Part 4

[Footnote 1: The correspondence between ancient and modern musical notation was first determined in a satisfactory way by Bellermann (_Die Tonleitern und Musiknoten der Griechen_), and Fortlage (_Das musicalische System der Griechen_).]

No account of the Perfect System is given by Aristoxenus, and there is no trace in his writings of an extension of the standard scale beyond the limits of the original octave. In one place indeed (_Harm._ p. 8, 12 Meib.) Aristoxenus promises to treat of Systems, 'and among them of the perfect System' ([Greek: peri te 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. [Greek: 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 [Greek: kai ha men autôn esti teleia, ha d' ou, atelê men tetrachordon, pentachordon, teleion de oktachordon.] This is a use of [Greek: teleios] which is likely enough to have come from Aristoxenus. The word was doubtless applied in each period to the most complete scale which musical theory had then recognised.

Little is known of the steps by which this enlargement of the Greek scale was brought about. We shall not be wrong in conjecturing that it was connected with the advance made from time to time in the form and compass of musical instruments[1]. Along with the lyre, which kept its primitive simplicity as the instrument of education and everyday use, the Greeks had the cithara ([Greek: kithara]), an enlarged and improved lyre, which, to judge from the representations on ancient monuments, was generally seen in the hands of professional players ([Greek: 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.

[Footnote 1: This observation was made by ancient writers, _e.g._ by Adrastus (Peripatetic philosopher of the second cent. A.D.): [Greek: epêuxêmenês de tês mousikês kai polychordôn kai polyphthongôn gegonotôn organôn tô proslêphthênai kai epi to bary kai epi to oxy tois pro[:y]parchousin oktô phthongois allous pleionas, homôs k.t.l. (Theon Smyrn. c. 6).]

The poet Ion, the contemporary of Sophocles, was the author of an epigram on a certain ten-stringed lyre, which seems to have had a scale closely approaching that of the Lesser Perfect System[1]. A little later we hear of the comic poet Pherecrates attacking the musician Timotheus for various innovations tending to the loss of primitive simplicity, in particular the use of twelve strings[2]. According to a tradition mentioned by Pausanias, the Spartans condemned Timotheus because in his cithara he had added four strings to the ancient seven. The offending instrument was hung up in the Scias (the place of meeting of the Spartan assembly), and apparently was seen there by Pausanias himself (Paus. iii. 12, 8).

[Footnote 1: The epigram is quoted in the pseudo-Euclidean _Introductio_, p. 19 (Meib.): [Greek: ho de] (sc. [Greek: Iôn]) [Greek: en dekachordô lyra] (_i.e._ in a poem on the subject of the ten-stringed lyre):--

[Greek: tên dekabamona taxin echousa tas symphônousas harmonias triodous; prin men s' heptatonon psallon dia tessara pantes Hellênes, spanian mousan aeiramenoi.]

'The triple ways of music that are in concord' must be the three conjunct tetrachords that can be formed with ten notes (_b c d e f g a b-flat c d_). This is the scale of the Lesser Perfect System before the addition of the Proslambanomenos.]

[Footnote 2: Pherecrates [Greek: cheirôn] fr. 1 (quoted by Plut. _de Mus._ c. 30). It is needless to refer to the other traditions on the subject, such as we find in Nicomachus (_Harm._ p. 35) and Boethius.]

A similar or still more rapid development took place in the flute ([Greek: aulos]). The flute-player Pronomus of Thebes, who was said to have been one of the instructors of Alcibiades, invented a flute on which it was possible to play in all the modes. 'Up to his time,' says Pausanias (ix. 12, 5), 'flute-players had three forms of flute: with one they played Dorian music; a different set of flutes served for the Phrygian mode ([Greek: harmonia]); and the so-called Lydian was played on another kind again. Pronomus was the first who devised flutes fitted for every sort of mode, and played melodies different in mode on the same flute.' The use of the new invention soon became general, since in Plato's time the flute was the instrument most distinguished by the multiplicity of its notes: cp. Rep. p. 399 [Greek: ti de? aulopoious 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 [Greek: proslambanomenos], applied to the lowest note of the Perfect System, points to a time when it was the last new addition to the scale. Plutarch in his work on the _Timaeus_ of Plato ([Greek: peri tês en Timaiô psychogonias]) speaks of the Proslambanomenos as having been added in comparatively recent times (p. 1029 _c_ [Greek: 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' ([Greek: 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[1]).

[Footnote 1: The term [Greek: hyperypatê] had all but disappeared from the text of Theon Smyrnaeus in the edition of Bullialdus (Paris, 1644), having been corrupted into [Greek: hypatê] or [Greek: parypatê] in every place except one (p. 141, 3). It has been restored from MSS. in the edition of Hiller (Teubner, Leipzig, 1878). The word occurs also in Aristides Quintilianus (p. 10 Meib.), where the plural [Greek: hyperypatai] is used for the notes below Hypatê, and in Boethius (_Mus._ i. 20).

It may be worth noticing also that Thrasyllus uses the words [Greek: diezeugmenê] and [Greek: hyperbolaia] in the sense of [Greek: nêtê diezeugmenôn] and [Greek: nêtê hyperbolaiôn] (Theon Smyrn. _l. c._).]

The notes of the Perfect System, with the intervals of the scale which they formed, are fully set out in the two treatises that pass under the name of the geometer Euclid, viz. the _Introductio Harmonica_ and the _Sectio Canonis_. Unfortunately the authorship of both these works is doubtful[1]. All that we can say is that if the Perfect System was elaborated in the brief interval between the time of Aristotle and that of Euclid, the materials for it must have already existed in musical practice.

[Footnote 1: _The Introduction to Harmonics_ ([Greek: eisagôgê harmonikê]) which bears the name of Euclid in modern editions (beginning with J. Pena, Paris, 1557) cannot be his work. In some MSS. it is ascribed to Cleonides, in others to Pappus, who was probably of the fourth century A.D. The author is one of the [Greek: harmonikoi] or Aristoxeneans, who adopt the method of equal temperament. He may perhaps be assigned to a comparatively early period on the ground that he recognises only the thirteen keys ascribed to Aristoxenus--not the fifteen keys given by most later writers (Aristides Quint., p. 22 Meib.). For some curious evidence connecting it with the name of the otherwise unknown writer Cleonides, see K. von Jan, _Die Harmonik des Aristoxenianers Kleonides_ (Landsberg, 1870). The _Section of the Canon_ ([Greek: kanonos katatomê]) belongs to the mathematical or Pythagorean school, dividing the tetrachord into two major tones and a [Greek: leimma] which is somewhat less than a semitone. In point of form it is decidedly Euclidean: but we do not find it referred to by any writer before the third century A.D.--the earliest testimony being that of Porphyry (pp. 272-276 in Wallis' edition).]

§ 19. _Relation of System and Key._

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

With regard to the [Greek: tonoi] or Keys of Aristoxenus we are not left in doubt. A system, as we have seen, is a series of notes whose _relative_ pitch is fixed. The key in which the System is taken fixes the absolute pitch of the series. As Aristoxenus expresses it, the Systems are melodies set at the pitch of the different keys ([Greek: tous tonous, eph' 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 [Greek: harmoniai]?

It appears from the language used by Plato in the _Republic_ that Greek musical instruments differed very much in the variety of modes or [Greek: harmoniai] of which they were susceptible. After Socrates has determined, in the passage quoted above (p. 7), that he will admit only two modes, the Dorian and Phrygian, he goes on to observe that the music of his state will not need a multitude of strings, or an instrument of all the modes ([Greek: panarmonion])[1]. 'There will be no custom therefore for craftsmen who make triangles and harps and other instruments of many notes and many modes. How then about makers of the flute ([Greek: aulos]) and players on the flute? Has not the flute the greatest number of notes, and are not the scales which admit all the modes simply imitations of the flute? There remain then the lyre and the cithara for use in our city; and for shepherds in the country a syrinx (pan's pipes).' The lyre, it is plain, did not admit of changes of mode. The seven or eight strings were tuned to furnish the scale of one mode, not of more. What then is the relation between the mode or [Greek: harmonia] of a lyre and the standard scale or [Greek: systêma] which (as we have seen) was based upon the lyre and its primitive gamut?

[Footnote 1: Plato, Rep. p. 399: [Greek: ouk ara, ên d' egô, polychordias ge oude panarmoniou hêmin deêsei en tais ôdais te kai melesin. Ou moi, ephê, phainetai. Trigônôn ara kai pêktidôn kai pantôn organôn hosa polychorda kai polyarmonia dêmiourgous ou threpsomen. Ou phainometha. Ti de? aulopoious ê aulêtas paradexei eis tên polin? ê ou touto polychordotaton, kai auta ta panarmonia aulou tynchanei onta mimêma? Dêla dê, ê d' hos. Lyra dê soi, ên d' egô, kai kithara leipetai, kai kata polin chrêsima; kai au kat' agrous tois nomeusi syrinx an tis eiê.]

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

If [Greek: harmonia] means 'key,' there is no difficulty. The scale of a lyre was usually the standard octave from 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[1].

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

§ 20. _Tonality of the Greek musical scale._

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

Arist. _Probl._ xix. 20: [Greek: Dia ti ean men tis 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 [Greek: te] and [Greek: kai], while others may be dispensed with, because the one class is necessary for language, but not the other: so with musical sounds the Mesê 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 Mesê, which determines them with reference to it ([Greek: 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 ([Greek: arthentos tou aitiou tou hêrmosthai kai tou synechontos])[1].

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 ([Greek: 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):

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

[Footnote 1: So in the Euclidean _Sectio Canonis_ the propositions which deal with the 'movable' notes, viz. Paranêtê and Lichanos (Theor. xvii) and Parhypatê and Tritê (Theor. xviii), begin by postulating the Mesê ([Greek: estô gar mesê ho B k.t.l.]).]

[Greek: 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[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 Hypatê, or even that it began with the Mesê. In what sense, then, was the Mesê a 'beginning' ([Greek: archê]), and the Hypatê an 'end'? In Aristotelian language the word [Greek: 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 ([Greek: 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 ([Greek: 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.

[Footnote 1: The term [Greek: hêgemôn] or 'leading note' of the tetrachord Mesôn, here applied to the Mesê, is found in the same sense in Plutarch, _De Mus._ c. 11, where [Greek: ho peri ton hêgemona keimenos tonos] means the disjunctive tone. Similarly Ptolemy (_Harm._ i. 16) speaks of the tones in a diatonic scale as being [Greek: en tois hêgoumenois 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 hêgoumenos tou enarmoniou genous]).]

Another instance of the use of [Greek: 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:

[Greek: 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 [Greek: 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_ ([Greek: schêmata, eidê]) of the interval which measured the compass of the scale in question. Thus, the interval of the Octave ([Greek: 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 ([Greek: 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 [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._