Part 7

TABLE LEGEND: Column A = Prosl. Column B = Hyp. Hypatôn. Column C = Hyp. Mesôn. Column D = Mesê. Column E = Par. Column F = Nêtê Diez. Column G = Nêtê Hyperb.

A B C D E F G

Mixo-lydian [Symbols] 4 id D > N \ = _e[Symbol: b] - e[Symbol: b]_ Lydian [Symbols] I- r c < c m = _d - d_ Phrygian [Symbols] E I- F 11 < Z = _c - c_ Dorian [Symbols] R E I' D ri N \ = _b[Symbol: b] - b[Symbol: b]_ Hypo-lydian [Symbols] H h r C I< c M = _a - a_ [Hypo-phrygian [Symbols] H I- F C < Z = _g - g_ [Hypo-dorian [Symbols] E /4 F 11 N = _f - f_

It will be evident that this scheme of notation tallies fairly well with what we know of the compass of Greek instruments about the end of the fifth century, and also with the account which Aristoxenus gives of the keys in use up to his time. We need only refer to what has been said above on p. 17 and p. 37.

It would be beyond the scope of this essay to discuss the date of the Greek musical notation. A few remarks, however, may be made, especially with reference to the high antiquity assigned to it by Westphal.

The alphabet from which it was derived was certainly an archaic one. It contained several characters, in particular [Symbols: F] for digamma, [Symbols: LI] for iota, and [Symbols: I-] for lambda, which belong to the period before the introduction of the Ionian alphabet. Indeed if we were to judge from these letters alone we should be led to assign the instrumental notation (as Westphal does) to the time of Solon. The three-stroke iota ([Symbols: I]), in particular, does not occur in any alphabet later than the sixth century B.C. On the other hand, when we find that the notation implies the use of a musical System in advance of any scale recognised in Aristotle, or even in Aristoxenus, such a date becomes incredible. We can only suppose either (1) that the use of [Symbols: Li] in the fifth century was confined to localities of which we have no complete epigraphic record, or (2) that [Symbols: i] as a form of iota was still known--as archaic forms must have been--from the older public inscriptions, and was adopted by the inventor of the notation as being better suited to his purpose than [Symbols: 1].

With regard to the place of origin of the notation the chief fact which we have to deal with is the use of the character [Symbols: I-] for lambda, which is distinctive of the alphabet of Argos, along with the commoner form [Symbols: <]. Westphal indeed asserts that both these forms are found in the Argive alphabet. But the inscription (C. I. 1) which he quotes[1] for [Symbols: <] really contains only [Symbols: t-] in a slightly different form. We cannot therefore say that the inventor of the notation derived it entirely from the alphabet of Argos, but only that he shows an acquaintance with that alphabet. This is confirmed by the fact that the form [Symbols: Li] for iota is not found at Argos. Probably therefore the inventor drew upon more than one alphabet for his purpose, the Argive alphabet being one.

[Footnote 1: _Harmonik und Melopöie_, p. 286 (ed. 1863). The true form of the letter is given by Mr. Roberts, _Greek Epigraphy_, p. 109.]

The special fitness of the notation for the scales of the Enharmonic genus may be regarded as a further indication of its date. We shall see presently that that genus held a peculiar predominance in the earliest period of musical theory--that, namely, which was brought to an end by Aristoxenus.

If the author of the notation--or the second author, inventor of the modified characters--was one of the musicians whose names have come down to us, it would be difficult to find a more probable one than that of Pronomus of Thebes. One of the most striking features of the notation, at the time when it was framed, must have been the adjustment of the keys. Even in the time of Aristoxenus, as we know from the passage so often quoted, that adjustment was not universal. But it is precisely what Pronomus of Thebes is said to have done for the music of the flute (_supra_, p. 38). The circumstance that the system was only used for instrumental music is at least in harmony with this conjecture. If it is thought that Thebes is too far from Argos, we may fall back upon the notice that Sacadas of Argos was the chief composer for the flute before the time of Pronomus[1], and doubtless Argos was one of the first cities to share in the advance which Pronomus made in the technique of his art.

[Footnote 1: Pausanias (iv. 27, 4) says of the founding of Messene: [Greek: eirgazonto de kai hypo mousuiês allês men oudemias, aulôn de Boiôtiôn kai Argeiôn; ta te Sakada kai Pronomou melê tote dê proêchthê malista eis hamillan.]]

§ 28. _Traces of the Species in the Notation._

Before leaving this part of the subject it will be well to notice the attempt which Westphal makes to connect the species of the Octave with the form of the musical notation.

The basis of the notation, as has been explained (p. 69), is formed by two Diatonic octaves, denoted by the letters of the alphabet from [Greek: a] to [Greek: n], as follows:

[Greek: ê i e l g m [digamma] th k d l b n z a] _ a b c d e f g a b c d e f g a_

In this scale, as has been pointed out (p. 71), the notes which are at the distance of an octave from each other are always expressed by two _successive_ letters of the alphabet. Thus we find--

[Greek: b - g] is the octave _e - e_, the Dorian species. [Greek: d - e] " " _c - c_, the Lydian species. [Greek: [digamma] - z]" " _g - g_, the Hypo-phrygian species. [Greek: ê - th] " " _a - a_, the Hypo-dorian species.

Westphal adopts the theory of Boeckh (as to which see p. 11) that the Hypo-phrygian and Hypo-dorian species answered to the ancient Ionian and Aeolian modes. On this assumption he argues that the order of the pairs of letters representing the species agrees with the order of the Modes in the historical development of Greek music. For the priority of Dorian, Ionian, and Aeolian he appeals to the authority of Heraclides Ponticus, quoted above (p. 9). The Lydian, he supposes, was interposed in the second place on account of its importance in education,--recognised, as we have seen, by Aristotle in the _Politics_ (viii. 7 _ad fin._). Hence he regards the notation as confirming his theory of the nature and history of the Modes.

The weakness of this reasoning is manifold. Granting that the Hypo-dorian and Hypo-phrygian answer to the old Aeolian and Ionian respectively, we have to ask what is the nature of the priority which Heraclides Ponticus claims for his three modes, and what is the value of his testimony. What he says is, in substance, that these are the only kinds of music that are truly Hellenic, and worthy of the name of modes ([Greek: harmoniai]). It can hardly be thought that this is a criticism likely to have weighed with the inventor of the notation. But if it did, why did he give an equally prominent place to Lydian, one of the modes which Heraclides condemned? In fact, the introduction of Lydian goes far to show that the coincidence--such as it is--with the views of Heraclides is mere accident. Apart, however, from these difficulties, there are at least two considerations which seem fatal to Westphal's theory:

1. The notation, so far as the original two octaves are concerned, must have been devised and worked out at some one time. No part of these two octaves can have been completed before the rest. Hence the order in which the letters are taken for the several notes has no historical importance.

2. The notation does not represent only the _species_ of a scale, that is to say, the relative pitch of the notes which compose it, but it represents also the absolute pitch of each note. Thus the octaves which are defined by the successive pairs of letters, [Greek:b-g, d-e], and the rest, are octaves of definite notes. If they were framed with a view to the ancient modes, as Westphal thinks, they must be the actual scales employed in these modes. If so, the modes followed each other, in respect of pitch, in an order exactly the reverse of the order observed in the keys. It need hardly be said that this is quite impossible. § 29. _Ptolemy's Scheme of Modes._

The first writer who takes the Species of the Octave as the basis of the musical scales is the mathematician Claudius Ptolemaeus (fl. 140-160 A.D.). In his _Harmonics_ he virtually sets aside the scheme of keys elaborated by Aristoxenus and his school, and adopts in their place a system of scales answering in their main features to the mediaeval Tones or Modes. The object of difference of key, he says, is not that the music as a whole may be of a higher or lower pitch, but that a melody may be brought within a certain compass. For this purpose it is necessary to vary the succession of intervals (as a modern musician does by changing the signature of the clef). If, for example, we take the Perfect System ([Greek: systêma ametabolon]) in the key of _a_ minor--which is its natural key,--and transpose it to the key of _d_ minor, we do so, according to Ptolemy, not in order to raise the general pitch of our music by a Fourth, but because we wish to have a scale with _b_ flat instead of _b_ natural. The flattening of this note, however, means that the two octaves change their species. They are now of the species _e - e_. Thus, instead of transposing the Perfect System into different keys, we arrive more directly at the desired result by changing the species of its octaves. And as there are seven possible species of the Octave, we obtain seven different Systems or scales. From these assumptions it follows, as Ptolemy shows in some detail, that any greater number of keys is useless. If a key is an octave higher than another, it is superfluous because it gives us a mere repetition of the same intervals[1].

[Footnote 1: _Harm._ ii. 8 [Greek: hoi de hyperekpiptontes tou dia pasôn tous ap' autou tou dia pasôn apôterô parelkontôs hypotithentai, tous autous aei ginomenous tois proeilêmmenois.]]

If we interpose a key between (_e.g._) the Hypo-dorian and the Hypo-phrygian, it must give us over again either the Hypo-dorian or the Hypo-phrygian scale[1]. Thus the fifteen keys of the Aristoxeneans are reduced to seven, and these seven are not transpositions of a single scale, but are all of the same pitch. See the table at the end of the book.

With this scheme of Keys Ptolemy combined a new method of naming the individual notes. The old method, by which a note was named from its relative place in the Perfect System, must evidently have become inconvenient. The Lydian Mesê, for example, was two tones higher than the Dorian Mesê, because the Lydian scale as a whole was two tones higher than the Dorian. But when the two scales were reduced to the same compass, the old Lydian Mesê was no longer in the middle of the scale, and the name ceased to have a meaning. It is as though the term 'dominant' when applied to a Minor key were made to mean the dominant of the relative Major key. On Ptolemy's method the notes of each scale were named from their places in it. The old names were used, Proslambanomenos for the lowest, Hypatê Hypatôn for the next, and so on, but without regard to the intervals between the notes. Thus there were two methods of naming, that which had been in use hitherto, termed 'nomenclature according to _value_' ([Greek: onomasia kata dynamin]), and the new method of naming from the various scales, termed 'nomenclature according to _position_' ([Greek: onomasia kata thesin]). The former was in effect a retention of the Perfect System and the Keys: the latter put in their place a scheme of seven different standard Systems.

[Footnote 1: _Harm._ ii. 11 [Greek: hôste mêd' an heteron eti doxai tô eidei ton tonon para ton proteron, all' hypodôrion palin, ê ton auton hypophrygion, oxyphônoteron tinos ê baryphônoteron monon.]]

In illustration of his theory Ptolemy gives tables showing in numbers the intervals of the octaves used in the different keys and genera. He shows two octaves in each key, viz. that from Hypatê Mesôn ([Greek: kata thesin]) to Nêtê Diezeugmenôn (called the octave [Greek: apo nêtês]), and that from Proslambanomenos to Mesê (the octave [Greek: apo mesês]). As he also gives the divisions of five different 'colours' or varieties of genus, the whole number of octaves is no less than seventy.

Ptolemy does not exclude difference of pitch altogether. The whole instrument, he says, may be tuned higher or lower at pleasure[1]. Thus the pitch is treated by him as modern notation treats the _tempo_, viz. as something which is not absolutely given, but has to be supplied by the individual performer.

Although the language of Ptolemy's exposition is studiously impersonal, it may be gathered that his reduction of the number of keys from fifteen to seven was an innovation proposed by himself[2]. If this is so, the rest of the scheme,--the elimination of the element of pitch, and the 'nomenclature by position,'--must also be due to him. Here, however, we find ourselves at issue with Westphal and those who agree with him on the main question of the Modes. According to Westphal the nomenclature by position is mentioned by Aristoxenus, and is implied in at least one important passage of the Aristotelian _Problems_. We have now to examine the evidence which he adduces to support his contention.

[Footnote 1: _Harm._ ii. 7 [Greek: pros tên toiautên diaphoran hê tôn organôn holôn epitasis ê palin anesis aparkei.]]

[Footnote 2: This may be traced in the occasionally controversial tone; as _Harm._ ii. 7 [Greek: hoi men ep' elatton tou dia pasôn phthasantes, hoi d' ep' auto monon, hoi de epi to meizon toutou, prokopên tina schedon toiautên aei tôn neôterôn para tous palaioterous thêrômenôn, anoikeion tês peri to hêrmosmenon physeôs te kai apokatastaseôs; hê monê perainein anankaion esti tên tôn esomenôn akrôn tonôn diastasin]. We may compare c. 11.]

§ 30. _Nomenclature by Position._

Two passages of Aristoxenus are quoted by Westphal in support of his contention. The first (p. 6 Meib.) is one in which Aristoxenus announces his intention to treat of Systems, their number and nature: 'setting out their differences in respect of compass ([Greek: megethos]), and for each compass the differences in form and composition and position ([Greek: tas te kata schêma kai kata synthesin kai kata thesin]), so that no element of melody,--either compass or form or composition or position,--may be unexplained.' But the word [Greek: thesis], when applied to Systems, does not mean the 'position' of single notes, but of groups of notes. Elsewhere (p. 54 Meib.) he speaks of the position of tetrachords towards each other ([Greek: tas tôn tetrachordôn pros allêla theseis]), laying it down that any two tetrachords in the same System must be consonant either with each other or with some third tetrachord. The other passage quoted by Westphal (p. 69 Meib.) is also in the discussion of Systems. Aristoxenus is pointing out the necessity of recognising that some elements of melodious succession are fixed and limited, others are unlimited:

[Greek: kata men oun ta megethê tôn diastêmatôn kai tas tôn phthongôn taseis apeira pôs phainetai einai ta peri melos, kata de tas dynameis kai kata ta eidê kai kata tas theseis peperasmena te kai tetagmena.]

'In the size of the intervals and the pitch of the notes the elements of melody seem to be infinite; but in respect of the values (_i.e._ the relative places of the notes) and in respect of the forms (_i.e._ the succession of the intervals) and in respect of the positions they are limited and settled.'

Aristoxenus goes on to illustrate this by supposing that we wish to continue a scale downwards from a [Greek: pyknon] or pair of small intervals (Chromatic or Enharmonic). In this case, as the [Greek: pyknon] forms the lower part of a tetrachord, there are two possibilities. If the next lower tetrachord is disjunct, the next interval is a tone; if it is conjunct, the next interval is the large interval of the genus ([Greek: hê men gar kata tonon eis diazeuxin agei to tou systêmatos eidos, hê de kata thateron diastêma ho ti dêpot' echei megethos eis synaphên]). Thus the succession of intervals is determined by the relative position of the two tetrachords, as to which there is a choice between two definite alternatives. This then is evidently what is meant by the words [Greek: kata tas theseis][1]. On the other hand the [Greek: thesis] of Ptolemy's nomenclature is the absolute pitch (_Harm._ ii. 5 [Greek: pote men par' autên tên thesin, to oxyteron haplôs ê baryteron, onomazomen]), and this is one of the elements which according to Aristoxenus are indefinite.

[Footnote 1: So Bacch. p. 19 Meib. [Greek: theseis de tetrachordôn hois to melos horizetai eisin hepta? synaphê, diazeuxis, hypodiazeuxis, k.t.l.] (see the whole passage).]

Westphal also finds the nomenclature by position implied in the passage of the Aristotelian _Problems_ (xix. 20) which deals with the peculiar relation of the Mesê to the rest of the musical scale. The passage has already been quoted and discussed (_supra_, p. 43), and it has been pointed out that if the Mesê of the Perfect System ([Greek: mesê kata dynamin]) is the key-note, the scale must have been an octave of the _a_-species. If octaves of other species were used, as Westphal maintains, it becomes necessary to take the Mesê of this passage to be the [Greek: mesê kata thesin], or Mesê by position. That is, Westphal is obliged by his theory of the Modes to take the term Mesê in a sense of which there is no other trace before the time of Ptolemy. But--

(1) It is highly improbable that the names of the notes--Mesê, Hypatê, Nêtê and the rest--should have had two distinct meanings. Such an ambiguity would have been intolerable, and only to be compared with the similar ambiguity which Westphal's theory implies in the use of the terms Dorian, &c.

(2) If the different species of the octave were the practically important scales, as Westphal maintains, the position of the notes in these scales must have been correspondingly important. Hence the nomenclature by position must have been the more usual and familiar one. Yet, as we have shown, it is not found in Aristotle, Aristoxenus or Euclid--to say nothing of later writers.

(3) The nomenclature by position is an essential part of the scheme of Keys proposed by Ptolemy. It bears the same relation to Ptolemy's octaves as the nomenclature by 'value' bears to the old standard octave and the Perfect System. It was probably therefore devised about the time of Ptolemy, if not actually by him.

§ 31. _Scales of the Lyre and Cithara._

The earliest evidence in practical music of any octaves other than those of the standard System is to be found in the account given by Ptolemy of certain scales employed on the lyre and cithara. According to this account the scales of the lyre (the simpler and commoner instrument) were of two kinds. One was Diatonic, of the 'colour' or variety which Ptolemy recognises as the prevailing one, viz. the 'Middle Soft' or 'Tonic' ([Greek: diatonon toniaion])[1].

[Footnote 1: We may think of this as a scale in which the semitones are considerably smaller, _i.e._ in which _c_ and _f_ are nearly a quarter of a tone flat.]

The other was a 'mixture' of this Diatonic with the standard Chromatic ([Greek: chrôma suntonon]): that is to say, the octave consisted of a tetrachord of each genus. These octaves apparently might be of any _species_, according to the key chosen[1]. On the cithara,--which was a more elaborate form of lyre, confined in practice to professional musicians,--six different octave scales were employed, each of a particular species and key. They are enumerated and described by Ptolemy in two passages (_Harm._ i. 16 and ii. 16), which in some points serve to correct each other.[2]

[Footnote 1: Ptol. _Harm._ ii. 16 [Greek: periechetai de ta men en tê lyra kaloumena sterea tonou tinos hypo tôn tou toniaiou diatonou arithmôn tou autou tonou, ta de malaka hypo tôn en tô migmati tou malakou chrômatos apithmôn tou autou tonou]. Here [Greek: tonou tinos] evidently means 'of any given key,' and [Greek: tou autou tonou] 'of that key.' There is either no restriction, or none that Ptolemy thought worth mentioning, in the choice of the key and species.]

[Footnote 2: The two passages enumerate the scales in a slightly different manner. In i. 16 they are arranged in view of the genus or colour into--

Pure Middle Soft Diatonic, viz.-- [Greek: sterea], of the lyre. [Greek: tritai] } of the cithara. [Greek: hypertropa] }

Mixture of Chromatic, viz.-- [Greek: malaka], of the lyre. [Greek: tropika], of the cithara.

Mixture of Soft Diatonic, viz.-- [Greek: parypatai], of the cithara.

Mixture of [Greek: diatonon syntonon], viz.-- [Greek: lydia] } of the cithara. [Greek: iastia] }

It is added, however, that in their use of this last 'mixture' musicians are in the habit of tuning the cithara in the Pythagorean manner, with two Major tones and a [Greek: leimma] (called [Greek: diatonon ditoniaion]).

In the second passage (ii. 16) the scales of the lyre are given first, then those of the cithara with the key of each. The order is the same, except that [Greek: parypatai] comes before [Greek: tropika] (now called [Greek: tropoi]), and [Greek: lydia] is placed last. The words [Greek: ta de lydia hoi tou toniaiou diatonou] [sc. [Greek: arithmoi periechousi]] [Greek: tou dôriou] cannot be correct, not merely because they contradict the statement of the earlier passage that [Greek: lydia] denoted a mixture with [Greek: diatonon syntonon] (or in practice [Greek: diatonon ditoniaion]), but also because the scales that do not admit mixture are placed first in the list in both passages. Hence we should doubtless read [Greek: ta de lydia hoi <tou migmatos> tou <di>toniaiou diatonou tou Dôriou].]

Of the six scales two are of the Hypo-dorian or Common species (_a-a_). One of these, called [Greek: tritai], is purely Diatonic of the Middle Soft variety; the intervals expressed by fractions are as follows:

_a_ 9/8 _b_ 28/27 _c_ 8/7 _d_ 9/8 _e_ 28/27 _f_ 8/7 _g_ 9/8 _a_

The other, called [Greek: tropoi] or [Greek: tropika], is a mixture, Middle Soft Diatonic in the upper tetrachord, and Chromatic in the lower:

_a_ 9/8 _b_ 22/21 _c_ 12/11 _c_[Symbols: sharp] 7/6 _e_ 28/27 _f_ 8/7 _g_ 9/8 _a_

Two scales are of the Dorian or _e_-species, viz. [Greek: parypatai], a combination of Soft and Middle Soft Diatonic:

_e_ 21/20 _f_ 10/9 _g_ 8/7 _a_ 9/8 _b_ 28/27 _c_ 8/7 d 9/8 _e_

and [Greek: lydia], in which the upper tetrachord is of the strict or 'highly strung' Diatonic ([Greek: diatonon syntonon]--our 'natural' temperament):

_e_ 28/27 _f_ 8/7 _g_ 9/8 _a_ 9/8 _b_ 16/15 _c_ 9/8 _d_ 10/9 _e_