THE MODES

OF

ANCIENT GREEK MUSIC

MONRO

London

HENRY FROWDE

Oxford University Press Warehouse

Amen Corner, E.C.

New York

MACMILLAN & CO., 66, FIFTH AVENUE

The Modes

of

Ancient Greek Music

BY

D. B. MONRO, M.A.

PROVOST OF ORIEL COLLEGE, OXFORD

HONORARY DOCTOR OF LETTERS IN THE UNIVERSITY OF DUBLIN

Oxford

AT THE CLARENDON PRESS

1894

Oxford

PRINTED AT THE CLARENDON PRESS

BY HORACE HART, PRINTER TO THE UNIVERSITY

DEDICATED

TO THE

PROVOST AND FELLOWS

OF TRINITY COLLEGE DUBLIN

xeinosynês heneka

Transcriber's Note:
The original text contained many words in the Greek alphabet. These words have been transliterated to the Latin alphabet. They appear in the text in bold font.
e.g. τροποι is written tropoi

PREFACE

The present essay is the sequel of an article on Greek music which the author contributed to the new edition of Smith's Dictionary of Greek and Roman Antiquities (London, 1890-91, art. Musica). In that article the long-standing controversy regarding the nature of the ancient musical Modes was briefly noticed, and some reasons were given for dissenting from the views maintained by Westphal, and now very generally accepted. A full discussion of the subject would have taken up more space than was then at the author's disposal, and he accordingly proposed to the Delegates of the Clarendon Press to treat the question in a separate form. He has now to thank them for undertaking the publication of a work which is necessarily addressed to a very limited circle.

The progress of the work has been more than once delayed by the accession of materials. Much of it was written before the author had the opportunity of studying two very interesting documents first made known in the course of last year in the Bulletin de correspondance hellénique and the Philologus, viz. the so-called Seikelos inscription from Tralles, and a fragment of the Orestes of Euripides. But a much greater surprise was in store. The book was nearly ready for publication last November, when the newspapers reported that the French scholars engaged in excavating on the site of Delphi had found several pieces of musical notation, in particular a hymn to Apollo dating from the third century B.C. As the known remains of Greek music were either miserably brief, or so late as hardly to belong to classical antiquity, it was thought best to wait for the publication of the new material. The French School of Athens must be congratulated upon the good fortune which has attended their enterprise, and also upon the excellent form in which its results have been placed, within a comparatively short time, at the service of students. The writer of these pages, it will be readily understood, had especial reason to be interested in the announcement of a discovery which might give an entirely new complexion to the whole argument. It will be for the reader to determine whether the main thesis of the book has gained or lost by the new evidence.

Mr. Hubert Parry prefaces his suggestive treatment of Greek music by some remarks on the difficulty of the subject. 'It still seems possible,' he observes, 'that a large portion of what has passed into the domain of "well-authenticated fact" is complete misapprehension, as Greek scholars have not time for a thorough study of music up to the standard required to judge securely of the matters in question, and musicians as a rule are not extremely intimate with Greek' (The Art of Music, p. 24). To the present writer, who has no claim to the title of musician, the scepticism expressed in these words appears to be well founded. If his interpretation of the ancient texts furnishes musicians like Mr. Parry with a somewhat more trustworthy basis for their criticism of Greek music as an art, his object will be fully attained.

TABLE OF CONTENTS

THE MODES OF ANCIENT GREEK MUSIC.

§ 1. Introductory.

The modes of ancient Greek music are of interest to us, not only as the forms under which the Fine Art of Music was developed by a people of extraordinary artistic capability, but also on account of the peculiar ethical influence ascribed to them by the greatest ancient philosophers. It appears from a well-known passage in the Republic of Plato, as well as from many other references, that in ancient Greece there were certain kinds or forms of music, which were known by national or tribal names—Dorian, Ionian, Phrygian, Lydian and the like: that each of these was believed to be capable, not only of expressing particular emotions, but of reacting on the sensibility in such a way as to exercise a powerful and specific influence in the formation of character: and consequently that the choice, among these varieties, of the musical forms to be admitted into the education of the state, was a matter of the most serious practical concern. If on a question of this kind we are inclined to distrust the imaginative temper of Plato we have only to turn to the discussion of the same subject in the Politics of Aristotle, and we shall find the Platonic view criticised in some important details, but treated in the main as being beyond controversy.

The word harmonia, 'harmony,' applied to these forms of music by Plato and Aristotle, means literally 'fitting' or 'adjustment,' hence the 'tuning' of a series of notes on any principle, the formation of a 'scale' or 'gamut.' Other ancient writers use the word tropos, whence the Latin modus and our mood or 'mode,' generally employed in this sense by English scholars. The word 'mode' is open to the objection that in modern music it has a meaning which assumes just what it is our present business to prove or disprove about the 'modes' of Greek music. The word 'harmony,' however, is still more misleading, and on the whole it seems best to abide by the established use of 'mode' as a translation of harmonia, trusting that the context will show when the word has its distinctively modern sense, and when it simply denotes a musical scale of some particular kind.

The rhythm of music is also recognized by both Plato and Aristotle as an important element in its moral value. On this part of the subject, however, we have much less material for a judgement. Plato goes on to the rhythms after he has done with the modes, and lays down the principle that they must not be complex or varied, but must be the rhythms of a sober and brave life. But he confesses that he cannot tell which these are (poia de poiou biou mimêmata ouk echô legein), and leaves the matter for future inquiry [1].

§ 2. Statement of the question.

What then are the musical forms to which Plato and Aristotle ascribe this remarkable efficacy? And what is the source of their influence on human emotion and character?

There are two obvious relations in which the scales employed in any system of music may stand to each other. They may be related as two keys of the same mode in modern music: that is to say, we may have to do with a scale consisting of a fixed succession of intervals, which may vary in pitch—may be 'transposed,' as we say, from one pitch or key to another. Or the scales may differ as the Major mode differs from the Minor, namely in the order in which the intervals follow each other. In modern music we have these two modes, and each of them may be in any one of twelve keys. It is evidently possible, also, that a name such as Dorian or Lydian might denote a particular mode taken in a particular key—that the scale so called should possess a definite pitch as well as a definite series of intervals.

According to the theory which appears now to prevail among students of Greek music, these famous names had a double application. There was a Dorian mode as well as a Dorian key, a Phrygian mode and a Phrygian key, and so on. This is the view set forth by Boeckh in the treatise which may be said to have laid the foundations of our knowledge of Greek music (De Metris Pindari, lib. III. cc. vii-xii). It is expounded, along with much subsidiary speculation, in the successive volumes which we owe to the fertile pen of Westphal; and it has been adopted in the learned and excellent Histoire et Théorie de la Musique de l'Antiquité of M. Gevaert. According to these high authorities the Greeks had a system of key (tonoi), and also a system of modes (harmoniai), the former being based solely upon difference of pitch, the latter upon the 'form' or species (eidos) of the octave scale, that is to say, upon the order of the intervals which compose it.

§ 3. The Authorities.

The sources of our knowledge are the various systematic treatises upon music which have come down to us from Greek antiquity, together with incidental references in other authors, chiefly poets and philosophers. Of the systematic or 'technical' writers the earliest and most important is Aristoxenus, a pupil of Aristotle. His treatise on Harmonics (harmonikê) has reached us in a fragmentary condition, but may be supplemented to some extent from later works of the same school. Among the incidental notices of music the most considerable are the passages in the Republic and the Politics already referred to. To these we have to add a few other references in Plato and Aristotle; a long fragment from the Platonic philosopher Heraclides Ponticus, containing some interesting quotations from earlier poets; a number of detached observations collected in the nineteenth section of the Aristotelian Problems; and one or two notices preserved in lexicographical works, such as the Onomasticon of Pollux.

In these groups of authorities the scholars above mentioned find the double use which they believe to have been made of the names Dorian, Phrygian, Lydian and the rest. In Aristoxenus they recognise that these names are applied to a series of keys (tonoi), which differed in pitch only. In Plato and Aristotle they find the same names applied to scales called harmoniai, and these scales, they maintain, differed primarily in the order of their intervals. I shall endeavour to show that there was no such double use: that in the earlier periods of Greek music the scales in use, whether called tonoi or harmoniai, differed primarily in pitch: that the statements of ancient authors about them, down to and including Aristoxenus, agree as closely as there is reason to expect: and that the passages on which the opposite view is based—all of them drawn from comparatively late writers—either do not relate to these ancient scales at all, or point to the emergence in post-classical times of some new forms or tendencies of musical art. I propose in any case to adhere as closely as possible to a chronological treatment of the evidence which is at our command, and I hope to make it probable that the difficulties of the question may be best dealt with on this method.

§ 4. The Early Poets.

The earliest of the passages now in question comes from the poet Pratinas, a contemporary of Aeschylus. It is quoted by Heraclides Ponticus, in the course of a long fragment preserved by Athenaeus (xiv. cc. 19-21, p. 624 c-626 a). The words are:

mête syntonon diôke mête tan aneimenan
Iasti mousan, alla tan messan neôn
arouran aiolize tô melei.

'Follow neither a highly-strung music nor the low-pitched Ionian, but turning over the middle plough-land be an Aeolian in your melody.' Westphal takes the word 'Iasti with syntonon as well as with aneimenan, and infers that there were two kinds of Ionian, a 'highly-strung' and a 'relaxed' or low-pitched. But this is not required by the words, and seems less natural than the interpretation which I have given. All that the passage proves is that in the time of Pratinas a composer had the choice of at least three scales: one (or more) of which the pitch was high (syntonos); another of low pitch (aneimenê), which was called Ionian; and a third, intermediate between the others, and known as Aeolian. Later in the same passage we are told that Pratinas spoke of the 'Aeolian harmony' (prepei toi pasin aoidolabraktais Aiolis harmonia). And the term is also found, with the epithet 'deep-sounding,' in a passage quoted from the hymn to Demeter of a contemporary poet, Lasus of Hermione (Athen. xiv. 624 e):

Damatra melpô Koran te Klymenoio alochon Meliboian,
hymnôn anagôn Aiolid' hama barybromon harmonian.

With regard to the Phrygian and Lydian scales Heraclides (l. c.) quotes an interesting passage from Telestes of Selinus, in which their introduction is ascribed to the colony that was said to have followed Pelops from Asia Minor to the Peloponnesus:

prôtoi para kratêras Hellênôn en aulois
synopadoi Pelopos matros oreias phrygion aeison nomon;
toi d' oxyphônois pêktidôn psalmois krekon
Dydion hymnon.

'The comrades of Pelops were the first who beside the Grecian cups sang with the flute (aulos) the Phrygian measure of the Great Mother; and these again by shrill-voiced notes of the pectis sounded a Lydian hymn.' The epithet oxyphônos is worth notice in connexion with other evidence of the high pitch of the music known as Lydian. The Lydian mode is mentioned by Pindar, Nem. 4. 45:

exyphaine glykeia kai tod' autika phorminx
Lydia syn harmonia melos pephilêmenon.

The Dorian is the subject of an elaborate jest made at the expense of Cleon in the Knights of Aristophanes, ll. 985-996:

alla kai tod' egô ge thaumazô tês hyomousias
autou phasi gar auton hoi paides hoi xynephoitôn
tên Dôristi monên enarmottesthai thama tên lyran,
allên d' ouk ethelein labein; kata ton kitharistên
orgisthent' apagein keleuein, hôs harmonian ho pais
outos ou dynatai mathein ên mê Dôrodokêsti.

§ 5. Plato.

Following the order of time, we come next to the passage in the Republic (p. 398), where Socrates is endeavouring to determine the kinds of music to be admitted for the use of his future 'guardians,' in accordance with the general principles which are to govern their education. First among these principles is the condemnation of all undue expression of grief. 'What modes of music (harmoniai),' he asks, are plaintive (thrênôdeis)?' 'The Mixo-lydian,' Glaucon replies, 'and the Syntono-lydian, and such-like.' These accordingly Socrates excludes. 'But again, drunkenness and slothfulness are no less forbidden to the guardians; which of the modes are soft and convivial (malakai te kai sympotikai)?' 'Ionian,' says Glaucon, 'and Lydian, those which are called slack (chalarai).' 'Which then remain?' 'Seemingly Dorian and Phrygian.' 'I do not know the modes,' says Socrates, 'but leave me one that will imitate the tones and accents of a brave man enduring danger or distress, fighting with constancy against fortune: and also one fitted for the work of peace, for prayer heard by the gods, for the successful persuasion or exhortation of men, and generally for the sober enjoyment of ease and prosperity.' Two such modes, one for Courage and one for Temperance, are declared by Glaucon to be found in the Dorian and the Phrygian. In the Laches (p. 188) there is a passing reference in which a similar view is expressed. Plato is speaking of the character of a brave man as being metaphorically a 'harmony,' by which his life is made consonant to reason—'a Dorian harmony,' he adds—playing upon the musical sense of the word—'not an Ionian, certainly not a Phrygian or a Lydian, but that one which only is truly Hellenic' (atechnôs Dôristi, all' ouk Iasti, oiomai de oude Phrygisti oude Lydisti, all' hê per monê Hellênikê estin harmonia). The exclusion of Phrygian may be due to the fact that the virtue discussed in the Laches is courage; but it is in agreement with Aristotle's opinion. The absence of Aeolian from both the Platonic passages seems to show that it had gone out of use in his time (but cp. [p. 11]).

The point of view from which Plato professes to determine the right modes to be used in his ideal education appears clearly in the passage of the Republic. The modes first rejected are those which are high in pitch. The Syntono-lydian or 'high-strung Lydian' is shown by its name to be of this class. The Mixo-lydian is similar, as we shall see from Aristotle and other writers. The second group which he condemns is that of the 'slack' or low-pitched. Thus it is on the profoundly Hellenic principle of choosing the mean between opposite extremes that he approves of the Dorian and Phrygian pitch. The application of this principle was not a new one, for it had been already laid down by Pratinas: mête syntonon diôke mête tan aneimenan.

The three chapters which Aristotle devotes to a discussion of the use of music in the state (Politics viii. cc. 5-7), and in which he reviews and criticises the Platonic treatment of the same subject, will be found entirely to bear out the view now taken. It is also supported by the commentary of Plutarch, in his dialogue on Music (cc. 15-17), of which we shall have something to say hereafter. Meanwhile, following the chronological order of our authorities, we come next to the fragment of Heraclides Ponticus already mentioned (Athen. xiv. p. 624 c-626 a).

§ 6. Heraclides Ponticus.

The chief doctrine maintained by Heraclides Ponticus is that there are three modes (harmoniai), belonging to the three Greek races—Dorian, Aeolian, Ionian. The Phrygian and Lydian, in his view, had no right to the name of mode or 'harmony' (oud' harmonian phêsi dein kaleisthai tên Phrygion, kathaper oude tên Lydion). The three which he recognized had each a marked ethos. The Dorian reflected the military traditions and temper of Sparta. The Aeolian, which Heraclides identified with the Hypo-dorian of his own time, answered to the national character of the Thessalians, which was bold and gay, somewhat overweening and self-indulgent, but hospitable and chivalrous. Some said that it was called Hypo-dorian because it was below the Dorian on the aulos or flute; but Heraclides thinks that the name merely expressed likeness to the Dorian character (Dôrion men autên ou nomizein, prosempherê de pôs ekeinê). The Ionian, again, was harsh and severe, expressive of the unkindly disposition fostered amid the pride and material welfare of Miletus. Heraclides is inclined to say that it was not properly a distinct musical scale or 'harmony,' but a strange aberration in the form of the musical scale (tropon de tina thaumaston schêmatos harmonias). He goes on to protest against those who do not appreciate differences of kind (tas kat' eidos diaphoras), and are guided only by the high or low pitch of the notes (tê tôn phthongôn exytêti kai barytêti); so that they make a Hyper-mixolydian, and another again above that. 'I do not see,' he adds, 'that the Hyper-phrygian has a distinct ethos; and yet some say that they have discovered a new mode (harmonia), the Hypo-phrygian. But a mode ought to have a distinct moral or emotional character (eidos echein ethous hê pathous), as the Locrian, which was in use in the time of Simonides and Pindar, but went out of fashion again.' The Phrygian and Lydian, as we have seen, were said to have been brought to the Peloponnesus by the followers of Pelops.

The tone as well as the substance of this extract makes it evident that the opinions of Heraclides on questions of theoretical music must be accepted with considerable reserve. The notion that the Phrygian and Lydian scales were 'barbarous' and opposed to Hellenic ethos was apparently common enough, though largely due (as we may gather from several indications) to national prejudice. But no one, except Heraclides, goes so far as to deny them the name of harmonia. The threefold division into Dorian, Aeolian and Ionian must also be arbitrary. It is to be observed that Heraclides obtains his Aeolian by identifying the Aeolian of Pratinas and other early poets with the mode called Hypo-dorian in his own time. The circumstance that Plato mentions neither Aeolian nor Hypo-dorian suggests rather that Aeolian had gone out of use before Hypo-dorian came in. The conjecture of Boeckh that Ionian was the same as the later Hypo-phrygian (De Metr. Pind. iii. 8) is open to a similar objection. The Ionian mode was at least as old as Pratinas, whereas the Hypo-phrygian was a novelty in the time of Heraclides. The protest which Heraclides makes against classifying modes merely according to their pitch is chiefly valuable as proving that the modes were as a matter of fact usually classified from that point of view. It is far from proving that there was any other principle which Heraclides wished to adopt—such, for example, as difference in the intervals employed, or in their succession. His 'differences of kind' (tas kat' eidos diaphoras) are not necessarily to be explained from the technical use of eidos for the 'species' of the octave. What he complains of seems to be the multiplication of modes—Hyper-mixolydian, Hyper-phrygian, Hypo-phrygian—beyond the legitimate requirements of the art. The Mixo-lydian (e.g.) is high-pitched and plaintive: what more can the Hyper-mixolydian be? The Hypo-phrygian is a new mode: Heraclides denies it a distinctive ethos. His view seems to be that the number of modes should not be greater than the number of varieties in temper or emotion of which music is capable. But there is nothing to show that he did not regard pitch as the chief element, or one of the chief elements, of musical expression.

The absence of the name Hypo-lydian, taken with the description of Hypo-dorian as 'below the Dorian,' would indicate that the Hypo-dorian of Heraclides was not the later mode of that name, but was a semitone below the Dorian, in the place afterwards occupied by the Hypo-lydian. This is confirmed, as we shall see, by Aristoxenus ([p. 18]).

§ 7. Aristotle—the Politics.

Of the writers who deal with music from the point of view of the cultivated layman, Aristotle is undoubtedly the most instructive. The chapters in his Politics which treat of music in its relation to the state and to morality go much more deeply than Plato does into the grounds of the influence which musical forms exert upon temper and feeling. Moreover, Aristotle's scope is wider, not being confined to the education of the young; and his treatment is evidently a more faithful reflexion of the ordinary Greek notions and sentiment. He begins (Pol. viii. 5, p. 1340 a 38) by agreeing with Plato as to the great importance of the subject for practical politics. Musical forms, he holds, are not mere symbols (sêmeia), acting through association, but are an actual copy or reflex of the forms of moral temper (en de tois melesin autois esti mimêmata tôn êthôn); and this is the ground of the different moral influence exercised by different modes (harmoniai). By some of them, especially by the Mixo-lydian, we are moved to a plaintive and depressed temper (diatithesthai odyrtikôterôs kai synestêkotôs mallon); by others, such as those which are called the 'relaxed' (aneimenai), we are disposed to 'softness' of mind (malakôterôs tên dianoian). The Dorian, again, is the only one under whose influence men are in a middle and settled mood (mesôs kai kathestêkotôs malista): while the Phrygian makes them excited (enthousiastikous). In a later chapter (Pol. viii. 7, p. 1342 a 32), he returns to the subject of the Phrygian. Socrates, he thinks, ought not to have left it with the Dorian, especially since he condemned the flute (aulos), which has the same character among instruments as the Phrygian among modes, both being orgiastic and emotional. The Dorian, as all agree, is the most steadfast (stasimôtatê), and has most of the ethos of courage; and, as compared with other modes, it has the character which Aristotle himself regards as the universal criterion of excellence, viz. that of being the mean between opposite excesses. Aristotle, therefore, certainly understood Plato to have approved the Dorian and the Phrygian as representing the mean in respect of pitch, while other modes were either too high or too low. He goes on to defend the use of the 'relaxed' modes on the ground that they furnish a music that is still within the powers of those whose voice has failed from age, and who therefore are not able to sing the high-pitched modes (oion tois apeirêkosi dia chronon ou rhadion adein tas syntonous harmonias, alla tas aneimenas hê physis hypoballei tois têlikoutois). In this passage the meaning of the words syntonos and aneimenos is especially clear.

In the same discussion (c. 6), Aristotle refers to the distinction between music that is ethical, music suited to action, and music that inspires religious excitement (ta men êthika, ta de praktika, ta ho enthousiastika). The last of these kinds serves as a 'purification' (katharsis). The excitement is calmed by giving it vent; and the morbid condition of the ethos is met by music of high pitch and exceptional 'colour' (tôn harmoniôn parekbaseis kai tôn melôn ta syntona kai parakechrôsmena).

In a different connexion (Pol. iv. 3, p. 1290 a 20), dealing with the opinion that all forms of government are ultimately reducible to two, viz. oligarchy and democracy, Aristotle compares the view of some who held that there are properly only two musical modes, Dorian and Phrygian,—the other scales being mere varieties of these two. Rather, he says, there is in each case a right form, or two right forms at most, from which the rest are declensions (parekbaseis),—on one side to 'high-pitched' and imperious oligarchies, on the other to 'relaxed' and 'soft' forms of popular government (oligarchikas men tas syntonôteras kai despotikônteras, tas d' aneimenas kai malakas dêmotikas). This is obviously the Platonic doctrine of two right keys, holding the mean between high and low.

§ 8. The Aristotelian Problems.

Some further notices of the harmoniai or modes are contained in the so-called Problems,—a collection which is probably not the work of Aristotle himself, but can hardly be later than the Aristotelian age. What is said in it of the modes is clearly of the period before the reform of Aristoxenus. In one place (Probl. xix. 48) the question is asked why the Hypo-dorian and Hypo-phrygian are not used in the chorus of tragedy. One answer is that the Hypo-phrygian has the ethos of action (êthos echei praktikon), and that the Hypo-dorian is the expression of a lofty and unshaken character; both of these things being proper to the heroic personages on the stage, but not to the chorus, which represents the average spectator, and takes no part in the action. Hence the music suited to the chorus is that of emotion venting itself in passive complaint:—a description which fits the other modes, but least of all the exciting and orgiastic Hypo-phrygian. On the contrary (the writer adds) the passive attitude is especially expressed by the Mixo-lydian. The view here taken of the Hypo-dorian evidently agrees with that of Heraclides Ponticus (supra, [p. 10]).

The relation which Plato assumes between high pitch and the excitement of passion, and again between lowness of pitch and 'softness' or self-indulgence (malakia kai argia), is recognized in the Problems, xix. 49 epei de ho men barys phthongos malakos kai êremaios estin, ho de oxys kinêtikos, k.t.l.: 'since a deep note is soft and calm, and a high note is exciting, &c.'

§ 9. The Rhetoric.

The word tonos occurs several times in Aristotle with the sense of 'pitch,' but is not applied by him to the keys of music. The nearest approach to such a use may be found in a passage of the Rhetoric (iii. 1, p. 1403 b 27).

Speaking of the rise of acting (hypokrisis), which was originally the business of the poet himself, but had grown into a distinct art, capable of theoretical as well as practical treatment, he observes that a similar art might be formed for oratory. 'Such an art would lay down rules directing how to use the voice so as to suit each variety of feeling,—when it should be loud, when low, when intermediate;—and how to use the keys, when the pitch of the voice should be high or low or middle (kai pôs tois tonois, oion oxeia kai bareia kai mesê, sc. phônê); and the rhythms, which to use for each case. For there are three things which men study, viz. quantity (i. e. loudness of sound), tune, and rhythm (tria gar esti peri hôn skopousi, tauta d' esti megethos, harmonia, rhythmos).' The passage is interesting as showing the value which Aristotle set upon pitch as an element of effect. And the use of harmonia in reference to the pitch of the voice, and as virtually equivalent to tonos, is especially worthy of note.

§ 10. Aristoxenus.

Our next source of information is the technical writer Aristoxenus, a contemporary and pupil of Aristotle. Of his many works on the subject of music three books only have survived, bearing the title harmonika otoicheia [2]. In the treatment adopted by Aristoxenus the chapter on keys follows the chapter on 'systems' (systêmata). By a systêma he means a scale consisting of a certain succession of intervals: in other words, a series of notes whose relative pitch is determined. Such a system may vary in absolute pitch, and the tonoi or keys are simply the different degrees of pitch at which a particular system is taken (tous tonous eph' ôn tithemena ta systêmata melôdeitai). When the system and the key are both given it is evident that the whole series of notes is determined.

Aristoxenus is the chief authority on the keys of Greek music. In this department he is considered to have done for Greece what Bach's Wohltemperirtes Clavier did for modern Europe. It is true that the scheme of keys which later writers ascribe to him.

'No one,' says Aristoxenus (p. 37 Meib.), 'has told us a word about the keys, either how they are to be arrived at (tina tropon lêpteon), or from what point of view their number is to be determined. Musicians assign the place of the keys very much as the different cities regulate the days of the month. The Corinthians, for example, will be found counting a day as the tenth of the month, while with the Athenians it is the fifth, and in some other place the eighth. Some authorities on music (harmonikoi) say that the Hypo-dorian is the lowest key, the Mixo-lydian a semitone higher, the Dorian again a semitone higher, the Phrygian a tone above the Dorian, and similarly the Lydian a tone above the Phrygian. Others add the Hypo-phrygian flute [i. e. the scale of the flute so called] at the lower end of the list. Others, again, looking to the holes of the flute (pros tên tôn aulôn trupêsin blepontes), separate the three lowest keys, viz. the Hypo-phrygian, Hypo-dorian, and Dorian, by the interval of three-quarters of a tone (trisi diesesin), but the Phrygian from the Dorian by a tone, the Lydian from the Phrygian again by three-quarters of a tone, and the Mixo-lydian from the Lydian by a like interval. But as to what determines the interval between one key and another they have told us nothing.'

It will be seen that (with one marked exception) there was agreement about the order of the keys in respect of pitch, and that some at least had reduced the intervals to the succession of tones and semitones which characterises the diatonic scale. The exception is the Mixo-lydian, which some ranked immediately below the Dorian, others above the Lydian. Westphal attributes this strange discrepancy to the accidental displacing of some words in the MSS. of Aristoxenus [3]. However this may be, it is plain that in the time of Aristoxenus considerable progress had been made towards the scheme of keys which was afterwards connected with his name. This may be represented by the following table, in which for the sake of comparison the later Hypo-lydian and Hypo-dorian are added in brackets:

Mixo-lydian
semitone - {
Lydian
tone -{
Phrygian
tone -{
Dorian
semitone - {
Hypo-dorian [Hypo-lydian]
tone -{
Hypo-phrygian
tone -{
[Hypo-dorian]

§ 11. Names of Keys (hypo-).

A point that deserves special notice at this place is the use of the prefix Hypo- (hypo-) in the names of keys. In the final Aristoxenean system Hypo- implies that a key is lower by the interval of a Fourth than the key to whose name it is prefixed. This convention served to bring out the special relation between the two keys, viz. to show that they are related (to use modern language) as the keys of a tonic and dominant. In the scheme of keys now in question there is only one instance of this use of Hypo-, namely in the Hypo-phrygian, the most recently introduced. It must have been on the analogy of this name that the term Hypo-dorian was shifted from the key immediately below the Dorian to the new key a Fourth below it, and that the new term Hypo-lydian was given to the old Hypo-dorian in accordance with its similar relation to the Lydian. In the time of Aristoxenus, then, this technical sense of Hypo- had not yet been established, but was coming into use. It led naturally to the employment of Hyper- in the inverse sense, viz. to denote a key a Fourth higher (the key of the sub-dominant). By further steps, of which there is no record, the Greek musicians arrived at the idea of a key for every semitone in the octave; and thus was formed the system of thirteen keys, ascribed to Aristoxenus by later writers. (See the scheme at the end of this book, Table II.) Whether in fact it was entirely his work may be doubted. In any case he had formed a clear conception—the want of which he noted in his predecessors—of the principles on which a theoretically complete scheme of keys should be constructed.

In the discussions to which we have been referring, Aristoxenus invariably employs the word tonos in the sense of 'key.' The word harmonia in his writings is equivalent to 'Enharmonic genus' (genos enarmonion), the genus of music which made use of the Enharmonic diësis or quarter-tone. Thus he never speaks, as Plato and Aristotle do, of the Dorian (or Phrygian or Lydian) harmonia, but only of the tonoi so named. There is indeed one passage in which certain octave scales are said by Aristoxenus to have been called harmoniai: but this, as will be shown, is a use which is to be otherwise explained ([see p. 54]).

§ 12. Plutarch's Dialogue on Music.

After the time of Aristoxenus the technical writers on music make little or no use of the term harmonia. Their word for 'key' is tonos; and the octachord scales which are distinguished by the succession of their intervals are called 'species of the octave' (eidê tou dia pasôn). The modes of the classical period, however, were still objects of antiquarian and philosophic interest, and authors who treated them from this point of view naturally kept up the old designation. A good specimen of the writings of this class has survived in the dialogus de musicâ of Plutarch. Like most productions of the time, it is mainly a compilation from earlier works now lost. Much of it comes from Aristoxenus, and there is therefore a special fitness in dealing with it in this place, by way of supplement to the arguments drawn directly from the Aristoxenean Harmonics. The following are the chief passages bearing on the subject of our enquiry:

(1) In cc. 15-17 we find a commentary of some interest on the Platonic treatment of the modes. Plutarch is dwelling on the superiority of the older and simpler music, and appeals to the opinion of Plato.

'The Lydian mode (harmonia) Plato objects to because it is high (oxeia) and suited to lamentation. Indeed it is said to have been originally devised for that purpose: for Aristoxenus tells us, in his first book on Music, that Olympus first employed the Lydian mode on the flute in a dirge (epikêdeion aulêsai Lydisti) over the Python. But some say that Melanippides began this kind of music. And Pindar in his paeans says that the Lydian mode (harmonia) was first brought in by Anthippus in an ode on the marriage of Niobe. But others say that Torrhebus first used that mode, as Dionysius the Iambus relates.'

'The Mixo-lydian, too, is pathetic and suitable to tragedy. And Aristoxenus says that Sappho was the inventor of the Mixo-lydian, and that from her the tragic poets learned it. They combined it with the Dorian, since that mode gives grandeur and dignity, and the other pathos, and these are the two elements of tragedy. But in his Historical Treatise on Music (historika tês harmonias hypomnêmata) he says that Pythoclides the flute-player was the discoverer of it. And Lysis says that Lamprocles the Athenian, perceiving that in it the disjunctive tone (diazeuxis) is not where it was generally supposed to be, but is at the upper end of the scale, made the form of it to be that of the octave from Paramesê to Hypatê Hypatôn (toiouton autês apergasasthai to schêma hoion to apo paramesês epi hypatên hypatôn). Moreover, it is said that the relaxed Lydian (epaneimenên Lydisti), which is the opposite of the Mixo-lydian, being similar to the Ionian (paraplêsian ousan tê Iadi), was invented by Damon the Athenian.'

'These modes then, the one plaintive, the other relaxed (eklelymenê), Plato properly rejected, and chose the Dorian, as befitting warlike and temperate men.'

In this passage the 'high-pitched Lydian' (Syntonolydisti) of Plato is called simply Lydian. There is every reason to suppose that it is the mode called Lydian by Aristotle and Heraclides Ponticus [4]. If this is so, it follows almost of necessity that the Lydian of Plato, called slack (chalara) by him—Plutarch's epaneimenê Lydisti—is to be identified with the later

Hypo-lydian. The point, however, is not free from difficulty: for (as we have seen, [p. 18]), the name Hypo-lydian is not in the list of keys given by Aristoxenus—the key which was ultimately called Hypo-lydian being known to him as the Hypo-dorian. If, however, the confusion in the nomenclature of the keys was as great as Aristoxenus himself describes, such a contradiction as this cannot be taken to prove much. [5]

The statement that the 'relaxed Lydian' was the opposite of the Mixo-lydian, and similar to the Ionian, has given rise to much speculation. In what sense, we naturally ask, can a key or a mode be said to be 'opposite' or 'similar' to another? I venture to think that it is evidently a mere paraphrase of Plato's language. The relaxed Lydian is opposed to the Mixo-lydian because it is at the other end of the scale in pitch; and it is similar to the Ionian because the two are classed together (as chalarai) by Plato.

The Mixo-lydian, according to Aristoxenus, was employed by the tragic poets in close union with the Dorian mode (labontas syzeuxai tê Dôristi). The fact that the Mixo-lydian was just a Fourth higher than the Dorian must have made the transition from the one to the other a natural and melodious one. As Aristoxenus suggested, it would be especially used to mark the passage from grandeur and dignity to pathos which is the chief characteristic of tragedy (hê men to

megaloprepes kai axiômatikon apodidôsin, hê de to pathêtikon, memiktai de dia toutôn tragôdia). It is worth noticing that this relation obtained in the scheme of the musicians who did not arrange the keys according to the diatonic scale, but in some way suggested by the form of the flute (hoi pros tên tôn aulôn trypêsin blepontes). It may therefore be supposed to have been established before the relative pitch of other keys had been settled.

So far the passage of Plutarch goes to confirm the view of the Platonic modes according to which they were distinguished chiefly, if not wholly, by difference of pitch. We come now, however, to a statement which apparently tends in the opposite direction, viz. that a certain Lamprocles of Athens noticed that in the Mixo-lydian mode the Disjunctive Tone (diazeuxis) was at the upper end of the scale (epi to oxy), and reformed the scale accordingly. This must refer to an octave scale of the form b c d e f g a b, consisting of the two tetrachords b-e and e-a, and the tone a-b. Such an octave may or may not be in the Mixo-lydian key: it is certainly of the Mixo-lydian species ([p. 57]).

In estimating the value of this piece of evidence it is necessary to remark, in the first place, that the authority is no longer that of Aristoxenus, but of a certain Lysis, of whom nothing else seems to be known. That he was later than Aristoxenus is made probable by his way of describing the Mixo-lydian octave, viz. by reference to the notes in the Perfect System by which it is exemplified (Hypatê Hypatôn to Paramesê). In Aristoxenus, as we shall see ([p. 31]), the primitive octave (from Hypatê to Nêtê) is the only scale the notes of which are mentioned by name. But even if the notice is comparatively early, it is worth observing that the Mixo-lydian scale thus ascribed to Lamprocles consists of two tetrachords of the normal type, viz. with the semitone or pyknon at the lower end of the scale (Diatonic e f g a, Enharmonic e e* f a). The difference is that they are conjunct, whereas in the primitive standard octave (e—e) the tetrachords are disjunct (e-a b-e). This, however, is a variety which is provided for by the tetrachord Synêmmenôn in the Perfect System, and which may have been allowed in the less complete scales of earlier times. In any case the existence of a scale of this particular form does not prove that the octaves of other species were recognised in the same way.

(2) In another passage (c. 6) Plutarch says of the ancient music of the cithara that it was characterised by perfect simplicity. It was not allowed, he tells us, to change the mode (metapherein tas harmonias) or the rhythm: for in the primitive lyrical compositions called 'Nomes' (nomoi) they preserved in each its proper pitch (tên oikeian tasin). Here the word tasis indicates that by harmoniai Plutarch (or the older author from whom he was quoting) meant particular keys. This is fully confirmed by the use of tonos in a passage a little further on (c. 8), where Plutarch gives an account of an innovation in this matter made by Sacadas of Argos (fl. 590 B.C.). 'There being three keys (tonoi) in the time of Polymnastus and Sacadas, viz. the Dorian, Phrygian and Lydian, it is said that Sacadas composed a strophe in each of these keys, and taught the chorus to sing them, the first in the Dorian, the second in the Phrygian, and the third in the Lydian key: and this composition was called the "three-part Nome" (nomos trimerês) on account of the change of key.' In Westphal's Harmonik und Melopöie (ed. 1863, p. 76, cp. p. 62) he explains this notice of the ancient modes (harmoniai, Tonarten), observing that the word tonos is there used improperly for what the technical writers call eidos tou dia pasôn.

(3) In a somewhat similar passage of the same work (c. 19) Plutarch is contending that the fewness of the notes in the scales used by the early musicians did not arise from ignorance, but was characteristic of their art, and necessary to its peculiar ethos. Among other points he notices that the tetrachord Hypatôn was not used in Dorian music (en tois Dôriois), and this, he says, was not because they did not know of that tetrachord—for they used it in other keys (tonoi)—but they left it out in the Dorian key for the sake of preserving its ethos, the beauty of which they valued (dia dê tên tou êthous phylakên aphêroun tou Dôriou tonou, timôntes to kalon autou). Here again Westphal (Aristoxenus, p. 476) has to take tonos to mean harmonia or 'mode' (in his language Tonart, not Transpositionsscala). For in the view of those who distinguish harmonia from tonos it is the harmonia upon which the ethos of music depends. Plutarch himself had just been saying (in c. 17) that Plato preferred the Dorian harmonia on account of its grave and elevated character (epei poly to semnon estin en tê Dôristi, tautên proutimêsen). On the other hand the usual sense of tonos is supported by the consideration that the want of the tetrachord Hypatôn would affect the pitch of the scale rather than the succession of its intervals.

It seems to follow from a comparison of these three passages that Plutarch was not aware of any difference of meaning between the words tonos and harmonia, or any distinction in the scales of Greek music such as has been supposed to be conveyed by these words. Another synonym of tonos which becomes very common in the later writers on music is the word tropos. [6] In the course of the passage of Plutarch already referred to (De Mus. c. 17) it is applied to the Dorian mode, which Plutarch has just called harmonia. As tropos is always used in the later writers of the keys (tonoi) of Aristoxenus, this may be added to the places in which harmonia has the same meaning.

§ 13. Modes employed on different Instruments.

In the anonymous treatise on music published by Bellermann[7] (c. 28), we find the following statement regarding the use of the modes or keys in the scales of different instruments:

'The Phrygian mode (harmonia) has the first place on wind-instruments: witness the first discoverers—Marsyas, Hyagnis, Olympus—who were Phrygians. Players on the water-organ (hydraulai) use only six modes (tropoi), viz. Hyper-lydian, Hyper-ionian, Lydian, Phrygian, Hypo-lydian, Hypo-phrygian. Players on the cithara tune their instrument to these four, viz. Hyper-ionian, Lydian, Hypo-lydian, Ionian. Flute-players employ seven, viz. Hyper-aeolian, Hyper-ionian, Hypo-lydian, Lydian, Phrygian, Ionian, Hypo-phrygian. Musicians who concern themselves with orchestic (choral music) use seven, viz. Hyper-dorian, Lydian, Phrygian, Dorian, Hypo-lydian, Hypo-phrygian, Hypo-dorian.

In this passage it is evident that we have to do with keys of the scheme attributed to Aristoxenus, including the two (Hyper-aeolian and Hyper-lydian) which were said to have been added after his time. The number of scales mentioned is sufficient to prove that the reference is not to the seven species of the octave. Yet the word harmonia is used of these keys, and with it, seemingly as an equivalent, the word tropos.

Pollux (Onom. iv. 78) gives a somewhat different account of the modes used on the flute: kai harmonia men aulêtikê Dôristi, Phrygisti, Lydios kai Iônikê, kai syntonos Lydisti hên Anthippos exeure. But this statement, as has been already pointed out ([p. 22]), is a piece of antiquarian learning, and therefore takes no notice of the more recent keys, as Hyper-aeolian and Hyper-ionian, or even Hypo-phrygian (unless that is the Ionian of Pollux). The absence of Dorian from the list given by the Anonymus is curious: but it seems that at that time it was equally unknown to the cithara and the water-organ. There is therefore no reason to think that the two lists are framed with reference to different things. That is to say, harmonia in Pollux has the same meaning as harmonia in the Anonymus, and is equivalent to tonos.

§ 14. Recapitulation— harmonia and tonos.

The inquiry has now reached a stage at which we may stop to consider what result has been reached, especially in regard to the question whether the two words harmonia and tonos denote two sets of musical forms, or are merely two different names for the same thing. The latter alternative appears to be supported by several considerations.

1. From various passages, especially in Plato and Aristotle, it has been shown that the modes anciently called harmoniai differed in pitch, and that this difference in pitch was regarded as the chief source of the peculiar ethical character of the modes.

2. The list of harmoniai as gathered from the writers who treat of them, viz. Plato, Aristotle, and Heraclides Ponticus, is substantially the same as the list of tonoi described by Aristoxenus ([p. 18]): and moreover, there is an agreement in detail between the two lists which cannot be purely accidental. Thus Heraclides says that certain people had found out a new harmonia, the Hypo-phrygian; and Aristoxenus speaks of the Hypo-phrygian tonos as a comparatively new one. Again, the account which Aristoxenus gives of the Hypo-dorian tonos as a key immediately below the Dorian agrees with what Heraclides says of the Hypo-dorian harmonia, and also with the mention of Hypo-dorian and Hypo-phrygian (but not Hypo-lydian) in the Aristotelian Problems. Once more, the absence of Ionian from the list of tonoi in Aristoxenus is an exception which proves the rule: since the name of the Ionian harmonia is similarly absent from Aristotle.

3. The usage of the words harmonia and tonos is never such as to suggest that they refer to different things. In the earlier writers, down to and including Aristotle, harmonia is used, never tonos. In Aristoxenus and his school we find tonos, and in later writers tropos, but not harmonia. The few writers (such as Plutarch) who use both tonos and harmonia do not observe any consistent distinction between them. Those who (like Westphal) believe that there was a distinction, are obliged to admit that harmonia is occasionally used for tonos and conversely.

4. If a series of names such as Dorian, Phrygian, Lydian and the rest were applied to two sets of things so distinct from each other, and at the same time so important in the practice of music, as what we now call modes and keys, it is incredible that there should be no trace of the double usage. Yet our authors show no sense even of possible ambiguity. Indeed, they seem to prefer, in referring to modes or keys, to use the adverbial forms dôristi, phrygisti, &c., or the neuter ta dôria, ta phrygia, &c., where there is nothing to show whether 'mode' or 'key,' harmonia or tonos, is intended.

§ 15. The Systems of Greek Music.

The arguments in favour of identifying the primitive national Modes (harmoniai) with the tonoi or keys may be reinforced by some considerations drawn from the history and use of another ancient term, namely systêma.

A System (systêma) is defined by the Greek technical writers as a group or complex of intervals (to ek pleionôn ê henos diastêmatôn synkeimenon Ps. Eucl.). That is to say, any three or more notes whose relative pitch is fixed may be regarded as forming a particular System. If the notes are such as might be used in the same melody, they are said to form a musical System (systêma emmeles). As a matter of abstract theory it is evident that there are very many combinations of intervals which in this sense form a musical System. In fact, however, the variety of systems recognised in the theory of Greek music was strictly limited. The notion of a small number of scales, of a particular compass, available for the use of the musician, was naturally suggested by the ancient lyre, with its fixed and conventional number of strings. The word for string (chordê) came to be used with the general sense of a note of music; and in this way the several strings of the lyre gave their names to the notes of the Greek gamut[8].

§ 16. The Standard Octachord System.

In the age of the great melic poets the lyre had no more than seven strings: but the octave was completed in the earliest times of which we have accurate information. The scale which is assumed as matter of common knowledge in the Aristotelian Problems and the Harmonics of Aristoxenus consists of eight notes, named as follows from their place on the lyre:

Nêtê (neatê or nêtê, lit. 'lowest,' our 'highest').
Paranêtê (paranêtê, 'next to Nêtê').
Tritê (tritê, i.e. 'third' string).
Paramesê (paramesê or paramesos, 'next to Mesê').
Mesê (mesê, 'middle string').
Lichanos (lichanos, i.e. 'forefinger' string).
Parhypatê (parypatê).
Hypatê (hypatê, lit. 'uppermost,' our 'lowest').

It will be seen that the conventional sense of high and low in the words hypatê and neatê was the reverse of the modern usage.

The musical scale formed by these eight notes consists of two tetrachords or scales of four notes, and a major tone. The lower of the tetrachords consists of the notes from Hypatê to Mesê, the higher of those from Paramesê to Nêtê: the interval between Mesê and Paramesê being the so-called Disjunctive Tone (tonos diazeuktikos). Within each tetrachord the intervals depend upon the Genus (genos). Thus the four notes just mentioned—Hypatê, Mesê, Paramesê, Nêtê—are the same for every genus, and accordingly are called the 'standing' or 'immoveable' notes (phthongoi hestôtes, akinêtoi), while the others vary with the genus, and are therefore 'moveable' (pheromenoi).

In the ordinary Diatonic genus the intervals of the tetrachords are, in the ascending order, semitone + tone + tone: i.e. Parhypatê is a semitone above Hypatê, and Lichanos a tone above Parhypatê. In the Enharmonic genus the intervals are two successive quarter-tones (diesis) followed by a ditone or major Third: consequently Parhypatê is only a quarter of a tone above Hypatê, and Lichanos again a quarter of a tone above Parhypatê. The group of three notes separated in this way by small intervals (viz. two successive quarter-tones) is called a pyknon. If we use an asterisk to denote that a note is raised a quarter of a tone, these two scales may be represented in modern notation as follows:

πμκνον = pyknon

In the Chromatic genus and its varieties the division is of an intermediate kind. The interval between Lichanos and Mesê is more than one tone, but less than two: and the two other intervals, as in the enharmonic, are equal.

The most characteristic feature of this scale, in contrast to those of the modern Major and Minor, is the place of the small intervals (semitone or pyknon), which are always the lowest intervals of a tetrachord. It is hardly necessary to quote passages from Aristotle and Aristoxenus to show that this is the succession of intervals assumed by them. The question is asked in the Aristotelian Problems (xix. 4), why Parhypatê is difficult to sing, while Hypatê is easy, although there is only a diesis between them (kaitoi diesis hekateras). Again (Probl. xix. 47), speaking of the old heptachord scale, the writer says that the Paramesê was left out, and consequently the Mesê became the lowest note of the upper pyknon, i.e. the group of 'close' notes consisting of Mesê, Tritê, and Paranêtê. Similarly Aristoxenus (Harm. p. 23) observes that the 'space' of the Lichanos, i.e. the limit within which it varies in the different genera, is a tone while the space of the Parhypatê is only a diesis, for it is never nearer Hypatê than a diesis or further off than a semitone.

§ 17. Earlier Heptachord Scales.

Regarding the earlier seven-stringed scales which preceded this octave our information is scanty and somewhat obscure. The chief notice on the subject is the following passage of the Aristotelian Problems:

Probl. xix. 47 dia ti hoi archaioi heptachordous poiountes tas harmonias tên hypatên all' ou tên nêtên katelipon: hê ou tên hypatên (leg. nêtên), alla tên nyn paramesên kaloumenên aphêroun kai to toniaion diastêma; echrônto de tê eschatê mesê tou epi to oxy pyknou; did kai mesên autên prosêloreusan [hê] oti ên tou men anô tetrachordon teleutê, tou de katô archê, kai meson eiche logon tonô tôn akrôn?

'Why did the ancient seven-stringed scales include Hypatê but not Nêtê? Or should we say that the note omitted was not Nêtê, but the present Paramesê and the interval of a tone (i.e. the disjunctive tone)? The Mesê, then, was the lowest note of the upper pyknon: whence the name mesê, because it was the end of the upper tetrachord and beginning of the lower one, and was in pitch the middle between the extremes.'

This clearly implies two conjunct tetrachords—

In another place (Probl. xix. 32) the question is asked, why the interval of the octave is called dia pasôn, not di' oktô,—as the Fourth is dia tessarôn, the Fifth dia pente. The answer suggested is that there were anciently seven strings, and that Terpander left out the Tritê and added the Nêtê. That is to say, Terpander increased the compass of the scale from the ancient two tetrachords to a full Octave; but he did not increase the number of strings to eight. Thus he produced a scale like the standard octave, but with one note wanting; so that the term di oktô was inappropriate.

Among later writers who confirm this account we may notice Nicomachus, p. 7 Meib. mesê dia tessarôn pros amphotera en tê heptachordô kata to palaion diestôsa: and p. 20 tê toinyn archaiotropô lyra toutesti tê heptachordô, kata synaphên ek duo tetrachordôn synestôsê k.t.l.

It appears then that two kinds of seven-stringed scales were known, at least by tradition: viz. (1) a scale composed of two conjunct tetrachords, and therefore of a compass less than an octave by one tone; and (2) a scale of the compass of an octave, but wanting a note, viz. the note above Mesê. The existence of this incomplete scale is interesting as a testimony to the force of the tradition which limited the number of strings to seven.

§ 18. The Perfect System.

The term 'Perfect System' (systêma teleion) is applied by the technical writers to a scale which is evidently formed by successive additions to the heptachord and octachord scales explained in the preceding chapter. It may be described as a combination of two scales, called the Greater and Lesser Perfect System.

The Greater Perfect System (systêma teleion meizon) consists of two octaves formed from the primitive octachord System by adding a tetrachord at each end of the scale. The new notes are named like those of the adjoining tetrachord of the original octave, but with the name of the tetrachord added by way of distinction. Thus below the original Hypatê we have a new tetrachord Hypatôn (tetrachordon hypatôn), the notes of which are accordingly called Hypatê Hypatôn, Parhypatê Hypatôn, and Lichanos Hypatôn: and similarly above Nêtê we have a tetrachord Hyperbolaiôn. Finally the octave downwards from Mesê is completed by the addition of a note appropriately called Proslambanomenos.

The Lesser Perfect System (systêma teleion elasson) is apparently based upon the ancient heptachord which consisted of two 'conjunct' tetrachords meeting in the Mesê. This scale was extended downwards in the same way as the Greater System, and thus became a scale of three tetrachords and a tone.

These two Systems together constitute the Perfect and 'unmodulating' System (systêma teleion ametabolon), which may be represented in modern notation [9] as follows:

No account of the Perfect System is given by Aristoxenus, and there is no trace in his writings of an extension of the standard scale beyond the limits of the original octave. In one place indeed (Harm. p. 8, 12 Meib.) Aristoxenus promises to treat of Systems, 'and among them of the perfect System' (peri te tôn allôn kai tou teleiou). But we cannot assume that the phrase here had the technical sense which it bore in later writers. More probably it meant simply the octave scale, in contrast to the tetrachord and pentachord—a sense in which it is used by Aristides Quintilianus, p. 11 Meib. synêmmenôn de eklêthê to holon systêma hoti tô prokeimenô teleiô tô mechri mesês synêptai, 'the whole scale was called conjunct because it is conjoined to the complete scale that reaches up to Mesê' (i.e. the octave extending from Proslambanomenos to Mesê). So p. 16 kai ha men autôn esti teleia, ha d' ou, atelê men tetrachordon, pentachordon, teleion de oktachordon. This is a use of teleios which is likely enough to have come from Aristoxenus. The word was doubtless applied in each period to the most complete scale which musical theory had then recognised.

Little is known of the steps by which this enlargement of the Greek scale was brought about. We shall not be wrong in conjecturing that it was connected with the advance made from time to time in the form and compass of musical instruments [10]. Along with the lyre, which kept its primitive simplicity as the instrument of education and everyday use, the Greeks had the cithara (kithara), an enlarged and improved lyre, which, to judge from the representations on ancient monuments, was generally seen in the hands of professional players (kitharôdoi). The development of the cithara showed itself in the increase, of which we have good evidence even before the time of Plato, in the number of the strings. The poet Ion, the contemporary of Sophocles, was the author of an epigram on a certain ten-stringed lyre, which seems to have had a scale closely approaching that of the Lesser Perfect System [11]. A little later we hear of the comic poet Pherecrates attacking the musician Timotheus for various innovations tending to the loss of primitive simplicity, in particular the use of twelve strings [12]. According to a tradition mentioned by Pausanias, the Spartans condemned Timotheus because in his cithara he had added four strings to the ancient seven. The offending instrument was hung up in the Scias (the place of meeting of the Spartan assembly), and apparently was seen there by Pausanias himself (Paus. iii. 12, 8).

A similar or still more rapid development took place in the flute (aulos). The flute-player Pronomus of Thebes, who was said to have been one of the instructors of Alcibiades, invented a flute on which it was possible to play in all the modes. 'Up to his time,' says Pausanias (ix. 12, 5), 'flute-players had three forms of flute: with one they played Dorian music; a different set of flutes served for the Phrygian mode (harmonia); and the so-called Lydian was played on another kind again. Pronomus was the first who devised flutes fitted for every sort of mode, and played melodies different in mode on the same flute.' The use of the new invention soon became general, since in Plato's time the flute was the instrument most distinguished by the multiplicity of its notes: cp. Rep. p. 399 ti de? aulopoious ê aulêtas paradexei eis tên polin? ê ou touto polychordotaton? Plato may have had the invention of Pronomus in mind when he wrote these words.

With regard to the order in which the new notes obtained a place in the schemes of theoretical musicians we have no trustworthy information. The name proslambanomenos, applied to the lowest note of the Perfect System, points to a time when it was the last new addition to the scale. Plutarch in his work on the Timaeus of Plato (peri tês en Timaiô psychogonias) speaks of the Proslambanomenos as having been added in comparatively recent times (p. 1029 c hoi de neôteroi ton proslambanomenon tonô diapheronta tês hypatês epi to bary taxantes to men holon diastêma dis dia pasôn epoiêsan). The rest of the Perfect System he ascribes to 'the ancients' (tous palaious ismen hypatas men dyo, treis de nêtas, mian de mesên kai mian paramesên tithemenous). An earlier addition—perhaps the first made to the primitive octave—was a note called Hyperhypatê, which was a tone below the old Hypatê, in the place afterwards occupied on the Diatonic scale by Lichanos Hypatôn. It naturally disappeared when the tetrachord Hypatôn came into use. It is only mentioned by one author, Thrasyllus (quoted by Theon Smyrnaeus, cc. 35-36 [13]).

The notes of the Perfect System, with the intervals of the scale which they formed, are fully set out in the two treatises that pass under the name of the geometer Euclid, viz. the Introductio Harmonica and the Sectio Canonis. Unfortunately the authorship of both these works is doubtful [14]. All that we can say is that if the Perfect System was elaborated in the brief interval between the time of Aristotle and that of Euclid, the materials for it must have already existed in musical practice.

§ 19. Relation of System and Key.

Let us now consider the relation between this fixed or standard scale and the varieties denoted by the terms harmonia and tonos.

With regard to the tonoi or Keys of Aristoxenus we are not left in doubt. A system, as we have seen, is a series of notes whose relative pitch is fixed. The key in which the System is taken fixes the absolute pitch of the series. As Aristoxenus expresses it, the Systems are melodies set at the pitch of the different keys (tous tonous, eph' hôn tithemena ta systêmata melôdeitai). If then we speak of Hypatê or Mesê (just as when we speak of a moveable Do), we mean as many different notes as there are keys: but the Dorian Hypatê or the Lydian Mesê has an ascertained pitch. The Keys of Aristoxenus, in short, are so many transpositions of the scale called the Perfect System.

Such being the relation of the standard System to the key, can we suppose any different relation to have subsisted between the standard System and the ancient 'modes' known to Plato and Aristotle under the name of harmoniai?

It appears from the language used by Plato in the Republic that Greek musical instruments differed very much in the variety of modes or harmoniai of which they were susceptible. After Socrates has determined, in the passage quoted above (p. 7), that he will admit only two modes, the Dorian and Phrygian, he goes on to observe that the music of his state will not need a multitude of strings, or an instrument of all the modes (panarmonion) [15]. 'There will be no custom therefore for craftsmen who make triangles and harps and other instruments of many notes and many modes. How then about makers of the flute (aulos) and players on the flute? Has not the flute the greatest number of notes, and are not the scales which admit all the modes simply imitations of the flute? There remain then the lyre and the cithara for use in our city; and for shepherds in the country a syrinx (pan's pipes).' The lyre, it is plain, did not admit of changes of mode. The seven or eight strings were tuned to furnish the scale of one mode, not of more. What then is the relation between the mode or harmonia of a lyre and the standard scale or systêma which (as we have seen) was based upon the lyre and its primitive gamut?

If harmonia means 'key,' there is no difficulty. The scale of a lyre was usually the standard octave from Hypatê to Nêtê: and that octave might be in any one key. But if a mode is somehow characterised by a particular succession of intervals, what becomes of the standard octave? No one succession of intervals can then be singled out. It may be said that the standard octave is in fact the scale of a particular mode, which had come to be regarded as the type, viz. the Dorian. But there is no trace of any such prominence of the Dorian mode as this would necessitate. The philosophers who recognise its elevation and Hellenic purity are very far from implying that it had the chief place in popular regard. Indeed the contrary was evidently the case [16].

§ 20. Tonality of the Greek musical scale.

It may be said here that the value of a series of notes as the basis of a distinct mode—in the modern sense of the word—depends essentially upon the tonality. A single scale might yield music of different modes if the key-note were different. It is necessary therefore to collect the scanty notices which we possess bearing upon the tonality of Greek music. The chief evidence on the subject is a passage of the Problems, the importance of which was first pointed out by Helmholtz [17].

It is as follows:

Arist. Probl. xix. 20: Dia ti ean men tis tên mesên kinêsê hêmôn, harmosas tas allas chordas, kai chrêtai tô organô, ou monon hotan kata ton tês mesês genêtai phthongon lypei kai phainetai anarmoston, alla kai kata tên allên melôdian, ean de tên lichanon ê tina allon phthongon, tote phainetai diapherein monon hotan kakeinê tis chrêtai? ê eulogôs touto symbainei? panta gar ta chrêsta melê pollakis tê mesê chrêtai, kai pantes hoi agathoi poiêtai pykna pros tên mesên apantôsi, kan apelthôsi tachy epanerchontai, pros de allên houtôs oudemian. kathaper ek tôn logôn eniôn exairethentôn syndesmôn ouk estin ho logos Hellênikos, hoion to te kai to kai, enioi de outhen lypousi, dia to tois men anankaion einai chrêsthai pollakis, ei estai logos, tois de mê, houtô kai tôn phthongôn hê mesê hôsper syndesmos esti, kai malista tôn kalôn, dia to pleistakis enyparchein ton phthongon autês.

'Why is it that if the Mesê is altered, after the other strings have been tuned, the instrument is felt to be out of tune, not only when the Mesê is sounded, but through the whole of the music,—whereas if the Lichanos or any other note is out of tune, it seems to be perceived only when that note is struck? Is it to be explained on the ground that all good melodies often use the Mesê, and all good composers resort to it frequently, and if they leave it soon return again, but do not make the same use of any other note? just as language cannot be Greek if certain conjunctions are omitted, such as te and kai, while others may be dispensed with, because the one class is necessary for language, but not the other: so with musical sounds the Mesê is a kind of 'conjunction,' especially of beautiful sounds, since it is most often heard among these.'

In another place (xix. 36) the question is answered by saying that the notes of a scale stand in a certain relation to the Mesê, which determines them with reference to it (hê taxis hê hekastês êdê di' ekeinên): so that the loss of the Mesê means the loss of the ground and unifying element of the scale (arthentos tou aitiou tou hêrmosthai kai tou synechontos) [18].

These passages imply that in the scale known to Aristotle, viz. the octave e-e, the Mesê a had the character of a Tonic or key-note. This must have been true a fortiori of the older seven-stringed scale, in which the Mesê united the two conjunct tetrachords. It was quite in accordance with this state of things that the later enlargement completed the octaves from Mesê downwards and upwards, so that the scale consisted of two octaves of the form a-a. As to the question how the Tonic character of the Mesê was shown, in what parts of the melody it was necessarily heard, and the like, we can but guess. The statement of the Problems is not repeated by any technical writer, and accordingly it does not appear that any rules on the subject had been arrived at. It is significant, perhaps, that the frequent use of the Mesê is spoken of as characteristic of good melody (panta ta chrêsta melê pollakis tê mesê chrêtai), as though tonality were a merit rather than a necessity.

Another passage of the Problems has been thought to show that in Greek music the melody ended on the Hypatê. The words are these (Probl. xix. 33):

Dia ti euarmostoteron apo tou oxeos epi to bary ê apo tou

bareos epi to oxy; poteron hoti to apo tês archês ginetai archesthai? hê gar mesê kai hêgemôn oxytatê tou tetrachordou; to de ouk ap' archês all' apo teleutês.

'Why is a descending scale more musical than an ascending one? Is it that in this order we begin with the beginning,—since the Mesê or leading note [19] is the highest of the tetrachord,—but with the reverse order we begin with the end?'

There is here no explicit statement that the melody ended on the Hypatê, or even that it began with the Mesê. In what sense, then, was the Mesê a 'beginning' (archê), and the Hypatê an 'end'? In Aristotelian language the word archê has various senses. It might be used to express the relation of the Mesê to the other notes as the basis or ground-work of the scale. Other passages, however, point to a simpler explanation, viz. that the order in question was merely conventional. In Probl. xix. 44 it is said that the Mesê is the beginning (archê) of one of the two tetrachords which form the ordinary octave scale (viz. the tetrachord Mesôn); and again in Probl. xix. 47 that in the old heptachord which consisted of two conjunct tetrachords (e-a-d) the Mesê (a) was the end of the upper tetrachord and the beginning of the lower one (hoti ên tou men anô tetrachordou teleutê, tou de katô archê). In this last passage it is evident that there is no reference to the beginning or end of the melody.

Another instance of the use of archê in connexion with the musical scale is to be found in the Metaphysics (iv. 11, p. 1018 b 26), where Aristotle is speaking of the different senses in which things may be prior and posterior:

Ta de kata taxin; tauta d' estin hosa pros ti hen hôrismenon diestêke kata ton logon, hoion parastatês tritostatou proteron, kai paranêtê nêtês; entha men gar ho koryphaios, entha de hê mesê archê.

'Other things [are prior and posterior] in order: viz. those which are at a varying interval from some one definite thing; as the second man in the rank is prior to the third man, and the Paranêtê to the Nêtê: for in the one case the coryphaeus is the starting-point, in the other the Mesê.'

Here the Mesê is again the archê or beginning, but the order is the ascending one, and consequently the Nêtê is the end. The passage confirms what we have learned of the relative importance of the Mesê: but it certainly negatives any inference regarding the note on which the melody ended.

It appears, then, that the Mesê of the Greek standard System had the functions of a key-note in that System. In other words, the music was in the mode (using that term in the modern sense) represented by the octave a-a of the natural key—the Hypo-dorian or Common Species. We do not indeed know how the predominant character of the Mesê was shown—whether, for example, the melody ended on the Mesê. The supposed evidence for an ending on the Hypatê has been shown to be insufficient. But we may at least hold that as far as the Mesê was a key-note, so far the Greek scale was that of the modern Minor mode (descending). The only way of escape from this conclusion is to deny that the Mesê of Probl. xix. 20 was the note which we have understood by the term—the Mesê of the standard System. This, as we shall presently see, is the plea to which Westphal has recourse.

§ 21. The Species of a Scale.

The object of the preceding discussion has been to make it clear that the theory of a system of modes—in the modern sense of the word—finds no support from the earlier authorities on Greek music. There is, however, evidence to show that Aristoxenus, and perhaps other writers of the time, gave much thought to the varieties to be obtained by taking the intervals of a scale in different order. These varieties they spoke of as the forms or species (schêmata, eidê) of the interval which measured the compass of the scale in question. Thus, the interval of the Octave (dia pasôn) is divided into seven intervals, and these are, in the Diatonic genus, five tones and two semitones, in the Enharmonic two ditones, four quarter-tones, and a tone. As we shall presently see in detail, there are seven species of the Octave in each genus. That is to say, there are seven admissible octachord scales (systêmata emmelê), differing only in the succession of the intervals which compose them.

Further, there is evidence which goes to connect the seven species of the Octave with the Modes or harmoniai. In some writers these species are described under names which are familiar to us in their application to the modes. A certain succession of intervals is called the Dorian species of the Octave, another succession is called the Phrygian species, and so on for the Lydian, Mixo-lydian, Hypo-dorian, Hypo-phrygian, and Hypo-lydian. It seems natural to conclude that the species or successions of intervals so named were characteristic in some way of the modes which bore the same names, consequently that the modes were not keys, but modes in the modern sense of the term.

In order to estimate the value of this argument, it is necessary to ask, (1) how far back we can date the use of these names for the species of the Octave, and (2) in what degree the species of the Octave can be shown to have entered into the practice of music at any period. The answer to these questions must be gathered from a careful examination of all that Aristoxenus and other early writers say of the different musical scales in reference to the order of their intervals.

§ 22. The Scales as treated by Aristoxenus.

The subject of the musical scales (systêmata) is treated by Aristoxenus as a general problem, without reference to the scales in actual use. He complains that his predecessors dealt only with the octave scale, and only with the Enharmonic genus, and did not address themselves to the real question of the melodious sequence of intervals. Accordingly, instead of beginning with a particular scale, such as the octave, he supposes a scale of indefinite compass,—just as a mathematician postulates lines and surfaces of unlimited magnitude. His problem virtually is, given any interval known to the particular genus supposed, to determine what intervals can follow it on a musical scale, either ascending or descending. In the Diatonic genus, for example, a semitone must be followed by two tones, so as to make up the interval of a Fourth. In the Enharmonic genus the dieses or quarter-tones can only occur two together, and every such pair of dieses (pyknon) must be followed in the ascending order by a ditone, in the descending order by a ditone or a tone. By these and similar rules, which he deduces mathematically from one or two general principles of melody, Aristoxenus in effect determines all the possible scales of each genus, without restriction of compass or pitch [20]. But whenever he refers for the purpose of illustration to a scale in actual use, it is always the standard octave already described (from Hypatê to Nêtê), or a part of it. Thus nothing can be clearer than the distinction which he makes between the theoretically infinite scale, subject only to certain principles or laws determining the succession of intervals, and the eight notes, of fixed relative pitch, which constituted the gamut of practical music.

The passages in which Aristoxenus dwells upon the advance which he has made upon the methods of his predecessors are of considerable importance for the whole question of the species of the Octave. There are three or four places which it will be worth while to quote.

1. Aristoxenus, Harm. p. 2, 15 Meib.: ta gar diagrammata autois tôn enarmoniôn (harmoniôn MSS.) ekkeitai monon systêmatôn, diatonôn d' ê chrômatikôn oudeis pôpoth' heôraken; kaitoi ta diagrammata g' autôn edêlou tên pasan tês melôdias taxin, en hois peri systêmatôn oktachordôn enarmoniôn (harmoniôn MSS.) monon elegon, peri de tôn allôn genôn te kai schêmatôn en autô te tô genei tontô kai tois loipois oud' epecheirei oudeis katamanthanein.

'The diagrams of the earlier writers set forth Systems in the Enharmonic genus only, never in the Diatonic or Chromatic: and yet these diagrams professed to give the whole scheme of their music, and in them they treated of Enharmonic octave Systems only; of other genera and other forms of this or any genus no one attempted to discover anything.'

2. Ibid. p. 6, 20 Meib.: tôn d' allôn katholou men kathaper emprosthen eipomen oudeis hêptai, henos de systêmatos Eratoklês epecheirêse kath' hen genos exarithmêsai ta schêmata tou dia pasôn apodeiktikôs tê periphora tôn diastêmatôn deiknys; ou katamathôn hoti, mê prosapodeichthentôn (qu. proapod.) tôn de tou dia pente schêmatôn kai tôn tou dia tessarôn pros de toutois kai tês syntheseôs autôn tis pot' esti kath' hên emmelôs syntithentai, pollaplasia tôn hepta symbainein gignesthai deiknytai.

'The other Systems no one has dealt with by a general method: but Eratocles has attempted in the case of one System, in one genus, to enumerate the forms or species of the Octave, and to determine them mathematically by the periodic recurrence of the intervals: not perceiving that unless we have first demonstrated the forms of the Fifth and the Fourth, and the manner of their melodious combination, the forms of the Octave will come to be many more than seven.'

The 'periodic recurrence of intervals' here spoken of may be illustrated on the key-board of a piano. If we take successive octaves of white notes, a-a, b-b, and so on, we obtain each time a different order of intervals (i.e. the semitones occur in different places), until we reach a-a again, when the series begins afresh. In this way it is shown that only seven species of the Octave can be found on any particular scale. Aristoxenus shows how to prove this from first principles, viz. by analysing the Octave as the combination of a Fifth with a Fourth.

3. Ibid. p. 36, 29 Meib.: tôn de systêmatôn tas diaphoras hoi men holôs ouk epecheiroun exarithmein, alla peri autôn monon tôn heptachordôn ha ekaloun harmonias tên episkepsin epoiounto, hoi de epicheirêsantes oudena tropon exêrithmounto.

For heptachordôn Meibomius and other editors read hepta oktachordôn—a correction strongly suggested by the parallel words systêmatôn oktachordôn in the first passage quoted.

'Some did not attempt to enumerate the differences of the Systems, but confined their view to the seven octachord Systems which they called harmoniai; others who did make the attempt did not succeed.'

It appears from these passages that before the time of Aristoxenus musicians had framed diagrams or tables showing the division of the octave scale according to the Enharmonic genus: and that a certain Eratocles—of whom nothing else is known—had recognised seven forms or species of the octachord scale, and had shown how the order of the intervals in the several species passes through a sort of cycle. Finally, if the correction proposed in the third passage is right, the seven species of the Octave were somehow shown in the diagrams of which the first passage speaks. In what respect Eratocles failed in his treatment of the seven species can hardly be conjectured.

Elsewhere the diagrams are described by Aristoxenus somewhat differently, as though they exhibited a division into Enharmonic dieses or quarter-tones, without reference to the melodious character of the scale. Thus we find him saying—

4. Harm. p. 28 Meib.: zêtêteon de to syneches ouch hôs hoi harmonikoi en tais tôn diagrammatôn katapyknôsesin apodidonai peirôntai, toutous apophainontes tôn phthongôn hexês allêlôn keisthai hois symbebêke to elachiston diastêma diechein aph' hautôn. ou gar to mê dynasthai dieseis oktô kai eikosin hexês melôdeisthai tês phônês estin, alla tên tritên diesin panta poiousa ouch hoia t' esti prostithenai.

'We must seek continuity of succession, not as theoretical musicians do in filling up their diagrams with small intervals, making those notes successive which are separated from each other by the least interval. For it is not merely that the voice cannot sing twenty-eight successive dieses: with all its efforts it cannot sing a third diesis [21].'

This representation of the musical diagrams is borne out by the passage in the Republic in which Plato derides the experimental study of music:

Rep. p. 531 a tas gar akouomenas au symphônias kai phthongous allêlois anametrountes anênyta, hôsper hoi astronomoi, ponousin. Nê tous theous, ephê, kai geloiôs ge, pyknômat' atta onomazontes kai paraballontes ta ôta, hoion ek geitonôn phônên thêreuomenoi, hoi men phasin eti katakouein en mesô tina êchên kai smikrotaton einai touto diastêma, hô metrêteon, hoi de k.t.l.

Here Socrates is insisting that the theory of music should be studied as a branch of mathematics, not by observation of the sounds and concords actually heard, about which musicians spend toil in vain. 'Yes,' says Glaucon, 'they talk of the close-fitting of intervals, and put their ears down to listen for the smallest possible interval, which is then to be the measure.' The smallest interval was of course the Enharmonic diesis or quarter of a tone, and this accordingly was the measure or unit into which the scale was divided. A group of notes separated by a diesis was called 'close' (pyknon, or a pyknôma), and the filling up of the scale in that way was therefore a katapyknôsis tou diagrammatos—a filling up with 'close-set' notes, by the division of every tone into four equal parts.

An example of a diagram of this kind has perhaps survived in a comparatively late writer, viz. Aristides Quintilianus, who gives a scale of two octaves, one divided into twenty-four dieses, the next into twelve semitones (De Mus. p. 15 Meib.). The characters used are not otherwise known, being quite different from the ordinary notation: but the nature of the diagram is plain from the accompanying words: hautê estin hê para tois archaiois kata dieseis harmonia, heôs κδ dieseôn to proteron diagousa dia pasôn, to deuteron dia tôn hêmitoniôn auxêsasa: 'this is the harmonia (division of the scale) according to dieses in use among the ancients, carried in the case of the first octave as far as twenty-four dieses, and dividing the second into semitones [22].'

The phrase hê kata dieseis harmonia, used for the division of an octave scale into quarter-tones, serves to explain the statement of Aristoxenus (in the third of the passages above quoted) that the writers who treated of octave Systems called them 'harmonies' (ha ekaloun harmonias). That statement has usually been taken to refer to the ancient Modes called harmoniai by Plato and Aristotle, and has been used accordingly as proof that the scales of these Modes were based upon the different species (eidê) of the Octave. But the form of the reference—'which they called harmoniai'—implies some forgotten or at least unfamiliar use of the word by the older technical writers. It is very much more probable that the harmoniai in question are divisions of the octave scale, as shown in theoretical diagrams, and had no necessary connexion with the Modes. Apparently some at least of these diagrams were not musical scales, but tables of all the notes in the compass of an octave; and the Enharmonic diesis was used, not merely on account of the importance of that genus, but because it was the smallest interval, and therefore the natural unit of measurement [23].

The use of harmonia as an equivalent for 'System' or 'division of the scale' appears in an important passage in Plato's Philebus (p. 17): all', ô phile, epeidan labês ta diastêmata hoposa esti ton arithmon tês phônês oxytêtos te peri kai barytêtos, kai hopoia, kai tous horous tôn diastêmatôn, kai ta ek toutôn hosa systêmata gegonen, ha katidontes hoi prosthen paredosan hêmin tois hepomenois ekeinois kalein auta harmonias, k.t.l. In this passage,—which has an air of technical accuracy not usual in Plato's references to music (though perhaps characteristic of the Philebus),—there is a close agreement with the technical writers, especially Aristoxenus. The main thought is the application of limit or measure to matter which is given as unlimited or indefinite—the distinction drawn out by Aristoxenus in a passage quoted below ([p. 81]). The treatment of the term 'System' is notably Aristoxenean (cp. Harm. p. 36 ta systêmata theôrêsai posa te esti kai poia atta, kai pôs ek te tôn diastêmatôn kai phthongôn synestêkota). Further, the use of harmonia for systêma, or rather of the plural harmoniai for the systêmata observed by the older musical theorists, is exactly what is noticed by Aristoxenus as if it were more or less antiquated. Even in the time of Plato it appears as a word of traditional character (hoi prosthen paredosan), his own word being systêma. It need not be said that there is no such hesitation, either in Plato or in Aristotle, about the use of harmoniai for the modes.

The same use of harmonia is found in the Aristotelian Problems (xix. 26), where the question is asked, dia ti mesê kaleitai en tais harmoniais, tôn de oktô ouk esti meson, i.e. how can we speak of the Mesê or 'middle note' of a scale of eight notes?

We have now reviewed all the passages in Aristoxenus which can be thought to bear upon the question whether the harmoniai or Modes of early Greek music are the same as the tonoi or Keys discussed by Aristoxenus himself. The result seems to be that we have found nothing to set against the positive arguments for the identification already urged. It may be thought, perhaps, that the variety of senses ascribed to the word harmonia goes beyond what is probable. In itself however the word meant simply 'musical scale [24].' The Pythagorean use of it in the sense of 'octave scale,' and the very similar use in reference to diagrams which represented the division of that scale, were antiquated in the time of Aristoxenus. The sense of 'key' was doubtless limited in the first instance to the use in conjunction with the names Dorian, &c., which suggested a distinction of pitch. From the meaning 'Dorian scale' to 'Dorian key' is an easy step. Finally, in reference to genus harmonia meant the Enharmonic scale. It is not surprising that a word with so many meanings did not keep its place in technical language, but was replaced by unambiguous words, viz. tonos in one sense, systêma in another, genos enarmonion in a third. Naturally, too, the more precise terms would be first employed by technical writers.

§ 23. The Seven Species.

([See the Appendix, Table I.])

In the Harmonics of Aristoxenus an account of the seven species of the Octave followed the elaborate theory of Systems already referred to ([p. 48]), and doubtless exhibited the application of that general theory to the particular cases of the Fourth, Fifth, and Octave. Unfortunately the existing manuscripts have only preserved the first few lines of this chapter of the Aristoxenean work (p. 74, ll. 10-24 Meib.).

The next source from which we learn anything of this part of the subject is the pseudo-Euclidean Introductio Harmonica. The writer enumerates the species of the Fourth, the Fifth, and the Octave, first in the Enharmonic and then in the Diatonic genus. He shows that if we take Fourths on a Diatonic scale, beginning with Hypatê Hypatôn (our b), we get successively b c d e (a scale with the intervals ½ 1 1), c d e f (1 1 ½) and d e f g (1 ½ 1). Similarly on the Enharmonic scale we get—

In the case of the Octave the species is distinguished on the Enharmonic scale by the place of the tone which separates the tetrachords, the so-called Disjunctive Tone (tonos diazeuktikos). Thus in the octave from Hypatê Hypatôn to Paramesê (b-b) this tone (a-b) is the highest interval; in the next octave, from Parhypatê Hypatôn to Tritê Diezeugmenôn (c-c), it is the second highest; and so on. These octaves, or species of the Octave, the writer goes on to tell us, were anciently called by the same names as the seven oldest Keys, as follows:

On the Diatonic scale, according to the same writer, the species of an Octave is distinguished by the places of the two semitones. Thus in the first species, b-b, the semitones are the first and fourth intervals (b-c and e-f): in the second, c-c, they are the third and the seventh, and so on. He does not however say, as he does in the case of the Enharmonic scale, that these species were known by the names of the Keys. This statement is first made by Gaudentius (p. 20 Meib.), a writer of unknown date. If we adopt it provisionally, the species of the Diatonic octave will be as follows:

§ 24. Relation of the Species to the Keys.

Looking at the octaves which on our key-board, as on the Greek scale, exhibit the several species, we cannot but be struck with the peculiar relation in which they stand to the Keys. In the tables given above the keys stand in the order of their pitch, from the Mixo-lydian down to the Hypo-dorian: the species of the same names follow the reverse order, from b-b upwards to a-a. This, it is obvious, cannot be an accidental coincidence. The two uses of this famous series of names cannot have originated independently. Either the naming of the species was founded on that of the keys, or the converse relation obtained between them. Which of these two uses, then, was the original and which the derived one? Those who hold that the species were the basis of the ancient Modes or harmoniai must regard the keys as derivative. Now Aristoxenus tells us, in one of the passages just quoted, that the seven species had long been recognised by theorists. If the scheme of keys was founded upon the seven species, it would at once have been complete, both in the number of the keys and in the determination of the intervals between them. But Aristoxenus also tells us that down to his time there were only six keys,—one of them not yet generally recognised,—and that their relative pitch was not settled. Evidently then the keys, which were scales in practical use, were still incomplete when the species of the Octave had been worked out in the theory of music.

If on the other hand we regard the names Dorian, &c. as originally applied to keys, we have only to suppose that these names were extended to the species after the number of seven keys had been completed. This supposition is borne out by the fact that Aristoxenus, who mentions the seven species as well known, does not give them names, or connect them with the keys. This step was apparently taken by some follower of Aristoxenus, who wished to connect the species of the older theorists with the system of keys which Aristoxenus had perfected.

The view now taken of the seven species is supported by the whole treatment of musical scales (systêmata) as we find it in Aristoxenus. That treatment from first to last is purely abstract and theoretical. The rules which Aristoxenus lays down serve to determine the sequence of intervals, but are not confined to scales of any particular compass. His Systems, accordingly, are not scales in practical use: they are parts taken anywhere on an ideal unlimited scale. And the seven species of the Octave are regarded by Aristoxenus as a scheme of the same abstract order. They represent the earlier teaching on which he had improved. He condemned that teaching for its want of generality, because it was confined to the compass of the Octave and to the Enharmonic genus, and also because it rested on no principles that would necessarily limit the species of the Octave to seven. On the other hand the diagrams of the earlier musicians were unscientific, in the opinion of Aristoxenus, on the ground that they divided the scale into a succession of quarter-tones. Such a division, he urged, is impossible in practice and musically wrong (ekmeles). All this goes to show that the earlier treatment of Systems, including the seven Species, had the same theoretical character as his own exposition. The only System which he recognises for practical purposes is the old standard octave, from Hypatê to Nêtê: and that System, with the enlargements which turned it into the Perfect System, kept its ground with all writers of the Aristoxenean school.

Even in the accounts of the pseudo-Euclid and the later writers, who treat of the Species of the Octave under the names of the Keys, there is much to show that the species existed chiefly or wholly in musical theory. The seven species of the Octave are given along with the three species of the Fourth and the four species of the Fifth, neither of which appear to have had any practical application. Another indication of this may be seen in the seventh or Hypo-dorian species, which was also called Locrian and Common (ps. Eucl. p. 16 Meib.). Why should this species have more than one name? In the Perfect System it is singular in being exemplified by two different octaves, viz. that from Proslambanomenos to Mesê, and that from Mesê to Nêtê Hyperbolaiôn. Now we have seen that the higher the octave which represents a species, the lower the key of the same name. In this case, then, the upper of the two octaves answers to the Hypo-dorian key, and the lower to the Locrian. But if the species has its two names from these two keys, it follows that the names of the species are derived from the keys. The fact that the Hypo-dorian or Locrian species was also called Common is a further argument to the same purpose. It was doubtless 'common' in the sense that it characterised the two octaves which made up the Perfect System. Thus the Perfect System was recognised as the really important scale.

Another consideration, which has been overlooked by Westphal and those who follow him, is the difference between the species of the Octave in the several genera, especially the difference between the Diatonic and the Enharmonic. This is not felt as a difficulty with all the species. Thus the so-called Dorian octave e-e is in the Enharmonic genus e e* f a b b* c e, a scale which may be regarded as the Diatonic with g and d omitted, and the semitones divided. But the Phrygian d-d cannot pass in any such way into the Enharmonic Phrygian c e e* f a b b* c, which answers rather to the Diatonic scale of the species c-c (the Lydian). The scholars who connect the ancient Modes with the species generally confine themselves to octaves of the Diatonic genus. In this they are supported by later Greek writers—notably, as we shall see, by Ptolemy—and by the analogy of the mediaeval Modes or Tones. But on the other side we have the repeated complaints of Aristoxenus that the earlier theorists confined themselves to Enharmonic octave scales. We have also the circumstance that the writer or compiler of the pseudo-Euclidean treatise, who is our earliest authority for the names of the species, gives these names for the Enharmonic genus only. Here, once more, we feel the difference between theory and practice. To a theorist there is no great difficulty in the terms Diatonic Phrygian and Enharmonic Phrygian meaning essentially different things. But the 'Phrygian Mode' in practical music must have been a tolerably definite musical form.

§ 25. The Ethos of Music.

From Plato and Aristotle we have learned some elements of what may be called the gamut of sensibility. Between the higher keys which in Greece, as in Oriental countries generally, were the familiar vehicle of passion, especially of the passion of grief, and the lower keys which were regarded, by Plato at least, as the natural language of ease and license, there were keys expressive of calm and balanced states of mind, free from the violent extremes of pain and pleasure. In some later writers on music we find this classification reduced to a more regular form, and clothed in technical language. We find also, what is still more to our purpose, an attempt to define more precisely the musical forms which answered to the several states of temper or emotion.

Among the writers in question the most instructive is Aristides Quintilianus. He discusses the subject of musical ethos under the first of the usual seven heads, that which deals with sounds or notes (peri phthongôn). Among the distinctions to be drawn in regard to notes he reckons that of ethos: the ethos of notes, he says, is different as they are higher or lower, and also as they are in the place of a Parhypatê or in the place of a Lichanos (p. 13 Meib. hetera gar êthê tois oxyterois, hetera tois baryterois epitrechei, kai hetera men parypatoeidesin, hetera de lichanoeidesin). Again, under the seventh head, that of melopoiia or composition, he treats of the 'regions of the voice' (topoi tês phônês). There are three kinds of composition, he tells us ([p. 28]), viz. that which is akin to Hypatê (hypatoeidês), that which is akin to Mesê (mesoeidês), and that which is akin to Nêtê (nêtoeidês). The first part of the art of composition is the choice (lêpsis) which the musician is able to make of the region of the voice to be employed (lêpsis men di' hês heuriskein tô mousikô perigignetai apo poiou tês phônês to systêma topou poiêteon, poteron hypatoeidous ê tôn loipôn tinos). He then proceeds to connect these regions, or different parts of the musical scale, with different branches of lyrical poetry. 'There are three styles of musical composition (tropoi tês melopoiias), viz. the Nomic, the Dithyrambic, and the Tragic; and of these the Nomic is netoid, the Dithyrambic is mesoid, and the Tragic is hypatoid.... They are called styles (tropoi) because according to the melody adopted they express the ethos of the mind. Thus it happens that composition (melopoiia) may differ in genus, as Enharmonic, Chromatic: in System, as Hypatoid, Mesoid, Netoid: in key, as Dorian, Phrygian: in style, as Nomic, Dithyrambic: in ethos, as we call one kind of composition "contracting" (systaltikê), viz. that by which we move painful feelings; another "expanding" (diastaltikê), that by which we arouse the spirit (thymos); and another "middle" (mesê), that by which we bring round the soul to calmness.'

This passage does not quite explicitly connect the three kinds of ethos—the diastaltic, the systaltic, the intermediate—with the three regions of the voice; but the connexion was evidently implied, and is laid down in express terms in the pseudo-Euclidean Introductio (p. 21 Meib.). According to this Aristoxenean writer, 'the diastaltic ethos of musical composition is that which expresses grandeur and manly elevation of soul (megaloprepeia kai diarma psychês andrôdes), and heroic actions; and these are employed by tragedy and all poetry that approaches the tragic type. The systaltic ethos is that by which the soul is brought down into a humble and unmanly frame; and such a disposition will be fitting for amatory effusions and dirges and lamentations and the like. And the hesychastic or tranquilly disposed ethos (hêsychastikon êthos) of musical composition is that which is followed by calmness of soul and a liberal and peaceful disposition: and this temper will fit hymns, paeans, laudations, didactic poetry and the like.' It appears then that difference in the 'place' (topos) of the notes employed in a composition—difference, that is to say, of pitch—was the element which chiefly determined its ethos, and (by consequence) which distinguished the music appropriate to the several kinds of lyrical poetry.

A slightly different version of this piece of theory is preserved in the anonymous treatise edited by Bellermann (§§ 63, 64), where the 'regions of the voice' are said to be four in number, viz. the three already mentioned, and a fourth which takes its name from the tetrachord Hyperbolaiôn (topos hyperboloeidês). In the same passage the boundaries of the several regions are laid down by reference to the keys. 'The lowest or hypatoid region reaches from the Hypo-dorian Hypatê Mesôn to the Dorian Mesê; the intermediate or mesoid region from the Phrygian Hypatê Mesôn to the Lydian Mesê; the netoid region from the Lydian Mesê to the Nêtê Synemmenôn; the hyperboloid region embracing all above the last point.' The text of this passage is uncertain; but the general character of the topoi or regions of the voice is clearly enough indicated.

The three regions are mentioned in the catechism of Bacchius (p. 11 Meib.): topous (MSS. tropous) de tês phônês posous legomen einai? treis. tinas? toutous; oxyn, meson, baryn. The varieties of ethos also appear (p. 14 Meib.): hê de metabolê kata êthos? hotan ek tapeinou eis megaloprepes; ê ex hêsychou kai synnou eis parakekinêkos. 'What is change of ethos? when a change is made from the humble to the magnificent; or from the tranquil and sober to violent emotion.'

When we compare the doctrine of musical ethos as we find it in these later writers with the indications to be gathered from Plato and Aristotle, the chief difference appears to be that we no longer hear of the ethos of particular modes, but only of that of three or (at the most) four portions of the scale. The principle of the division, it is evident, is simply difference of pitch. But if that was the basis of the ethical effect of music in later times, the circumstance goes far to confirm us in the conclusion that it was the pitch of the music, rather than any difference in the succession of the intervals, that principally determined the ethical character of the older modes.

§ 26. The Ethos of the Genera and Species.

Although the pitch of a musical composition—as these passages confirm us in believing—was the chief ground of its ethical character, it cannot be said that no other element entered into the case.

In the passage quoted above from Aristides Quintilianus (p. 13 Meib.) it is said that ethos depends first on pitch (hetera êthê tois oxyterois, hetera tois baryterois), and secondly on the moveable notes, that is to say, on the genus. For that is evidently involved in the words that follow: kai hetera men parypatoeidesin, hetera de lichanoeidesin. By parypatoeideis and lichanoeideis he means all the moveable notes (phthongoi pheromenoi): the first are those which hold the place of Parhypatê in their tetrachord, viz. the notes called Parhypatê or Tritê: the second are similarly the notes called Lichanos or Paranêtê. These moveable notes, then, give an ethos to the music because they determine the genus of the scale. Regarding the particular ethos belonging to the different genera, there is a statement of the same author ([p. 111]) to the effect that the Diatonic is masculine and austere (arrhenôpon d' esti kai austêroteron), the Chromatic sweet and plaintive (hêdiston te kai goeron), the Enharmonic stirring and pleasing (diegertikon d' esti touto kai êpion). The criticism doubtless came from some earlier source.

Do we ever find ethos attributed to this or that species of the Octave? I can find no passage in which this source of ethos is indicated. Even Ptolemy, who is the chief authority (as we shall see) for the value of the species, and who makes least of mere difference of pitch, recognises only two forms of modulation in the course of a melody, viz. change of genus and change of pitch [25].

§ 27. The Musical Notation.

As the preceding argument turns very much upon the practical importance of the scale which we have been discussing, first as the single octave from the original Hypatê to Nêtê, then in its enlarged form as the Perfect System, it may be worth while to show that some such scale is implied in the history of the Greek musical notation.

The use of written characters (sêmeia) to represent the sounds of music appears to date from a comparatively early period in Greece. In the time of Aristoxenus the art of writing down a melody (parasêmantikê) had come to be considered by some persons identical with the science of music (harmonikê),—an error which Aristoxenus is at some pains to refute. It is true that the authorities from whom we derive our knowledge of the Greek notation are post-classical. But the characters themselves, as we shall presently see, furnish sufficient evidence of their antiquity.

The Greek musical notation is curiously complicated. There is a double set of characters, one for the note assigned to the singer, the other for those of the lyre or other instrument. The notes for the voice are obviously derived from the letters of the ordinary Ionic alphabet, multiplied by the use of accents and other diacritical marks. The instrumental notes were first explained less than thirty years ago by Westphal. In his work Harmonik und Melopöie der Griechen (c. viii Die Semantik) he showed, in a manner as conclusive as it is ingenious, that they were originally taken from the first fourteen letters of an alphabet of archaic type, akin to the alphabets found in certain parts of Peloponnesus. Among the letters which he traces, and which point to this conclusion, the most-significant are the digamma, the primitive crooked iota

, and two forms of lambda,

and

, the latter of which is peculiar to the alphabet of Argos. Of the other characters

, which stands for alpha, is best derived from the archaic form

. For beta we find

, which may come from an archaic form of the letter[26]. The character

, as Westphal shows, is for

, or delta with part of one side left out. Similarly the ancient

, when the circle was incomplete, yielded the character C . The crooked iota (