonists during the lifetime of Aristoxenus.The separate trails of these two systems are kept in view through-out the book. The culmination is reached when Sebastian Virdungand Martin Agricola exhibit graphic and textual evidence of anattempt that was under weigh early in the sixteenth century forfusing the two systemsthe Keyboard scale in use by the Churchmusicians, and the Harmonia of flutes and shawms by town bands,and among the Folk. The process of transformation is discussedand illustrated in Chapter vii.

While there is, of course, a plentiful supply of a priori evidenceof the existence of the Aulos Harmoniai, the evidence for theactual use by the Ancient Greeks of these modal sequences, withthe ratios I have assigned to themon ascertained factsis setforth in detail in Chapter v. The most striking, positive testi-mony of all is, I consider, first the brief dictum of Aristotle,already mentioned, on the Harmonia as based upon a number andequal measure (iao/isrola), and secondly the Harmonic Canon ofFlorence, a unique document which reveals the sequence resultingfrom an aliquot division by a modal determinant, applied segmentby segment, and to each degree by name in the Perfect ImmutableSystem. To these may be added the identification of somehalf-dozen of Ptolemy's shades of the Generawhen arrangedin sequencewith my statement of the modal ratios of the Tonos.

But one of the greatest tributes to the Greek genius offeredby the Art of Music is, in my opinion, the subtle and originaluse made of the basic principle underlying the Modal Harmonia,in the inception of the scheme of Greek musical notation. Hereit is found that the ingenious idea worked out in this schemeconsists in the use of two progressionsboth duly recognized assequentially inevitableon the one hand of the letters of theGreek Alphabet, and on the other of the arithmetical progressionof ratios. How the juxtaposition of these two sequences occursin the notation of the Tonoi (established in the Tables of Alypius)in such a manner that for every letter symbol there isexpressedor implieda ratio number, is explained in Appendix No. i, inwhich only a brief interpretation of the system could be included,

X THE GREEK AULOSfor the adequate treatment of the questions involved would requirea book to itself. The use I have made of the modal ratios inthe interpretation of the Fragments of Greek Music in Chapter ixwill, I hope, be found useful : they direct our attention to thecharacteristic modal features of the Harmonia displayed in themusic with great emphasis as closes ; but whether we should bejustified in regarding this usage as consciously imposed by canonsof composition is doubtful. These few relics of Greek Musicregarded as prototypesform an apt introduction to our questfor the Harmonia in survival or rebirth in the Folk music ofmany distant lands. It is startling to find a native musician inSumatra, for instance, every whit as susceptible as the Greeks,to the characteristic features of the Hypophrygian Harmonia, thusaffording evidence of the inherent power of these universal modes.The emergence of the Hypophrygian mode in Sumatra is onlyone of many such examples recorded in Chapter ix. The originof the Ecclesiastical Modes is traced in Appendix No. 2 to a radicalchange of mode from Dorian to Phrygian in the Perfect ImmutableSystem of the Tonoi.

The possibilities of the adoption of the new language of Music,derived from the Ancient Greek Harmoniai, for use in moderncompositionwhich have been considered in Appendix No. 3

have for some years been exploited by one modern composer,Elsie Hamilton, and performances of her compositions givenin London since 19 17 (invariably received with enthusiasmby the audience) may be remembered by some of the readers.The general adoption of this new language of music not merelyentails a mastery of the novel intonation of the dialects, as wellas a resigned acceptance of technical difficulties concerned withmusical instruments ; but unfortunately initial attempts sooner orlater come up against economic barriers which, however, a con-siderable increase in adherents would tend to minimize. Thecrucial test will ultimately resolve itself into the decisive query :does the new language of music provide increased facilities fordifferentiated expression of more subtle psychological reactionsand feelings, which are unobtainable with the older language ofmusic ?

Finally, future investigators in this domain will be well-advisedto seek first of all the reed-blown pipe with equidistant fingerholes,for its verdict is final : modality at discretion. If when testedthe pipe should emit a scale resembling our modern major (i.e.the Greek Hypolydian Harmonia) let the inquirer not be led tofalse conclusions, but first try the effect of other mouthpieces

PREFACE xi

the more primitive the betterwith a longer stem extruding fromthe resonator. There are two kinds of scale which cannot beascribed to a reed-blown pipe, bored according to the principleof equal measure : (i) the ditonal scale, (2) any one scale regardedas standard.

I do not forget what I owe to Mabel Goschen (Mrs. GerardCobb) ; for it was as a result of the many happy months spentwith her in Dresden in the 'nineties, that our common in-terest and enthusiasm became centred in the instruments of theorchestra ; it was, in fact, at her suggestion that I began to gathermaterials which eventually led to my work in the archaeologyof Music.

During the many years spent in the preparation of this volume,so many kind services, rendered by colleagues and fellow-workersin this field of research, gifts of general literature, musical instru-ments, photographs, &c, have been lavished upon me, that I amglad to be able to recall and associate with me in this publicationthe names of the many who have encouraged and stimulated mein my work. Foremost of all my grateful thanks are due to myclose friend, Elsie Hamilton (of Adelaide, South Australia), forher unvarying readiness to help on this work in every possibleway, so that I have been able to devote these many years to theinvestigations and experiments upon which The Greek Aulos isbased, and to the research for confirmatory evidence in the literarysources. As a composer, Elsie Hamilton has, besides, shownherself ever ready (as may be read in Appendix No. 3) to co-operatein the endeavour to make the new (old) language of Music,founded upon the Harmonia, a practical reality in the music ofour own day, and of the immediate futurea project which findsitself checked ever and anon by economic barriers.

To Professor J. F. Mountford, I am deeply indebted for oneof the rarest gifts from one worker to another, namely a dis-interested and constant interest displayed over many years, notonly in the somewhat revolutionary thesis of this volume, butextended generously also to the smallest details. He has willinglydiscussed difficult issues, and offered shrewd and pertinent criti-cism, valuable advice and encouragement. To my lasting regret,however, I realize that the disclosure, during our long correspon-dence, of new but unpublished ideas and data, may have causedhim to postpone his own separate contributions to the study ofGreek Music.

Warm appreciation and heartfelt thanks are due to my devotedand efficient secretary, Miss Annie Copperwaite, who has been

xii THE GREEK AULOSof the greatest assistance to me in typing the chapters

;copying

diagrams and tables ; in the boring of innumerable flutes andpipes and finally in preparing the work for the press, when shehelped very materially in carrying out the exceptionally heavytask of revising chapters, written over a long period of years,in correcting proofs and in making the index.

I am deeply indebted also to the Institute of Archaeology, inthe University of Liverpool (and primarily to Professor JohnGarstang and Sir Robert Mond), who have granted me the dis-tinction of holding their fellowship in the Archaeology of Musiccontinuously since 191 5. The confidence they have shown duringthis long period in the value of the work I had undertaken hasbeen an unfailing source of strength and inspiration to me.

I also offer sincere thanks to Sir Robert Mond for his appre-ciative interest and for various contributions in aid of my inves-tigations, of books, and musical instruments, including twointeresting sets of panpipes from Sicily, tuned to the modalintervals of the Harmonia, and for a case containing some 50flutes, obtained for me from Egypt, most of them precisely boredto give one of the Harmoniai (see Table XI).

To Mr. A. H. Fox Strangways I owe much, and notably myinitiation into the mysteries of cents, some twenty years ago. Onimportant questions of origins of scales and musical systems, ourviews tend to diverge fundamentally. I have, indeed, spent manyhours on end with him in stimulating and enjoyable discussion,but on certain issues there is invariably a clash of opinions, with-out any hope of convincing the opponent. Nevertheless, the factthat both are so keen adds zest, so that in spite of all we remainfriends.

I gladly take this opportunity of recording my indebtednessto the late Miss Maisie F. Grant (daughter of Mrs. Grant ofLiverpool), a most enthusiastic, gifted and highly efficient studentof all this lore concerning the Harmoniai. During her travels inmany parts of the East, she did valuable work : measuring flutesnotably in the Cairo Museumtesting and comparing data withthe modal monochord

;discussing scales, &c, with native musi-

cians and Arabian professors, and carefully noting results. Fromher visit to South Africa she brought back many musical instru-ments ; she induced friends in India to collect flutes for her.All of these valuable specimens and data she bequeathed to mewhen her early death in Egypt deprived me of a valued collaborator.

My hearty thanks are due to many besides for gifts of instru-ments : the late Mrs. Ludwig Mond and Sir Robert Mond ; to

PREFACE xiii

Feroza (Mrs. P. A. Narielwala of Bombay) ; Mr. George Kauf-mann, M.A. ; the late Mr. H. A. Burgess ; Mr. T. J. Bezemer(Holland) ; Mr. Soekawati of Batavia ; Mr. C. Lekkerkerker,Director of the Bali Institute (Colonial Inst, in Amsterdam)

;

Mrs. Elizabeth Ayres Kidd (of Winnetka, 111., U.S.A.); MissMarian Storm (of Uruapan, Mexico) ; Canon Galpin ; Dr. A. N.Tucker ; the Egypt Exploration Society, and to Mr. O. H. Myers,Director of Excavations at Armant, Egypt. To Miss Anita Berry,Hon. Organizer of the Arts League of Service ; Miss W. Roelvinkand Miss Mary Wilbers (Holland) ; Miss Carita Stenbeck (Fin-land) ; Miss Florence Pertz for an album of gramophone records' Die Musik d. Orients ', and finally for constant supplies of wheatand oat stalks, and river reeds to Mrs. W. Copperwaite and Mrs.Percy Gurney of Clifton, Beds.

For gifts of books, pamphlets, off-prints and photographs, mysincere thanks are due to the late Mrs. Ludwig Mond ; Dr. OttoAndersson ; Professor J. F. Mountford ; the late Mr. A. J.Hipkins ; Professor Dayton C. Miller (Cleveland, Ohio, U.S.A.) ;Professor Jacques Handschin (Zurich) ; the late Miss HortensePanum (Denmark) ; Dr. Rudolf Wagner (Furth) ; M. TheodoreReinach ; M. Victor Loret ; M. Victor Ch. Mahillon (Brussels)

;

M. Ed. Pottier (Louvre, Paris) ; Professor Dr. Joh. Wolff ; Dr.E. M. von Hornbostel ; Baron Alex. Kraus (Florence and Fiesole)

;

Sir Donald Tovey ; Professor Percival Kirby (Johannesburg) ;Dr. Manfred Bukofzer (Basel) ; Mr. L. Langwill (Edinburgh)

;

Mr. A. A. Pearson (Folk Song) ; the late Dr. W. G. McNaught

;

Professor H. J. W. Tillyard, and Miss V. C. C. Collum. 1For permission to reproduce unpublished tables and data I

am greatly indebted to Dr. Jaap Kunst (Batavia and Amsterdam)(see Chapter viii). To Herr E. Koch-Griinberg for authorizationto use passages and tables from E. M. von Hornbostel's Appendixto his late father's book, Zwei Jahre unter den Indianern von N. W.Brazilien. To the Director of the British Museum for permissionto reproduce photographs, and likewise to M. Alex. Philadelpheus,Director of the National Museum at Athens ; and to Dr. Legrain,Director of the University Museum at Philadelphia for a full-sizephotograph of the Pipes of Ur (see Table XIV and PI. 18).

I am also grateful for all the kind assistance given to me inthe Reading Room at the British Museum by the Superintendents,past and present, especially to Mr. G. Barwick, and to Mr. A. J.Ellis, M.A., and also to Mr. F. G. Rendell, F.S.A. (assistant

1 The Music of Growth, by Collum (Partridge, London, 1933), and extracts fromthe Shoo King (tr. by W. H. Medhurst, Sen.).

xiv THE GREEK AULOSsuperintendent) ; and to Mr. A. H. Smith of the Graeco-Romandepartment.

I am glad to acknowledge here also how stimulating has beenthe effect of the generous appreciation of my work, bestowedupon me by Sir Percy C. Buck and Sir W. H. Hadow and others,on various occasions.

Nor do I forget finally how much I owe to staunch and valuedfriends for so readily proffering assistance of every kind : tomy friend William Busch with whom, as a creative musician,I have enjoyed many stimulating and fruitful discussions onaspects of music of vital interest to my subject. To my friendsMiss Zabelle Boyajian (for information on Armenian folk songs)

;

to Miss Netta Peacock, and Mrs. Elizabeth Johnson, B.A., fortheir willing help in checking references at the British Museum.To Muriel Campbell with special reference to Anthropology, andto Jessie Cameron in respect of Palaeography ; also to Mrs. EthelGillespie (Australia) ; to Miss Dorothy Fraser ; and to Mr. andMrs. R. Chatwin.

Finally, my grateful thanks to Dr. A. Maud Swanson for herwise and stimulating care and interest during the strenuousmonths of 1937-8.

KATHLEEN SCHLESINGERHlGHGATELondon, N.6

INTRODUCTION

WHAT was the nature of Greek music and how did it differ fromour own ? A full and complete answer to these questions wouldbe of enormous interest both to the student of Greek literature

arid philosophy and to the musician who concerns himself with the develop-ment of his art.

The curiosity of the Greek scholar is aroused especially by a passagein the third book of Plato's Republic (398c~399e), where the philosopherdiscusses the music suitable for his Ideal State. The education of thecitizens of this State was not to consist of the acquirement of accomplish-ments, it was not to be even a merely intellectual process, but primarilya moral one. With this ethical end in view, Plato was prepared to includemusic as one of the studies of a young person. By a suitable training inmusic of the best and most fitting kinds, the child would be guided tovirtue and his soul would be led in the right path. In a perfect worldgood music was to be no less important than good and moral literature.Some types of music current in Greece were regarded by Plato as unsuit-able for use in his Commonwealth. The scales (ag/uovlai), such as theMixolydian and the Syntonolydian, in which lamentations were composed,and those which, like the Ionian and the Lydian, were adapted to effeminateor convivial songs were rejected ; and two scales only, the Dorian and thePhrygian, were left which would represent the noble endurance of a braveman in battle or the sobriety and moderation of a citizen at peace. Thisview of music, which is analogous to Plato's application of moral criteriato the judgement of literature, is something more than a young man'sdogmatism ; for it is reiterated in the Laws (Sizb), a work written whenPlato had a still wider experience of men and affairs behind him. To theend of his life he held that music is in itself the representation or repro-duction in another medium of goodness or badness in the soul, and thatby hearing good music a child is brought into contact with a good souland so through music is assisted on the path towards virtue.

Nor does this doctrine arise from some personal idiosyncrasy of Plato ;for in his Politics (viii, 4-8), Aristotle expresses a similar view. Whileadmitting that it is legitimate to make use of music simply as a relaxation,he is quite clear that music has a tendency to form the moral characterand influence the very soul.

It is in rhythms and melodies [he says] that we have the most realistic imitationsof anger and mildness as well as of courage and temperance and all their oppositesand of moral qualities in general. This we can see from actual experience ; forwhen listening to such imitations we suffer a change within our soul. But to acquire

xv

xvi THE GREEK AULOSthe habit of feeling pleasure or pain upon the occurrence of resemblances is clearlyallied to having the same feelings in the presence of the original [p. 1340a].

A little later (p. 1342a) he says : ' Clearly we must make use of all scales(&Q[iovuu), but not all in the same way ; for education we must use themost ethical (rjdixwTaraig) scales.'We ourselves appreciate the transient effects of music on our emotions

and we understand that some kinds of music are exciting and others sooth-ing. But our likes and dislikes are determined by considerations of melodi-ousness or cacophony, or by the skill of the composer's harmonies andcounterpoint, or by the almost intellectual pleasure in formal developments.We do not praise or condemn a musical work because of its possible effectson our own souls or characters, or even on those of our neighbours. WhetherPlato and Aristotle were right in attributing such power to music need notconcern us here ; the essential point is that they associated with theirvarious scales (aQ/zovtai) distinctive categories of feeling. Their testimonyin this matter is confirmed by many passages in the lyric, tragic, and comicpoets, and most strikingly by the anecdote of the composer Philoxenus,who found it impossible to write a dithyramb in a scale other than thePhrygian usually associated with that type of poem. This well-attestedsensitivity of the Greeks is not to be explained by supposing that in aestheticappreciation they differed fundamentally from ourselves. The reason mustbe that their music was capable, in some way which modern music is not,of expressing clearly the varying shades of feeling.

The musician is attracted to the study of Greek music not merelybecause any manifestation of the art of organized sound is of interest tohim ; but largely because of a widespread impression that the music ofWestern Europe is in some obscure way derived from that of ancientGreece. There is a tradition that St. Ambrose of Milan, in the secondhalf of the fourth century, took four modes ' from the Greeks ', and madethem the basis of ecclesiastical music ; and that later Pope Gregory theGreat added four more. This tradition does not account for the fact thatthe Church system has eight modes, whereas the ancient Greek system fromwhich they are supposed to be taken had only seven ; or for the fact thatthe interval sequences of the Church modes do not correspond with whatwe know of the Greek modes of the same names. The tradition, indeed,is not based on any solid authority ; so far as St. Ambrose is concerned,it seems that his innovation was the introduction, not of ' modes ' hithertounknown to Western Europe, but of antiphonal singing from the GreekChurch of Antioch ; and Pope Gregory's services to Church music con-sisted in the systematization of the corpus of antiphons already existing,and the setting up of a school at Rome for the training of Church singers.Nevertheless, it is true that the Church modes, Dorian, Phrygian, Lydian,&c, do bear names which, by some channels and for some reason, musthave been derived from Greece ; and the tracing of that connexion, how-ever tenuous it might prove to be, is a fascinating inquiry for musicologists.Furthermore, such common musical terms as ' tone ', ' tetrachord

',

' melody ', ' harmony ', ' diatonic ', ' chromatic ', ' enharmonic ', and ' dia-

INTRODUCTION xvii

pason ', all testify to some kind of continuity ; whether that continuity issimply a vague one of modified theory or whether it is a more solid one

of practice is a question which cannot be settled without an adequateknowledge of Greek music itself.

What, then, did Greek music sound like ? The answer to the questioncould in no case be a simple one ; for the total impression made by a pieceof music depends upon a number of factors. To commence with a pointwhich is not of fundamental importance, we should need to know some-thing of the timbre of ancient instruments and something of the principlesof voice production which were admired by singers and listeners. Theimportance of differences of tonal quality can easily be appreciated bycomparing the effects of performing the same piece of music on a harpsi-chord and on a modern piano, or by listening to the same piece on a recorderand on a modern concert flute. Were the ancient lyres and citharas andother stringed instruments which are depicted in vase paintings of thetimbre of the harp, or were they more like the banjo and guitar ? Wasthe aulos (avXog), which modern translators generally render by the word' flute ', really like a modern flute or was it more like the clarinet or oboe ?We are so accustomed to the methods of voice production favoured by well-trained and sophisticated singers and approved by critics that we acceptthem as entirely natural ; but one has not even to go outside Europe torealize from the singers of genuine folk-song that a shrill, nasal, and forcedvocalization, which would be anathema in the concert hall of a city, canbe acclaimed as a satisfying and artistic achievement. Would the songssung by a Greek tragic chorus remind us of the choir of St. Paul's or ofthe peasant in the uplands of Andalusia ? Much of the charm of ourmusic lies in its form, in the interplay of contrasting and complementarythemes, and in the development of a melodic or harmonic idea. Wecannot assume, however, that even the separate stanzas of the shorter songsof the Greek lyric poets were set to a simple recurring melody ; still lesscan we conjecture the form of the music of an elaborate dithyramb or theprinciples of composition which guided the musicians who competed inthose contests of aulos and cithara playing which were features of theGreek games. Indeed, of all the possible features of Greek music, theonly one which we can feel certain of being able to apprehend from therange of our own experience is the Greeks' neglect of harmony ; for it iscertain that their choruses sang in unison or at the octave, and that theinstrumental accompaniment was in unison with the voice except for afew passing notes.

The points which have just been mentioned, however, do not includethe most important question which needs to be answered about Greekmusic. Even when we have reconstructed as accurately as we can a Greekcithara and found that it has a full round tone, and discovered that theaulos had a quality approximating to that of an oboe, we can gain no usefulconception of Greek music until we have acquired some definite informa-tion about the Greek scales. We need to know on what principles theywere constructed, what intervals composed them, what tonic or focal point

b

xviii THE GREEK AULOSthey possessed, how they were used in relation to one another, and, if pos-sible, how they developed historically. We need a clear understandingnot only of the Harmoniai (dgfiovim) of which Plato and Aristotle speak,but also of the other scales, Octave Species (etSrj rov dta naowv), Tonoi(tovoi), &c, which are mentioned by Greek writers.

Our modern pianoforte scale with its twelve equal semitones to theoctave is the worst possible approach to the understanding of Greek music

;

for this scale is a comparatively recent compromise designed to secure ascomplete a freedom as possible of modulation from one key to another.The nature of this compromise is easily understood if we start from thefact that the physical basis of sound is a series of pulsations in the air.The rate at which these vibrations succeed each other determines the pitchof a note, so that the more vibrations per second there are, the higher inpitch is the note produced. A musical interval, therefore, can properlybe defined only by expressing the ratio between the vibration frequenciesof the two bounding notes. Now the interval called an octave is producedby two notes whose frequency ratio is 2 : i ; and a Perfect Fifth by noteswhose frequency ratio is 3 : 2. Two notes which are seven octaves aparthave a frequency ratio of (2 : i) 7 , which represents a relation of 1 to 128

;

and two notes which are twelve Perfect Fifths apart have a frequency ratioof (3 : 2) 12 , which represents a relation of 1 to 129745. The pianofortescale ignores this difference between 128 and 129-745, and while keepingthe octaves in true intonation adjusts the Fifths by flattening so that twelveof them coincide with the seven octaves. In an analogous way the lesserconcord of the Third is also adjusted, with the result that while there aretwelve equal semitones within the pianoforte octave, not a single note isin just intonation. There is no doubt that this ' tempered ' scale has insome ways widened the boundaries of the art of music, but it has doneso at the expense of some blunting of our ears. Though we enjoy thebrightness of a Perfect Fifth played on the open strings of a violin, ourears have grown accustomed to accepting a ' tempered ' Fifth as if it werePerfect.

In dealing with Greek music, therefore, we must be prepared to putout of our heads all conceptions derived from our modern scale. Nor isan acquaintance with our major and minor ' modes ' likely to help us tounderstand the variety of scales used by the Greeks ; for apart from thefact that our major and minor now involve false intonations, the differencesbetween themthe flattening of the third and sixth degrees in the minorare not as striking or as significant as their similarity in having a commonTonic and Dominant. The difficulty a modern musician has in distin-guishing between scales of different structure from our own is shown byour reactions to Byzantine, Hindu, Arabian, and Chinese music. They allsound ' foreign ' to us, despite the difference between them, much in thesame way that French and German sound simply ' foreign ' to a monoglotEnglishman. To understand Greek music we must be ready, if necessary,to learn another musical language and train our ears to its separate dialects.How then are we to discover the nature of the Greek scales ? The evidence

INTRODUCTION xixis of various types and it is necessary to say something about them if thepresent book is to be placed in its true relation to earlier work.

Naturally one would turn first of all to the Greeks themselves to seewhat they have to tell us about their own music. In the poets and prosewriters there are many allusions to the art of music ; but with few excep-tions they are of a vague and general nature and afford no clue to thefundamental principles. Here and there, as in the dialogues of Plato, thereare more technical references ; but they are of such a kind that a wideacquaintance with the musical theory of the Greeks would be necessary tounderstand their implications. Whereas Plato used musical analogies toelucidate his philosophical argument, we should have to work back fromhis philosophy to understand his musical illustration. However, there isstill extant in Greek a corpus of theoretical writings on music which amountto not less than six hundred moderate sized pages. The most voluminousof these writings are : the considerable fragments of the treatise on theelements of music (called ag/xovivA aToiysla) in three books from the penof Aristoxenus (flourished about 320 B.C.), the pupil of Aristotle ; thethree books on music {nsol fiovoixfjg) by Aristides Quintilianus, whowrote probably during the first or second century of the Roman Empire

;

the three books (rd dofiovixd) by Claudius Ptolemy, the great Alexandrianmathematician of the second century after Christ ; and finally the incom-pete commentary on Ptolemy written by Porphyrius in the third century.Chief amongst the works of lesser extentbut not always of inferior impor-tanceare : a number of discussions of acoustic and artistic questions inthe corpus of Problems attributed to Aristotle ; a series of simple acousticalpropositions scientifically demonstrated by Euclid (fl. 300 B.C.) in his Divisionof the monochord (xarazo

iurj xavovoq) ; a short but very lucid treatise

(elaaycoyi] dofioviy.r/) formerly attributed to Euclid but written probablyby a certain Cleonides of uncertain date

; a section on concords in themathematical work of Theon of Smyrna (fl. a.d. 120) ; and three shortelementary treatises by Gaudentius, Nicomachus, and Bacchius who wrotebetween the end of the first and the end of the fourth centuries of ourera. Mention must also be made of a work on music (nsgl fxovaixfjq)attributed to the young Plutarch, in which matters of theory are mingledwith snippets of musical history ; and of Athenaeus (fl. a.d. 230) in thefourth and fourteenth books of whose Deipnosophistae there are manyanecdotes relating to music and musicians.

From such a bulk of material it might be thought that little wouldremain unknown of Greek music and that all problems would be capableof easy solution. But such is very far from being the case for severalreasons. In the first place, these theoretical writings are of such varyingdate that they range over not less than six centuries ; and though a com-paratively late writer may often be relying for his information upon a muchearlier authority, it is not always easy to ascertain the parts which havesuch authority behind them ; and in any case there is very little, if any-thing, which can be traced back to the writings of Lasus of Hermione(fl. 525 B.C.), Hippasus of Metapontum (fl. 500), Glaucus of Rhegium (fl. 450),

XX THE GREEK AULOSPhilolaus (fl. 440), Heraclides Ponticus (fl. 400), or Archytas (fl. 390).How can we decide whether a piece of theory penned in the first centuryof the Roman Empire is applicable to the music of Pindar and Aeschylus ?Between the sixth century B.C. and the beginning of our era the art ofmusic must inevitably have undergone some changes, and the innovationsof practice must to some extent be reflected in the presentations of theory.The earlier Greek writers, for example, down to and including Plato andAristotle, speak of Harmoniai, but in the theory books surprisingly littleis said of such scales ; in their place we read of Octave Species (e'tdrj rovdid. naawv), Systems {avarrjfiuxa), Tonoi {xovoi). What change of practicedoes such a change of nomenclatare conceal ?

In the second place, the theoretical writers frequently offer us a greatdeal of elementary information which we do not need, and seem to omitjust those points about which we require most guidance. Naturally theywere writing for their own times and their own purposes ; some, likeAristoxenus, were concerned with stressing their own point of view andderiding their opponents

;others, like Cleonides, frankly reduced their

subject to its smallest dimensions ; and all of them were handicapped bythe inevitable inability of a theorist to do more than give the osteologyof the art.

A third and most vital inconvenience arises from the fact that thetheorists fall into two schools which are not reconcilable : the Pythagoreansand the Aristoxenians ; and the information we derive from a given writeris largely coloured by the doctrines of the school to which he adheres.According to tradition, Pythagoras (fl. 500) introduced from Egypt intoEurope the knowledge of mathematical acoustics ; whether that be trueor not, it is certain that his immediate successors had some knowledge ofthose mathematical ratios which are connected with the physical basis ofsound. They perceived that a string which played a certain note was justtwice the length of a string, of the same tension, which would play theoctave above ; or again, if you placed a movable bridge or stop one-thirdof the way along a string playing bottom Doh, the remaining two-thirdswould play the note Soh a Perfect Fifth above. Now the Pythagoreanschool of philosophy attributed great power and influence to Number andbelieved that the whole of the Universe could be reduced to a set of numericalrelations. In the art of music, though a hasty observer might say that itwas based on nothing more than pure sensations with no objective validity,the Pythagoreans found a clearly demonstrated set of ratios such as theywere seeking ; more than anything else, music seemed to bring them intoclose contact with that Number which they looked upon as the UltimateReality. Although this discovery gave to the art of music a philosophicsanction, it did not lead to a satisfactory, comprehensive, or even trustworthytheory of music ; for fundamentally the Pythagoreans were more interestedin their mathematics than in music, and they tended to reduce the divinityof the Muses to a mathematical proposition. They judged musical intervalsnot according to the pleasure they gave the ear, but according to whethertheir ratios could be reduced to one or other of their favourite formulae,

INTRODUCTION xxisuch as n : 2n, n : jti, n : n i. In their investigations they were inter-ested in obtaining the ' right answer ', and consequently we cannot feelcertain that in their discussions of musical intervals they have not selectedjust those which suited their immediate need ; and it is beyond doubtthat they neglected the other scales in favour of the Dorian. From theirpseudo-musical speculations there grew the doctrine of the Harmony ofthe Spheres according to which the sun, moon, and planets, as they wentalong their orbits, were supposed to make sounds which could be identifiedwith the notes of the Dorian scale ; and such guesses at the foundationsof the cosmos did more than the legitimate mathematical investigations towithdraw the study of music from its proper track.

Sharply distinguished from this metaphysical theory of music is thesystem which was first enunciated by Aristoxenus. For him pure mathe-matics and physics had no attraction. He postulated that in music theear is the sole and final arbiter and that a mathematical formula has littleor nothing to do with music. In this he was absolutely wrong, so far astheory goes ; and so far as the art of music is concerned, he was onlypartially right. Ears differ in sensitivity and one naturally asks what kindof ear is to be the sole criterion ; is it to be the ear of a highly criticalmusician or of the average listener ? To rely only upon the ear for thedata of a system of musical theory is to use a rough-and-ready method

;

and Aristoxenus himself was content to speak vaguely of a ' semitone '

without any precise definition of what he meant by the term. As anadjunct to this doctrine was his contention that the progression of soundfrom low notes to high could be regarded as a continuous line, at anypoint of which the voice could rest, and any section of which could bedivided into any number of equal parts. Aristoxenus found it easy toassert that a tone is the difference between a Perfect Fifth and a PerfectFourth and that a semitone is exactly half that interval. But the Pytha-goreans would have told him, and modern acoustics would confirm them,that the tone which is the difference between a Perfect Fifth (ratio 3 : 2)and a Perfect Fourth (ratio 4 : 3) is represented by the ratio 9 : 8 (= f -f- f) ;and that since the ratio 9 : 8 cannot be equally divided unless we use surds

(3 :2V 2), there can be no interval which when taken twice will producesuch a 9 : 8 tone. This linear conception of intervals, however, lies at thevery root of the Aristoxenian theory and proves to be a quite impenetrablebarrier to a proper knowledge of the nature of Greek scales. It would begrotesque to suggest that this theory can be entirely neglected or to denythat from it we can infer much that is worth knowing ; but for the funda-mental question about the size of the intervals of the Greek scales it istoo unscientific to be of real service.

Nevertheless, since the Aristoxenian theory, especially as expoundedin the later treatises, has a superficial lucidity which has misled some ofthe most painstaking students of Greek music, it will be well to indicatehere its major features. At its basis is a two-octave scale called the GreaterPerfect System {avoTr\jia rileiov /xelov), of which a very rough ideamight be obtained by playing the white notes of a pianoforte from A to

xxii THE GREEK AULOSa'. This System consists of fifteen notes, each with a distinctive name,separated from each other by a tone (T) or a semitone (S), and groupedinto tetrachords :

o> c-

- c si 9,a 2 P< 5 e * o .3 S

i

g a. K 8 i .2S K K

INTRODUCTION xxiiiHigh (avvrovov) Diatonic : i"2 I ISoft (fiaAaxov) Diatonic : 1 34 liTonic {xoviaTov) Chromatic : 1 X I 9"Hemiolic (rj/Mofaov) Chromatic : 38 38 IfSoft (fxa/.ay.ov) Chromatic : 13 13Enharmonic : 14 14 2

The Aristoxenian theory thus outlined has a certain neatness to commendit and is easily apprehended

;but, apart from the fact that it is unscientific

in its description of intervals, it is in many respects unsatisfactory andraises a host of problems in itself. This is not the place to subject it toa thorough analysis ; but three points may be mentioned. Firstly, thedoctrine of the genera-which must be an attempt to bring the subtleintonations of the practical art within the scope of the theorywouldimply that there was not only a diatonic Lydian octave species consistingof T T S T T T S, but also an enharmonic Lydian octave of i 2 i i 2 I !Yet it seems incredible that such a scale, beginning and ending with aquartertone interval, could have had any existence except in theory ; wecan conceive neither how it originated nor how it entered into practice.Secondly, there is not in any Aristoxenian writer a single hint of the tonalityof the Greater Perfect System as a whole ; nor is anything said about thetonality of the various Octave Species. Yet it is quite as important forthe understanding of a musical scale to know what is its focal point as itis to know the size of its intervals ; for the intervals are musically mean-ingless except when related to a tonic, which need not be the first noteof the scale. And thirdly, there is the tantalizing problem of relating theOctave Species to the Harmoniai of the earlier writers. The names areattached to the Species only in Bacchius ; and his list contains names,like Hypodorian, which are never applied to any Harmonia and yet omitsnames like Syntonolydian.

Since the theoretical writers fail to give us all the information we desire,we are compelled to turn to other possible sources of evidence. Of thesewe may mention first the Greek musical notations, of which one was usedfor instruments and the other for the voice. Both notations are basedultimately on alphabetic signs ; and in the treatise of Alypius (of uncertaindate) we have an almost complete list of the signs and verbal descriptionsof them for all three genera in the fifteen Tonoi. As the art of musicdevelops, the need for a notation arises and we may well suppose that somekind of notation was in common use at least as early as the time of Pindar.Presumably the notations we possess contain within them a kind of kernelor nucleus around which there have been later accretions ; and if we coulddecide what are the original signs which formed that nucleus, we shouldhave some evidence for the state of music at the time when the notationwas first evolved. The most generally accepted interpretation of the signsis due to the investigations of Fortlage and Bellermann, published inde-pendently in 1847, according to which the lowest note of the lowest Tonosis equated with the F below the bass stave, and the highest note of the

xxiv THE GREEK AULOShighest Tonos with the G above the treble stave. The intervening signsare equated for each diatonic Tonos with the notes of a minor scale andthe intervals are assumed to be approximately those used in modern music.Many writers have felt doubts about the validity of this interpretation

;

for in many of its details it is not homogeneous. But though variousattempts have been made to solve the problems, none of the alternativeinterpretations has been commonly accepted. This much, however, cansafely be s^id : no theory of Greek music is likely to be near the truthunless it provides a satisfactory account of the notation as we possess itand explains how it arose from an earlier and less complicated scheme.

A third-type of evidence lies in the few fragments of music in Greeknotation which we still possess. The most extensive are the Delphic Hymnswhich were composed during the second century B.C. and contain nearlytwo hundred bars of tolerably consecutive melody. The hymns to Nemesis,the Sun, and the Muse, attributed to a certain Mesomedes, were composedduring the second century of our era. The other pieces are incompleteand very brief

,

only one of them, the fragment of a chorus from theOrestes of Euripides, has any definite claim to be the kind of music Platoand Aristotle might have heard. These fragments are not only of widelydiffering dates of composition, but their interpretation is dependent uponthat of the Greek notation in which they are preserved. Whatever theymay seem to teach us about the principles of musical composition or evenabout the tonality of the Greek scales, they cannot of themselves give usany information about the Greek intervals.

Finally there is the evidence which ancient instruments may provide.Not even a well-preserved lyre or cithara could be of any value to us

;

for the testimony of such instruments is entirely dependent upon thetension of their strings. With wind instruments, however, the case issomewhat different ; for provided that they are not too seriously damagedit is possible to make facsimiles of them ; and by good fortune the HistoriaPlantarum of Theophrastus (fi. 300 B.C.) and the Historia Naturalisof Pliny the Elder (fl. a.d. 70) contain valuable information about thereed mouthpieces which were a vital part of instruments of the aulostype. But the instruments preserved from antiquity are few in number(see Howard, ' The AvXog or Tibia ' in Harvard Studies in Class. Philol,Vol. iv). In the circumstances it is perhaps not surprising that little atten-tion has hitherto been devoted to the records of Greek music lying dormantin these auloi. Howard, indeed, did make facsimiles of them ; but hisresults are unsatisfactory because he did not probe deeply enough into theacoustic problems involved or define with the necessary precision the inter-vals of the scales. But it is just this line of investigation, scientificallyconducted and correlated with the records of instruments not of Greekprovenance, that is the foundation of the present book.

Before passing to a brief survey of modern studies of Greek music, itis worth while to point out that some kind of theoretic knowledge of thesubject has never entirely died out in Europe. The fact that so many ofthe Greek treatises on music were written during the Roman Empire shows

INTRODUCTION XXV

that the Greek theory was felt to be a sufficient account of music longafter the Greek states had lost their political independence and the culturalhegemony of the world had passed from Athens to Alexandria and thento Rome. The Romans themselves were not moved by music as were theGreeks, and in the great Roman writers there are only the most casualand uninformative references to the art ; and much of the serious music-making even in the Empire was due to professional musicians of Greekorigin. However, there is a succinct account of the Aristoxenian theory

in the De Architectura of Yitruvius, the architect who lived in the Augustanage. In the first half of the fifth century, Martianus Capella gave an out-line of musical theory in the ninth book of his De Nuptiis Philologiae, anda century later Boethius composed a separate work on music in which thetheory differs from what we find in the Greek writers more through mis-understanding than through deliberate intent. In the Institutiones ofCassiodorus, which contains a compendium of knowledge useful for themonks of the new foundation at Vivarium, there is a section on musicwhich is clearly based on Greek authorities of whom Gaudentius, Alypius,and Ptolemy are mentioned by name. The writers on ecclesiastical music(contained in Scriptores Ecclesiastici de Musica, edited by Gerbert, 1784)had little or no knowledge directly of the Greek theorists, but relied to agreat extent upon Boethius and upon one another ; but a great deal oftheir theory is an attempt to adapt a garbled version of Greek theory tothe facts of the music of their own times and their pages bristle with' Phrygians ', ' Dorians ', ' Hypermixolydians ' and 1 netes diezeugmenon '.

It was only gradually that an adequate theory for the ecclesiastical modes,based on the doctrine of the four Finals, was evolved, somewhere betweenthe eighth and eleventh centuries ; and though by the eleventh centurythe doctrine of Authentic and Plagal modes had established itself andmuch of the Latinized Greek jargon had been jettisoned, nevertheless theinfluence of Greek theory persisted in the attribution of names like Dorianand Lydian to the Church Modes.

The scholars of the Renascence were too busily occupied with theirstudies of the literary masterpieces of Greece and in the search for newmanuscripts of standard authors to devote their attention to so subsidiarya subject as Greek music ; and except for the Latin translations of Euclidand Cleonides by Georgius Valla (1498) no attempt was made to studyGreek musical theory. In the sixteenth century there appeared only theincompetent Latin translation of Aristoxenus by Gogavinus (1542) and theGreek text of Euclid with a Latin translation by Joannes Pena (1557).The next century, however, saw the publication of all the remaining treatisesof importance. Jan van Meurs published the Greek text of Aristoxenus,Alypius (without the Greek signs), Nicomachus, and Bacchius between1606 and 1623. In 1652 M. Meibom, a better scholar than van Meursthough prone to prefer his own ingenuity to the evidence of his manu-scripts, re-edited Aristoxenus, Bacchius, Euclid, Nicomachus, and Alypius(with the musical signs), and published Gaudentius and Aristides Quin-tilianus for the first time. The first edition of the hymns of Mesomedes

XXVI THE GREEK AULOSwas published by Vincenzo Gallilei in 1581. To John Wallis, Professorof Geometry in the University of Oxford, we owe the first editionsof Ptolemy (1682) and Porphyrius (1699). Van Meurs, Meibom, andWallis equipped their editions with notes and commentaries which,though restricted for the most part to the interpretation of the particularauthor under discussion, did nevertheless gradually extend knowledge ofthe subject as a whole. In particular, Wallis appended to his edition ofPtolemy a chapter (De Veterum Harmonica ad Hodiernam comparata) inwhich he skilfully gathered together such information as could be derivedfrom the theorists and completely outdistanced the account which AthanasiusKircher published in his Musurgia Universalis (1650) before Ptolemy andPorphyrius were available. In the eighteenth century, knowledge of Greekmusic filtered through to purely musical works, and writers like Hawkinsand Burney included chapters on the subject in their general historiesof music.

In the nineteenth century by far the most important name connectedwith the study is that of Rudolf Westphal, professor of Greek at Moscow,who not only edited Aristoxenus and Plutarch's de Musica, but in a seriesof lengthy volumes attempted to fuse all our information derived fromtheorists, antiquarians, and classical writers into a coherent whole. Withhis wide erudition he was able to elucidate many matters of detail ; butat the basis of his work was a belief that the Aristoxenian system of theoryprovided the essential key which, with a little manipulation, would unlockall the secret places. He does, indeed, make use of Ptolemy and thePythagorean writers ; but they are subsidiary to the charms of Aristoxenus,the difficulties of whose system were not apprehended by Westphal, muchless squarely faced. His exposition was given an even wider currency bythe publication of the two volumes of F. A. Gevaert's Histoire et Theoriede la Musique de VAntiquite (1 875) ; and later writers who have undertakenthe difficult task of presenting a comprehensive account of Greek music,such as H. Riemann in his Handbuch der Musikgeschichte and M. Emmanuelin Lavignac's Encyclopedic de la Musique, have been influenced, if not dom-inated, by the example and methods of Westphal and Gevaert. Neverthe-less, as has been suggested above, the Aristoxenian system cannot, by itsvery nature, tell us anything like the whole truth about the Greek scales.Dissatisfaction with the solutions of Westphal and his followers has tendedto grow since the publication of the Orestes fragment of music in 1892and of the Delphic Hymns in 1893 ; for these pieces were not easilyaccommodated to the Aristoxenian scheme. The interpretation of thenotation, which was forced into support of Aristoxenus, has been assailed,notably by A. Greif (in Revue des Etudes Grecques, 1909) and by C. Torr(On the Interpretation of Greek Music, 1896) ; and further studies ofdifficult passages of Aristides Quintilianus and Plutarch, which were brushedaside by Westphal or treated in an unconvincing fashion, have emphasizedthe distrust of Aristoxenus. The present position is fairly summed up byMr. Winnington-Ingram in his recent book, Mode in Ancient Greek Music.(1936)

:

INTRODUCTION xxviiNot even the main course of development of Greek music, far less the full details

of its modalities, can be established on the evidence. It is a result to give rise topessimism ; and the prospects of further advance in our knowledge are not bright.. . . Yet complete despondency is as unnecessary as it is ignoble. Every studentof the subject must from time to time have the feeling that there is a certain amountof evidence, particularly concerning the earlier stages of Greek music, that is stillunrelated together, and must hope that one day he will strike upon the true, theilluminating hypothesis which is to relate it.

So we come to the present book. Miss Schlesinger needs no corn^mendation to any one who is aware of her established reputation

-as a

historian of musical instruments or who has read her important chapter' The Significance of Musical Instruments in the Evolution of Music ' inthe Introductory Volume of the Oxford History of Music (1929). Thebasis of her work is an investigation extending over nearly a quarter ofa century into the capabilities of wind instruments, both of the type ofthe primitive flute and of the primitive pipe, to which latter category theaulos belongs. It is an especially important feature of the author's workthat it has not been confined to paper calculations, but is firmly foundedon a practical knowledge of the instruments concerned. A considerablenumber of pipes and flutes from various parts of the world have beencollected and played upon ; their scales have been carefully noted down,their intervals accurately measured ; and the results have been repeatedlychecked and compared with one another. Alongside of these actual speci-mens, facsimiles have been made of such of the remains of Greek auloias are available for accurate measurement and of a number of ancientpipes found in Egypt ; they have all been fitted with mouthpieces whoseindividual properties have also been subjected to rigorous tests. Thestriking result of these investigations is that a simple principle seems tohave operated in the Greek aulos as it does in many primitive pipes : theirfmgerholes are placed equidistantly and the effective length of pipe andmouthpiece combined is a multiple of the distance between the holes.The practical and theoretical consequences of this principle of equalmeasurement are worked out in great detail in the following pages, andthe reader is introduced to a widespread, natural, and almost inevitablemusical language whose existence has hitherto been unsuspected by theorists.The author, however, has done more than experiment with actual pipesand facsimiles of pipes. She brings the results of her practical acousticsinto relation with the written testimony of the Greeks ; and in an appendixshe demonstrates how the Greek musical notation was originally designedfor the Harmoniai and expanded to meet the needs of later times. Theline of investigation here pursued is in principle simple ; in its workingout it is full of surprises. Though this book upsets many of our previousnotions of the intervals of the Greek scales, and especially of the way theywere related to one another, there can be no doubt that all further studyof Greek music will be indebted to Miss Schlesinger's pioneer work. Itis, I venture to think, the most original and illuminating contribution yetmade to a difficult and fascinating subject.

J. F. MOUNTFORD

CONTENTS

THE ORIGIN AND GENESIS OF THE HARMONIA ON THE AULOS :DEMONSTRATION OF THE MODAL PRINCIPLE IN OPERATION

Introductory. Outline of the Theory of the Harmoniai. Equal Measurein Acoustic Theory. Modal Determinants (= M.D.). The MixolydianHarmonia. The Genesis of the Modal Material of the Mixolydian Mode.The Mixolydian Harmonia in the Diatonic Octave. The Lydian Harmonia.The Phrygian Harmonia. The Dorian Harmonia. The HypolydianHarmonia. The Hypophrygian Harmonia." The Hypodorian Harmonia.The Bastard Hypodorian. The Aulos as Origin of the Harmoniai. TheModal System based upon the Operation of the Principle of Equal Measure.The Ethos of the Mode based upon the characteristic Features peculiar toeach Harmonia. Professor H. S. Macran : the ' overlooked factor '.

THE AULOS : ITS SIGNIFICANCE IN THE HISTORY OF GREEK MUSICThe Aulos as Mode-bringer. The a priori Claim. The Importance of theMouthpiece. The Tonic as Starting-note bears a different Ratio in eachMode (Arist. Quint.). Equidistant Fingerholes on Aulos or Flute cannotproduce Equal Intervals. The Management of the Breath-stream in play-ing the Aulos. The Two Types of Mouthpiece. The Primitive Double-reed Mouthpiece preserves the Integrity of the Modal Scale. The Beating-reed Mouthpiece. The Influence of Tongue-length and Width onPitch exhibited in the Beating-reed Mouthpiece. Fundamental StructuralChange in the Harmonia brought about by the Unique Properties of theBeating-reed Mouthpiece. Significance of the Aulete's Attitude whileplaying the Aulos, illustrated on Vase Paintings at the British Museum.The Musical and Technical Significance of the Aulete's Two Movements,while playing, which are denoted by Aristotle, Aristoxenus and Plutarchby the opposites avaa-nav and Karao-nav. Polemic directed by Aristoxenusagainst the Aulos. The Effect of increased Pressure of Breath on Pitchand Harmonics. Aristotle on the Aulos and its Mouthpieces. Theo-phrastus on the Mouthpieces of the Aulos. Technical and Musical Possi-bilities of the Double Aulos. A change of Mode on the Aulos. Ptolemy'sReference to the Beating-reed Mouthpiece of the Auloi. The Feats ofPronomus, the Theban. Macrobius on the Position of the Fingerhole.Find of Fragments of Auloi at Meroe by Professor John Garstang (Liv.Univ.). The Feat of Midas of Agrigentum.

THE AULOS, PART II : THE AULOS IN ANCIENT AND MODERN THEORY :ITS MOUTHPIECES AND MODALITY

The Reactions of Reed-blown Pipes. The Incidence of Length in WindInstruments in the Determination of Pitch. The Incidence of Diameterin the Mouthpiece. The Open Pipe : The Closed Pipe. .FundamentalResonance and the Determination of Pitch. Part played by the Mouthpieceof the Aulos. The Double-reed Mouthpiece. The Proper Note of theMouthpiece. The Determination of Pitch from Length on a DR Mp.Significant and Unique Property of the Double-reed Mouthpiece. TheStruggle for Mastery between Mouthpiece and Resonator. The modusoperandi of the Proportional Law productive of the Harmonia-on the Aulos.Puzzling Properties of the Aulos and its Mouthpieces. Unsuspected Factorin the Interior of the Aulos. The Arche dominates the Inner Reactionsof the Aulos Resonator. The Plan of the Harmonia in the Interior of theAulos. How the Modality of an Aulos may be judged. Bulbs on an Aulosare a sign of a change of Harmonia. Ten Main Points concerning the Double-reed Mouthpiece. The Beating-reed Mouthpiece. The double Move-ment of the Tongue of the Beating-reed Mouthpiece. Implications ofthe Feat of Midas of Agrigentum. Plato on Empiricism in Aulos Music.

xxix

XXX THE GREEK AULOSCHAP. PAGE

Momentous significance of shortening the Tongue of the Beating-reedMouthpiece. Change to Elaborate Playing on the Aulos. Performanceof Aulos Loret xxiii with Beating-reed Tongue of Mouthpiece shortenedby one-third. Piper persuaded by Pythagoras to change the Modalityof his Aulos from Phrygian to Dorian Spondaic. Examples of the Per-formance of Reed Mouthpieces under various Conditions. Concerningthe Octave Relation in Auloi (Porphyry's Comm. on Ptol., i, 8). Noteson Debatable Points in the Quotation from Porphyry. The Ethos of theHarmonia.

IV THE HARMONIA AS MODAL BASIS OF THE PERFECT IMMUTABLE SYSTEMAND OF THE TONOI AND THEIR NOTATION 138

Introductory. Evolution of the Greater Complete System from the Speciesof the Seven Harmoniai. The Four Periods in the Development of theGreek Musical System. The Nomenclature of the Degrees of the Scale :The Onomasiai Kata Thesin and Kata Dynamin. Modal Implicationsof the Historical Development of the Kithara. The Practical Basis of theSpecies. The Order in which the Species occur is the Reverse of that ofthe Harmoniai and of the Tonoi. Omega, the Common Tonic of theHarmoniai. Birth of the Tonos. Modal Significance of the TetrachordSynemmenon. The Modal Basis of the P.I.S. confirmed by Ptolemy'sFormulae. Modal Origin of Ptolemy's Syntonic Chromatic. The SevenHarmoniai restored by Ptolemy through the Mechanism of the Tonoi.Four Stages in the Development of the Tonos marked by a change ofStarting-note. Stage I : Hypate Meson as Starting-note and Modal Pivot.Stage II : Hypate Hypaton as Starting-note now becomes the Modal Pivot.Stage III : The Modal Pivot changes to Proslambanomenos as Starting-note. Stage IV : Fundamental Modal Change in the P.I.S. from Dorianto Phrygian. The Tonoi as Curtailed Modes.

V EVIDENCE IN SUPPORT OF THE MODAL SYSTEM 1 70The Harmonia's Modal Principle of Equal Measure confirmed by Aristotle.The Evidence of the Canon of Florence. The Common Modal Starting-note according to Aristides Quintilianus. The Mese as Arche. The 12Polemics of Aristoxenus against the Harmonists. Polemics 1 and 2 :Concerning the Harmonia. Polemic 3 : The close-packed Scales of theHarmonists. Polemic 4 : Concerning the Tonoi. Polemic 5 : Notationas the Goal of Harmonic. Polemic 6 : The Theory of the Aulos and ofthe Pipe-scales. Polemic 7 : The Aulos as the ' Foundation of the Orderof Harmony.' Polemic 8 : Eratocles and the Harmonists in general treatonly of the Octave. Polemic 9 : Concerning Systems. Polemic 10 :Eratocles determines the Species by the Recurrence of the Intervals.Polemic 1 1 : The Harmonists assert that Points of Pitch consist of Ratiosand Rates of Vibration. Polemic 12 : On the Twenty-eight ConsecutiveDieses. The Characteristic Ratio 1 1 /io of the Dorian Harmonia, ascendingfrom the Tonic, Hypate to Parhypate Meson. Eleven, the only Deter-minant Number that could place Mese upon the Fourth Degree of theScale. The Ratio 11 /io as first Diesis on the Tonic confirmed by AristidesQuintilianus (p. 123M.). Further support for the use of Ratio 11/10 inthe Tonos from Ptolemy. Definition of the Diesis by Aristides Quinti-lianus (p. 123 M). The Ratio 11/10 as Spondeiasmos and Eklysis. TheEkbole, interval of Five Dieses. The 28 Dieses of the Harmonists accord-ing to Aristoxenos and Aristides Quintilianus. ' 28 ' as the Ratio Numberof the Mixolydian Tonic, and as Hypate Hypaton in the Tonos. BriefRecapitulation.

VI THE CYLINDRICAL MODAL FLUTE WITH EQUIDISTANT FINGERHOLESEMBODYING THE HARMONIA (FLUTE i) 220

The Harmonia installed on Aulos and Flute. The Significance of Diameterin the Acoustics of the Modal Flute. The Aulos alone gave birth to theHarmonia. The Harmonia on the Flute. Formula No. 1 (v.f. from Length).Formula No. 2 (Length from v.f.). Formula No. 3 (to find the Position ofHole 1). The Significance of the Increment of Distance (I.D.). The FourAspects of the Increment of Distance. Nine Aspects of Allowance inrespect of Diameter in Modal Flutes. The Classification of Modal Flutes.The Three Experimental Sensa Flutes. The Modal Sequence of theHypophrygian Harmonia on Flute ' Sensa C '.

CONTEXTS xxxi

VII THE CYLINDRICAL MODAL FLUTE IN THEORY AND PRACTICE 24

1

Introductory. Five Important Factors in the Acoustics of the ModalFlute Recapitulated. Extension of Compass by Half-stopping in theModal Flute. Extension of Compass by Cross-fingering in the ModalFlute. Experiments on the Mond Flute in the Theory and Practice ofCross-fingering. Demonstration of the Significance of Formula No. 3in the Pitch-determination of the Cross-fingered Note. Further Examplesdemonstrated on Flute ' Sensa C '. Cross-fingering as a Means of Transi-tion from one Musical System to another. The Evidence of Virdungand Agricola on Cross-fingering. Agricola's Cross-fingering tested inPractice. Hypolydian Flutes cross-fingered give the Authentus Protus.The Diameter in Cylindrical Tubes in Octave Relation : the ChineseFormula. Purity of Intonation in Modal Flutes, in spite of ExcessDiameter in Upper Half of Pipe. Types of Flutes other than Transverse.The Transverse Flute in Ancient India : Treatises by Bharata and Sarang-dev. Implications inferred from Sarangdev's Table of 15 Modal Fluteswith Equidistant Fingerholes. The Transverse Flute in Evolution inEurope. The Ditonal Scale adopted by the Arabs. The Duplication ofthe First Tetrachord in the Octave Scale. The Modal Flute in Syro-Arabic Sources : Al-Farabi's Evidence. The Influence of Diameterrecognized by Ptolemy. Al-Farabi describes Flutes and Pipes with Equi-distant Fingerholes. The Lute Accordance No. 3, introduced by Ishaq al-Mausili (Fourth, Fifth, Fourth). Ishaq's Classification by Courses(Majari) corresponding to the Modal Species. The Wosta of Zalzal(= Ratio 27 . 22) implies the use of the Lydian Species of M.D. 27. FurtherModal Implications of the Wosta of Zalzal. Our Minor and Major Modesare akin to the Majari through Wosta (Min. Third), or through Binsir(Maj. Third) of Arabian Lute Accordance. The Modal Scales of theOctoechos traced in Ishaq's Classification of Melodies, and in his LuteAccordance. Al-Farabi and Al-Kindi stress the Ditonal Scale : Ishaqal-Mausiii the Modal Species of the Harmonia. The Modal Flute basedon Proportional Modality breaks new Ground.

VIII SURVEY OF THE SCALES AND SYSTEMS FORMING THE BASIS OFFOLK MUSIC 291

Introductory. Brief Inquiry into the Origins of Folk Music. The Originsof Scales. The Evidence of Vedda Music. The Evidence from Green-land. Brief Survey of Scales or Musical Systems forming the Basis of Primi-tive and Folk Music. Scales derived from a Cycle of Ascending Fourthsor Descending Fifths, on a given Fundamental C = 128 v.p.s. DorianHarmonia or ' Pentatonic in Transition with a Sixth Step ' ? Ditonal Scalefrom Cycle of Fifths or Hypolydian Harmonia ? A separate Origin forthe Pentatonic and Heptatonic. The Myth of so-called Equal-steppedScales. Dr. Erich M. von Hornbostel. Hornbostel's Cycle of BlownFifths (Blasquintenzirkel). The Basis of Hornbostel's Theory of the'Blasquintenzirkel' in his own words (Engl, and Germ.). Entails theFalsification of an Acoustic Principle. The Lay View of the Influence ofDiameter on Pitch. The Alleged Flatness of Overtones from ClosedPipes repudiated by Acoustic Law. The Records of Brazilian Panpipesblown by Hornbostel actually exhibit Overtones, pure, sharp and flat,where all are alleged to be flat. Correct and Faulty Methods of BlowingPanpipes. Analysis of Results given in Figs. 67 and 68. Even the Resultsobtained by Wrong Methods of Blowing suggest the Harmonia as Origin.The Antique Peruvian Flute ' San Ramon ' is in a different Category fromthe Panpipes. Dr. Manfred Buko ef's Strictures on the Blasquinten-zirkel. Evidence from an Agariche from Bolivia : all Overblown Fifths,pure. Is there in Closed Pipes a natural Balance between the InteriorLength + Diameter and the Exte or Length omitting Diameter ? TheBlowing of the Panpipes has provejl to be the Undoing of the Theory ofBlown Fifths. Unequivocal Rejection oi the Thefery of the Blasquinten-zirkel. The Contribution of Dr. Jaap Funst from the Music of Java andBali. The Harmoniai, identified from Dr. Kunst's Records as Origin ofthe Slendro and Pelog Scales of Java and Bali. The Flutes from Java andBali embody the Harmoniai in their Equidistant Fingerholes. Duplicationof the First Tetrachord on the Fourth or Fifth Degree in Evidence in someJavanese and Balinese Scales. The Music of the Folk in South Africa.The Music of the Bantu Folk of South Africa based upon the HarmonicSeries. The South African Natives have . discovered the Different

xxxii THE GREEK AULOSCHAP. PAGE

Reactions of Open and Closed Pipes, closing them at will to increase theCompass. A Kind of Transverse Flute in use by the Venda, Swazi,Pedi, and other Tribes.

IX QUEST FOR THE HARMONIA AS SURVIVAL OR REBIRTH IN FOLK MUSIC 35

1

Indications of the Survival or Rebirth of the Harmonia. Evidence of thePractical Use of the Harmonia in Ancient Greece. Fragment of Pindar'sFirst Pythian Ode in the Hypophrygian Harmonia. The Fragment displaysall the Hypophrygian Modal Characteristics, and five closes on the KwXa.The three Hymns attributed to Mesomedes : The First Hymn : ' To theMuse ', in the Hypophrygian Mode. The Second Hymn : ' To the Sun ',in the Hypophrygian Harmonia. The Third Hymn : ' To Nemesis ', inthe Hypophrygian Species. The Epitaph of Sicilus may be read in theHypophrygian or Phrygian Species. Fragment from the Orestes ofEuripides in the Hypophrygian Species. The Paean Fragment in theBerlin Papyrus (discovered by Dr. W. Schubart in 1918) : Hypophrygianor Phrygian Species. Discovery of a Christian Hymn (in the OxyrhynchusPapyri) : Pseudo-Hypophrygian Species. The Two Delphic Hymns :The Delphic Hymn No. 1 in the Hypolydian Harmonia. The DelphicHymn No. 2 in the Dorian Harmonia. The Prototypes of Greek Musicall exhibit the Modal Characteristics of the Harmonia. The CharacteristicIntervals of Folk Music defined by Ratios, Vibration Frequencies andCents. The Modal Characteristics of the Harmonia in Early MedievalChants. Hucbald's Evidence. Survival of Modal Pivots in earlyMedieval Liturgical Chants. The Era of Polyphonic Music heraldsthe Wane of the Harmonia in Liturgical Chants. Brief Reference to theCanon of Florence and to the Divisions of the Monochord. Cross-fingering on the Flute as Evidence of the Survival of the Harmonia in theSixteenth Century. The Dorian Harmonia in Folk Music : Evidencefrom the Incas of Peru. The Scale of the Dorian Harmonia of M.D. 11erroneously diagnosed as Pentatonic. Evidence from Hindostan, Hungaryand Rumania. Evidence from New Mecklenburg, Turkey and the Jewsof the Yemen. The Lydian Harmonia in Folk Music. The PhrygianHarmonia in Folk Music. Evidence from Synagogue Chants ; fromNew Mecklenburg, Rumania, The Pawnees, Peru and Sumatra of theHypophrygian Harmonia. The Hypodorian Harmonia in Folk Music.The Mixolydian Harmonia as Rag Malkos in Hindostan. The HypolydianHarmonia in Folk-song : e.g. in East Greenland. The Closing of theCycle : from Ancient to Modern Greece.

X RECORDS OF MEASUREMENTS AND PERFORMANCE : (i) OF AULOI,(2) OF FLUTES, PRECEDED BY EXPLANATORY NOTES 408

APPENDIX I : A BRIEF OUTLINE OF THE MODAL BASIS OF THE SCHEMEOF GREEK NOTATION 519

The Older Accepted Interpretation by Bellermann. The System ofNotation based upon Modality. The Priority of the Vocal Notation.The Main Features of the Vocal Notation. Important Facts indicated bythe System of Notation. Mese as the Modal Nucleus of the System ofNotation in each Tonos. Tests as a Challenge to the Accepted Inter-pretation of Bellermann. Test I. Test II. Test III. Test IV. Test V.

APPENDIX II : THE ORIGIN OF THE ECCLESIASTICAL MODES : THEIRRELATION TO THE MODAL SYSTEM OF THE HARMONIAI 531

Recapitulation of Stages in the Development of the P.I.S. The Modalityof the P.I.S. transformed from Dorian into Phrygian. The Rise of a NewSystem of Conjunct Modal Scales : The Birth of the Plagal Modes. TwoExamples of the New Independent Conjunct Modal Scales based uponProslambanomenos. The Octoechos in use in the Greek Church in theFourth Century a.d. Confirmation from Arabian Sources. Ishaq'sMajra through Wosta identified as Phrygian Modal Species. Confirma-tion of the Origin of the Ecclesiastical Modes from the Writings of EarlyMedieval Theorists.

APPENDIX III : A NEW LANGUAGE OF MUSIC : POSSIBILITIES OFTHE ANCIENT MODES FOR USE IN MODERN COMPOSITION 541

INDEX 547

DIAGRAMSFIG. PAGE

1. DIAGRAM ILLUSTRATING THE SEVENFOLD MONOCHORD DIVISIONSBY MODAL DETERMINANTS OF THE SEVEN HARMONIAI 5

2. THE ARCHAI OF THE SEVEN HARMONIAI IN POSITION IN THEHARMONIC SERIES ON F AND C 7

3. GENESIS OF THE MIXOLYDIAN MODAL MATERIAL RESULTING FROMTHE ALIQUOT DIVISION BY DETERMINANT 14 ON THE F STRING 8

4. THE MIXOLYDIAN HARMONIA IN THE DIATONIC GENUS RESULTINGFROM THE ALIQUOT DIVISION BY DETERMINANT 14 12

5. GENESIS OF THE LYDIAN HARMONIA BY THE ALIQUOT DIVISIONBY DETERMINANT 1 3 1

7

6. LYDIAN HARMONIA (DIATONIC GENUS) RESULTING FROM THEALIQUOT DIVISION BY DETERMINANT 1 3 1

8

7. GENESIS OF THE PHRYGIAN HARMONIA BY THE ALIQUOT DIVISIONBY DETERMINANT 12 1

9

8. PHRYGIAN HARMONIA (DIATONIC GENUS) RESULTING FROM THEALIQUOT DIVISION BY DETERMINANT 12 ON C 20

9. TO ILLUSTRATE THE FILLING IN OF THE SEPTIMAL THIRD OF RATIO7 : 6 ON THE AULOS 21

10. THE FILLING IN OF THE SEPTIMAL THIRD ILLUSTRATED IN GREEKNOTATION 22

11. GENESIS OF THE DORIAN HARMONIA THROUGH THE ALIQUOTDIVISION BY DETERMINANT 22 ON THE F STRING 23

12. THE DORIAN HARMONIA (DIATONIC GENUS) RESULTING FROM THEALIQUOT DIVISION BY DETERMINANT II. PRIMITIVE FORMCONNECTED WITH THE NAME OF TERPANDER 24

13. DORIAN HARMONIA, COMPLETE OCTAVE SCALE ON F = 88 V.P.S.RESULTING FROM THE ALIQUOT DIVISION BY DETERMINANT 22 25

14. GENESIS OF THE HYPOLYDIAN HARMONIA BY THE ALIQUOT DIVISIONBY 20 ON THE C STRING = 64 V.P.S. THE FINDING OF THEARCHE IN THE HARMONIC SERIES 25

15. HYPOLYDIAN HARMONIA (DIATONIC GENUS) RESULTING FROM THEALIQUOT DIVISION BY DETERMINANT 20 ON THE AULOS 26

16. GENESIS OF THE HYPOPHRYGIAN HARMONIA RESULTING FROM THEALIQUOT DIVISION BY MODAL DETERMINANT 1 8 27

17. HYPOPHRYGIAN HARMONIA (DIATONIC GENUS) RESULTING FROMTHE ALIQUOT DIVISION BY DETERMINANT 1 8 28

18. GENESIS OF THE HYPODORIAN HARMONIA RESULTING FROM THEALIQUOT DIVISION BY MODAL DETERMINANT 1 6. THE FINDINGOF THE ARCHE IN THE HARMONIC SERIES 28

19. THE HYPODORIAN HARMONIA OF MODAL DETERMINANT 16 (DIATONICGENUS) RESULTING FROM THE ALIQUOT DIVISION BY DETER-MINANT 16 ON C 29

xxxiii

xxxiv THE GREEK AULOSFIG. PAGE20. THE SEVEN HARMONIAI EXPRESSED IN SUPERPARTICULAR RATIOS OF

LENGTHS OF STRING OR PIPE, TAKEN WITHIN THE OCTAVEFROM C = 64 V.P.S. TO C = 1 28 V.P.S. 30

21. THE MODAL SCALE ON THE DORIAN AULOS 3922. MODES (HARMONIAI) RESULTING FROM THE DISPOSITION OF EQUI-

DISTANT FINGERHOLES 4223. EGYPTIAN WALL PAINTING FROM A TOMB IN THEBES, SHOWING

musician with double pipes PL 3. Facing 48By courtesy of the Director, British Museum

24. MOMENTOUS SIGNIFICANCE OF SHORTENING THE VIBRATING TONGUEOF THE MOUTHPIECE, BY ONE-THIRD OF ITS LENGTH, ON THEHYPOLYDIAN AULOS OF M.D. 20 WITH 3 FINGERHOLES.BIRTH OF OUR MAJOR SCALE OF DUPLICATED TETRACI IORDS 52

25. TESTS ON B-R. MOUTHPIECES FOR REGIONAL PITCH. OCTAVE SHIFTON TONGUE OF MOUTHPIECE ; AND HARMONICS 64

26. THE DOUBLE AULOI BORED TO GIVE THE HYPODORIAN MODALOCTAVE OF MODAL DETERMINANT 1 6 68

27. SUGGESTED FEAT OF PRONOMUS, THE THEBAN. THREE MODESPLAYED UPON THE SAME AULOS BY CHANGING THE EXTRUSIONOF THE MOUTHPIECE 70

28. THE POMPEIAN AULOI (WITH REVOLVING BANDS) AND, TO THERIGHT, AULOI SURMOUNTED BY A MOUTHPIECE SUGGESTIVEOF A MODERN CLARINET OR FLAGEOLET PI. 12. Facing 70Phot. Brogi.

29. DRAWING OF THE FRAGMENTS OF AN AULOS WITH REVOLVING BANDS 77Candia Museum. Drawn by Professor J. L. Myres

30. BIRTH OF THE SEVEN-MODAL SPECIES OF THE G.C.S. FROM THEKITHARA OF 15 STRINGS (WITHOUT RETUNING) 142

31. CONCERNING THE CONFUSION BETWEEN THE HARMONIAI, THEIRSPECIES AND THE TONOI, WHICH AROSE FROM THE FACT THATTHE ORDER OF THE SPECIES IN THE P.I.S. WAS THE REVERSE OFTHAT OF THE MODES IN THE TONOI 148

32. EXAMPLES OF THE TONOS WITH ITS HOMONYM HARMONIA AND ITSSPECIES I55

33. THE MODAL RATIOS OF THE PERFECT IMMUTABLE SYSTEM, IDENTI-FIED with ptolemy's formulae for the chroai 157

34. examples of the tonos as curtailed mode, exhibited in threestages of development from the ancient dorianharmonia between 168-9

35 . THE DORIAN OCTOCHORDAL HARMONIA EXPANDED FROM M.D. 1 1 TO 22 1 7336. THE MODAL IMPLICATIONS OF THE CANON OF FLORENCE ACCORDING

TO AUTHOR ' A ', LINES 1-3 17537. THE SEVEN HARMONIAI ON A COMMON FUNDAMENTAL F. WITHIN

THE SYSTEM OF THE TONOI, WITH THEIR MODAL RATIOS BYK. S. AND SYMBOLS OF NOTATION FROM ALYPIUS I7%~9

38. THE DESCENDING MODAL SEQUENCE FROM MESE 1 8539. REQUIRED A PHRYGIAN ENHARMONIC SPECIES OF THE P.I.S. 19640. THE MODAL RATIOS OF THE P.I.S. IDENTIFIED WITH PTOLEMY'S

FORMULAE FOR THE CHROAI 201op. cit., ii, 14

41. THE DEFINITION OF THE DIESIS. THE DIESIS OF ARISTIDES 205p. 123M.

DIAGRAMS XXXVFIG. PAGE

42. THE ENHARMONIC PYKNON OF THE ANCIENTS 207Plut., ' de Mus.', pp. 48-51 (ed. Weil and Reinach

43. SCHEME OF THE HYPOLYDIAN HARMONIA EXTENDED TO TWOOCTAVES KATA THESIN AND KATA DYNAMIN, WITH RATIOS OFTHE EKBOLE AND EKLYSIS 208This is the scheme implied in the Canon of Florence by 1 A ' (lines 1-3)

44. THE TWENTY-EIGHT DIESES OF THE HARMONISTS, A SUGGESTION.(TWO DIESES IN EACH PYKNUMFOUR IN EACH OCTAVEFORTHE SEVEN HARMONIAI.) TOTAL : TWENTY-EIGHT 214

45. THE MIXOLYDIAN HARMONIA AS TONAL AND MODAL SPECIES 21

J

46. THE MIXOLYDIAN AS THE OPPOSITE OF THE HYPOLYDIAN 2l8Plut., ' deMus.', Cap. 16, 157 (ed. Weil and Reinach) cf. Figs. 43 and 45

47. SCHEME SHOWING CROSS-FINGERING, PERFORMANCE AND RESULTON THE MOND FLUTE, NO. 2 247

48. THE COMPASS OF THE MOND FLUTE WITH CROSS-FINGERED NOTESFOR THE FIRST FOUR HOLES 249N.B.X indicates cross-fingering ; N.F. indicates normal fingering

49. AGRICOLA'S SCHEME OF CROSS-FINGERING 254~5Schiveizer, ' Pfeiffen des Discant's Scala und Fundament ' (ed. 154$, p. 172)

50. AGRICOLA'S SCHEME OF CROSS-FINGERING FOR THE SCHWEIZER 258-9Pfeiffen (1) ' Des Discants Scala ' ; (2) ' Des Tenors Scala ' (ed. 1528, p. 30)

51. THE TECHNICAL IMPLICATIONS OF SARANGDEV'S FLUTE, NO. 12 266See Grosset, op. cit., pp. 353-4

52. MODAL SEQUENCE IMPLIED BY GROSSET 'S INCREMENT OF DISTANCE,MODAL DETERMINANT 20 267

53. MODAL DETERMINANT 12 26754. MODAL SEQUENCE PRODUCED BY I.D. OF 2 ANGULAS + DIAMETER

OF FINGERHOLE (= -049). MODAL DETERMINANT 12 26855. LUTE ACCORDANCE OF ISHAQ-AL-MAUSILI BY FOURTH, FIFTH,

FOURTH, IN THE HYPOLYDIAN SPECIES IN THE MAJRA THROUGHBINSIR 278

56. THE PHRYGIAN SPECIES WITH DUPLICATED CONJUNCT TETRACHORDON THE LUTE, WITH THE ACCORDANCE NO. 3 OF ISHAQ 280

57. AL-FARABl'S ACCORDANCE OF THE LUTE OF 4 STRINGS TUNED INFOURTHS 28lSee Kosegarten, op. cit., p. 45

58. AL-FARABl'S PIPE (AULOS) WITH HIS ARABIAN NOTATION. SCALEOF PIPE WITH APPROXIMATION TO LUTE SCALE (FIG. 57) between 282-3

59. AL-FARABl'S AULOS (AS IN FIG. 58) WITH RATIOS OF THE HYPO-LYDIAN HARMONIA (BY K. S.) COMPARED WITH THOSE OF THELUTE WITH ISHAQ 'S ACCORDANCE 284Cf. Fig. 55

60. AL-FARABl'S PIPE WITH NINE FINGERHOLES BORED FOR THE HYPO-PHRYGIAN HARMONIA FROM EXIT, OR FOR THE HYPODORIANFROM HOLE I. RATIOS BY K. S. 286Cf. Figs. 58 and 59

61. THE ACCORDANCE OF THE LUTE BY ISHAQ. TUNED IN OCTAVESFROM MATHNA AND ZIR 287

THE USUAL ACCORDANCE ACCORDING TO YAHIA AND AL-FArABI62. TRANSFORMATIONS OF THE DORIAN AULOS WITH THE RATIOS AND

CENTS OF THE INTERVALS OF THE THREE MODAL SCALES.(CONJECTURE BY K. S.) 288

xxxvi THE GREEK AULOS

63. DERIVATION OF THE HEPTATONIC SCALE FROM A CYCLE OF7 ASCENDING PERFECT FOURTHS FROM C = 1 28 V.P.S. 302

64. THE PARENT HEPTATONIC AND ITS SPECIES DERIVED FROM THE CYCLEOF FOURTHS ON C AND G, THE PROTOTYPE OF THE DITONALDORIAN SPECIES OF THE GRAECO-ROMAN THEORISTS 303

65. HEPTATONIC SCALE WITH ITS SPECIES DERIVED FROM A CYCLE OF12 ASCENDING PERFECT FIFTHS 3/2 ON C = 64 V.P.S. 304

66. A SIBELIUS THEME FROM THE SECOND MOVEMENT (SYMPHONYNO. 2 IN D, 1902, OP. 43, BREITKOPF AND HARTEL, N.Y.BRANCH). PRESENTED WITH SYMBOLS OF GREEK NOTATIONBY K. S. 308

67. BRAZILIAN PANPIPES, NOS. V.B. 6322/23 32IKoch-Griinberg, op. cit., Table i

68. RESULTS OF THE COMPARISONS OF THE VIBRATION FREQUENCIES OFPANPIPES V.B. 6322/23 WITH THE RATIOS AND THE VIBRATIONFREQUENCIES OF THE RELATED HARMON IA, SUPPLIED BY K. S. 322

69. THE ANTIQUE PERUVIAN CLAY FLUTE SAN RAMON (V.A. 15901)FROM THE BOLIVAR COLLECTION 326The Flute has five Fingerholes in front and one in backSee Koch-Griinberg, op. cit., Table vii, p. 390

70. TESTS CARRIED OUT ON AN AGARICHE (PANPIPE) SHOWING CORRE-SPONDENCE OF PITCH WITH FORMULA : DIFFERENCE INVIBRATION FREQUENCY DUE TO (a) INTERNAL MEASUREMENT,(B) EXTERNAL ; A = DIAMETER 329-3O

71. VIBRATION FREQUENCY OF THE TONIC OF EACH SPECIES IN EACHharmonia taken on c = 128 ; f = 176 ; g = 192 v.p.s. 335

72. identification (by k. s.) of the harmoniai in the ancientpelog (heptatonic) scale of java and bali from therecords of dr. jaap kunst. the proto-pelog and pelogin transition 336

73. examples of the scales slendro (pentatonic) and pelog(heptatonic) in use in the gamelans of java and bali,identified with the harmoniai from the records ofdr. jaap kunst (by k. s.) 338-9

74. modal schemes of eleven slendro javanese scales identifiedfrom dr. kunst 's tables v and vi in which vibrationfrequencies are given (by k. s.) with the ratios of theintervals 34o-i

75. (tune) played with swazi, narrow bore instrument in g|) 346op. cit., p. 115

76. PEDI SCALE OF TRANSVERSE FLUTE WITH THREE FINGERHOLES 348op. cit., p. 125, No. I

77. SPECIMEN TUNE PLAYED BY A KARANGA ON THE OMBGWE 350op. cit., p. 130

78. THE FIVE CLOSES ON THE Kw\a. RATIOS BY K. S. 35779. RHYTHMICAL TRANSCRIPTION OF THE FRAGMENT OF PINDAR'S

FIRST PYTHIAN ODE 359From the Greek Version, first published by Athanasius Kircher in ' MusurgiaUniversalis ', Vol. x,p. 541. (Rhythm adapted from Gevaert's version)

80. FROM ' THE HYMN TO THE MUSE ' Els Movaav. MESOMEDES FIVEHYPOPHRYGIAN CLOSES (RATIOS BY K. S.). 361

81. THE SCALE OF THE EPITAPH TO SICILUS 36382. SECOND STEP IN THE HEPTATONIC SCALE OF THE HARMONIA ON

c = 128 v.p.s. 371

DIAGRAMS xxxviiPIG.

83. THE AUGMENTED SECOND OF RATIO 15/13 = 247 CENTS IN FOLKMUSIC ON TONIC C = 128 V.P.S. ; ON TONIC G = 192 V.P.S. 372

84. THE INTERVAL OF THE THIRD ON THE TONIC IN FOLK MUSIC TONICSC = 128 V.P.S. ; AND G = 192 V.P.S. 373

85. (A) FLAT FOURTHS IN FOLK MUSIC. (b) THE RAISED FOURTH INFOLK MUSIC 374

86. THE FIFTHS IN FOLK MUSIC 37687. CHARACTERISTIC INTERVALS AND FEATURES OF THE SEVEN HARMONIAI 37788. HUCBALD'S SCHEME OF ANTIPHONS IN THE PROTUS AUTHENTUS

WITH GREEK NOTATION OF THE LYDIAN TONOS 379p. 120, Gerb., op. cit.

89. ' HYMN TO THE SUN ' OF THE INCAS OF PERU 385' AA, Sumak Kancakchaska ' , No. 10 {pp. cit., p. 247). (Collected byA. Robles, from Huanuco)

90. PASTORAL (NO. 195) HACIENDA DE TOTORA, PERU. PLAYED ON THEKENA (FLUTE) BY KAPAKUTI 386

91. RUMANIAN SONG FROM THE MARAMUROS NO. 53 (c) 388Collected by Bela Bartok, op. cit., p. 40

92. MELODY FOR THE SUN FESTIVAL DANCE IN KING, NEW MECKLENBURG 39393. CLOSES FROM THE HAKO SONG OF THE PAWNEES (HYPOPHRYGIAN) 395

(K. S.)

94. PERUVIAN PASTORAL (NO. 197) IN THE HYPOPHRYGIAN HARMONIA 395Hacienda de Totora, Peru, from ' La Mus. des Incas ', by D'Harcourt

95. TUNE NO. 9 (a). MUSIC OF THE KUBUS OF SUMATRA 396p. 373, op. cit.

96. ' LLIW GWYN RHOSYN YR HAF.' MODAL VERSION BY K. S. (ASSUNG BY MISS ISABEL DODDS) 399

97. FROM A SONG IN RAG MALKOS 40OA. H. Fox Strangways, op. cit., p. 28g, lines 3 and 4

98. ' THE GOPl'S COMPLAINT ' (MIXOLYDIAN HARMONIA) 4OIRecorded by Ratan Devi

99. RECITATIVE SONG FROM EAST GREENLAND 402[00. ESKIMO SONG (iN SAME SCALE TRANSPOSED) 402

Collected by R. Stein. ' Eskimo Music ', p. 340 (ap. Thalbitzer, p. 35)[01. THE KATAPYKNOTIC APPARATUS IN OPERATION IN THREE TONOI

(DORIAN, PHRYGIAN, AND LYDIAN) facing 52I102. NUCLEUS OF THE SCHEME OF NOTATION. THE ENHARMONIC PYKNA

OF THE SEVEN HARMONIAI IN THE SYNEMMENON 524103. RATIO 26 IN THE TONOI, TRACED BY MEANS OF ITS INCIDENCE AS

CHROMATIC PARANETE DIEZEUGMENON 526104. THE ORIGIN OF THE ECCLESIASTICAL MODES IN THE FOURTH

DEVELOPMENT OF THE PERFECT IMMUTABLE SYSTEM (iN THEHYPOLYDIAN TONOS) IN THE PHRYGIAN MODALITY 533

105. ORIGIN OF THE ECCLESIASTICAL MODES CONFIRMED FROM ARABIANSOURCES. THE OCTOECHOS ON THE LUTE OF ISHAQ (cf. FigS. 55and 61, Chap, vii, Ishdq's Lute), the majra of wosta =phrygian species 538-9

106. ' sunrise ' (from agave) 543107. funeral march (from agave) 543108. ' sunrise ' (from agave) 544109. from ' agave ', with allowances for pianoforte approxima-

tion, species of dorian mode (c 22) 544

PLATESAULETE PLAYING ON THE DOU