The Modes of Ancient Greek Music Part 4

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

It appears from the language used by Plato in the _Republic_ that Greek musical instruments differed very much in the variety of modes or [Greek: harmoniai] of which they were susceptible. After Socrates has determined, in the pa.s.sage 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 mult.i.tude of strings, or an instrument of all the modes ([Greek: panarmonion])[1]. 'There will be no custom therefore for craftsmen who make triangles and harps and other instruments of many notes and many modes. How then about makers of the flute ([Greek: aulos]) and players on the flute? Has not the flute the greatest number of notes, and are not the scales which admit all the modes simply imitations of the flute? There remain then the lyre and the cithara for use in our city; and for shepherds in the country a syrinx (pan's pipes).' The lyre, it is plain, did not admit of changes of mode. The seven or eight strings were tuned to furnish the scale of one mode, not of more. What then is the relation between the mode or [Greek: harmonia] of a lyre and the standard scale or [Greek: systema] which (as we have seen) was based upon the lyre and its primitive gamut?

[Footnote 1: Plato, Rep. p. 399: [Greek: ouk ara, en d' ego, polychordias ge oude panarmoniou hemin deesei en tais odais te kai melesin. Ou moi, ephe, phainetai. Trigonon ara kai pektidon kai panton organon hosa polychorda kai polyarmonia demiourgous ou threpsomen. Ou phainometha. Ti de? aulopoious e auletas paradexei eis ten polin? e ou touto polychordotaton, kai auta ta panarmonia aulou tynchanei onta mimema? Dela de, e d' hos. Lyra de soi, en d' ego, kai kithara leipetai, kai kata polin chresima; kai au kat' agrous tois nomeusi syrinx an tis eie.]

The [Greek: aulos] was not exactly a flute. It had a mouthpiece which gave it the character rather of the modern oboe or clarinet: see the _Dictionary of Antiquities_, S. V. TIBIA. The [Greek: panarmonion] is not otherwise known, and the pa.s.sage in Plato does not enable us to decide whether it was a real instrument or only a scale or arrangement of notes.]

If [Greek: harmonia] means 'key,' there is no difficulty. The scale of a lyre was usually the standard octave from Hypate to Nete: and that octave might be in any one key. But if a mode is somehow characterised by a particular succession of intervals, what becomes of the standard octave? No one succession of intervals can then be singled out. It may be said that the standard octave is in fact the scale of a particular mode, which had come to be regarded as the type, viz. the Dorian. But there is no trace of any such prominence of the Dorian mode as this would necessitate. The philosophers who recognise its elevation and h.e.l.lenic purity are very far from implying that it had the chief place in popular regard. Indeed the contrary was evidently the case[1].

[Footnote 1: The pa.s.sage quoted above from the _Knights_ of Aristophanes (p. 7) is sufficient to show that a marked preference for the Dorian mode would be a matter for jest.]

-- 20. _Tonality of the Greek musical scale._

It may be said here that the value of a series of notes as the basis of a distinct mode--in the modern sense of the word--depends essentially upon the _tonality_. A single scale might yield music of different modes if the key-note were different. It is necessary therefore to collect the scanty notices which we possess bearing upon the tonality of Greek music. The chief evidence on the subject is a pa.s.sage of the _Problems_, the importance of which was first pointed out by Helmholtz[1]. It is as follows:

Arist. _Probl._ xix. 20: [Greek: Dia ti ean men tis ten mesen kinese hemon, harmosas tas allas chordas, kai chretai to organo, ou monon hotan kata ton tes meses genetai phthongon lypei kai phainetai anarmoston, alla kai kata ten allen melodian, ean de ten lichanon e tina allon phthongon, tote phainetai diapherein monon hotan kakeine tis chretai? e eulogos touto symbainei? panta gar ta chresta mele pollakis te mese chretai, kai pantes hoi agathoi poietai pykna pros ten mesen apantosi, kan apelthosi tachy epanerchontai, pros de allen houtos oudemian. kathaper ek ton logon enion exairethenton syndesmon ouk estin ho logos h.e.l.lenikos, hoion to te kai to kai, enioi de outhen lypousi, dia to tois men anankaion einai chresthai pollakis, ei estai logos, tois de me, houto kai ton phthongon he mese hosper syndesmos esti, kai malista ton kalon, dia to pleistakis enyparchein ton phthongon autes.]

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

[Footnote 1: _Die Lehre von den Tonempfindungen_, p. 367, ed. 1863.]

In another place (xix. 36) the question is answered by saying that the notes of a scale stand in a certain relation to the Mese, which determines them with reference to it ([Greek: he taxis he hekastes ede di' ekeinen]): so that the loss of the Mese means the loss of the ground and unifying element of the scale ([Greek: arthentos tou aitiou tou hermosthai kai tou synechontos])[1].

These pa.s.sages imply that in the scale known to Aristotle, viz. the octave _e - e_, the Mese _a_ had the character of a Tonic or key-note. This must have been true _a fortiori_ of the older seven-stringed scale, in which the Mese united the two conjunct tetrachords. It was quite in accordance with this state of things that the later enlargement completed the octaves from Mese downwards and upwards, so that the scale consisted of two octaves of the form _a-a_. As to the question how the Tonic character of the Mese was shown, in what parts of the melody it was necessarily heard, and the like, we can but guess. The statement of the _Problems_ is not repeated by any technical writer, and accordingly it does not appear that any rules on the subject had been arrived at. It is significant, perhaps, that the frequent use of the Mese is spoken of as characteristic of _good_ melody ([Greek: panta ta chresta mele pollakis te mese chretai]), as though tonality were a merit rather than a necessity.

Another pa.s.sage of the _Problems_ has been thought to show that in Greek music the melody ended on the Hypate. The words are these (_Probl._ xix. 33):

[Greek: Dia ti euarmostoteron apo tou oxeos epi to bary e apo tou]

[Footnote 1: So in the Euclidean _Sectio Canonis_ the propositions which deal with the 'movable' notes, viz. Paranete and Lichanos (Theor. xvii) and Parhypate and Trite (Theor. xviii), begin by postulating the Mese ([Greek: esto gar mese ho B k.t.l.]).]

[Greek: bareos epi to oxy; poteron hoti to apo tes arches ginetai archesthai? he gar mese kai hegemon oxytate tou tetrachordou; to de ouk ap' arches all' apo teleutes.]

'Why is a descending scale more musical than an ascending one?

Is it that in this order we begin with the beginning,--since the Mese or leading note[1] is the highest of the tetrachord,--but with the reverse order we begin with the end?'

There is here no explicit statement that the melody ended on the Hypate, or even that it began with the Mese. In what sense, then, was the Mese a 'beginning' ([Greek: arche]), and the Hypate an 'end'? In Aristotelian language the word [Greek: arche] has various senses. It might be used to express the relation of the Mese to the other notes as the basis or ground-work of the scale. Other pa.s.sages, however, point to a simpler explanation, viz. that the order in question was merely conventional. In _Probl._ xix. 44 it is said that the Mese is the beginning ([Greek: arche]) of one of the two tetrachords which form the ordinary octave scale (viz. the tetrachord Meson); and again in _Probl._ xix. 47 that in the old heptachord which consisted of two conjunct tetrachords (_e-a-d_) the Mese (_a_) was the end of the upper tetrachord and the beginning of the lower one ([Greek: hoti en tou men ano tetrachordou teleute, tou de kato arche]). In this last pa.s.sage it is evident that there is no reference to the beginning or end of the melody.

[Footnote 1: The term [Greek: hegemon] or 'leading note' of the tetrachord Meson, here applied to the Mese, is found in the same sense in Plutarch, _De Mus._ c. 11, where [Greek: ho peri ton hegemona keimenos tonos] means the disjunctive tone. Similarly Ptolemy (_Harm._ i. 16) speaks of the tones in a diatonic scale as being [Greek: en tois hegoumenois topois], the semitones [Greek: en tois hepomenois] (sc. of the tetrachord): and again of the ratio 5:4 (the major Third) as the 'leading' one of an Enharmonic tetrachord ([Greek: ton epitetarton hos estin hegoumenos tou enarmoniou genous]).]

Another instance of the use of [Greek: arche] in connexion with the musical scale is to be found in the _Metaphysics_ (iv. 11, p. 1018 _b_ 26), where Aristotle is speaking of the different senses in which things may be prior and posterior:

[Greek: Ta de kata taxin; tauta d' estin hosa pros ti hen horismenon diesteke kata ton logon, hoion parastates tritostatou proteron, kai paranete netes; entha men gar ho koryphaios, entha de he mese arche.]

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

Here the Mese is again the [Greek: arche] or beginning, but the order is the ascending one, and consequently the Nete is the end. The pa.s.sage confirms what we have learned of the relative importance of the Mese: but it certainly negatives any inference regarding the note on which the melody ended.

It appears, then, that the Mese of the Greek standard System had the functions of a key-note in that System. In other words, the music was in the _mode_ (using that term in the modern sense) represented by the octave _a-a_ of the natural key--the Hypo-dorian or Common Species. We do not indeed know how the predominant character of the Mese was shown--whether, for example, the melody ended on the Mese.

The supposed evidence for an ending on the Hypate has been shown to be insufficient. But we may at least hold that as far as the Mese was a key-note, so far the Greek scale was that of the modern Minor mode (descending). The only way of escape from this conclusion is to deny that the Mese of _Probl._ xix. 20 was the note which we have understood by the term--the Mese of the standard System. This, as we shall presently see, is the plea to which Westphal has recourse.

-- 21. _The Species of a Scale._

The object of the preceding discussion has been to make it clear that the theory of a system of modes--in the modern sense of the word--finds no support from the earlier authorities on Greek music.

There is, however, evidence to show that Aristoxenus, and perhaps other writers of the time, gave much thought to the varieties to be obtained by taking the intervals of a scale in different order. These varieties they spoke of as the _forms_ or _species_ ([Greek: schemata, eide]) of the interval which measured the compa.s.s of the scale in question. Thus, the interval of the Octave ([Greek: dia pason]) is divided into seven intervals, and these are, in the Diatonic genus, five tones and two semitones, in the Enharmonic two ditones, four quarter-tones, and a tone. As we shall presently see in detail, there are seven species of the Octave in each genus. That is to say, there are seven admissible octachord scales ([Greek: systemata emmele]), differing only in the succession of the intervals which compose them.

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

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

-- 22. _The Scales as treated by Aristoxenus._

The subject of the musical scales ([Greek: systemata]) is treated by Aristoxenus as a general problem, without reference to the scales in actual use. He complains that his predecessors dealt only with the octave scale, and only with the Enharmonic genus, and did not address themselves to the real question of the melodious sequence of intervals. Accordingly, instead of beginning with a particular scale, such as the octave, he supposes a scale of indefinite compa.s.s,--just as a mathematician postulates lines and surfaces of unlimited magnitude. His problem virtually is, given any interval known to the particular genus supposed, to determine what intervals can follow it on a musical scale, either ascending or descending. In the Diatonic genus, for example, a semitone must be followed by two tones, so as to make up the interval of a Fourth. In the Enharmonic genus the dieses or quarter-tones can only occur two together, and every such pair of dieses ([Greek: pyknon]) must be followed in the ascending order by a ditone, in the descending order by a ditone or a tone. By these and similar rules, which he deduces mathematically from one or two general principles of melody, Aristoxenus in effect determines all the possible scales of each genus, without restriction of compa.s.s or pitch[1]. But whenever he refers for the purpose of ill.u.s.tration to a scale in actual use, it is always the standard octave already described (from Hypate to Nete), or a part of it. Thus nothing can be clearer than the distinction which he makes between the theoretically infinite scale, subject only to certain principles or laws determining the succession of intervals, and the eight notes, of fixed relative pitch, which const.i.tuted the gamut of practical music.

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

1. Aristoxenus, _Harm._ p. 2, 15 Meib.: [Greek: ta gar diagrammata autois ton enarmonion] ([Greek: harmonion] MSS.) [Greek: ekkeitai monon systematon, diatonon d' e chromatikon oudeis popoth' heoraken; kaitoi ta diagrammata g' auton edelou ten pasan tes melodias taxin, en hois peri systematon oktachordon enarmonion] ([Greek: harmonion] MSS.) [Greek: monon elegon, peri de ton allon genon te kai schematon en auto te to genei tonto kai tois loipois oud' epecheirei oudeis katamanthanein.]

[Footnote 1: The investigation occupies a considerable s.p.a.ce in his _Harmonics_, viz. pp. 27-29 Meib. (from the words [Greek: peri de synecheias kai tou hexes]), and again pp. 58-72 Meib.]

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

2. Ibid. p. 6, 20 Meib.: [Greek: ton d' allon katholou men kathaper emprosthen eipomen oudeis heptai, henos de systematos Eratokles epecheirese kath' hen genos exarithmesai ta schemata tou dia pason apodeiktikos te periphora ton diastematon deiknys; ou katamathon hoti, me prosapodeichthenton] (qu.

[Greek: proapod.]) [Greek: ton de tou dia pente schematon kai ton tou dia tessaron pros de toutois kai tes syntheseos auton tis pot' esti kath' hen emmelos synt.i.thentai, pollaplasia ton hepta symbainein gignesthai deiknytai.]

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

The 'periodic recurrence of intervals' here spoken of may be ill.u.s.trated 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 a.n.a.lysing the Octave as the combination of a Fifth with a Fourth.