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 iota, and two forms of lambda, lambda1 and lambda2, the latter of which is peculiar to the alphabet of Argos. Of the other characters alpha1, which stands for alpha, is best derived from the archaic form archaic_alpha. For beta we find archaic_beta, which may come from an archaic form of the letter[26]. The character delta1, as Westphal shows, is for delta2, or delta with part of one side left out. Similarly the ancient circle_dot, when the circle was incomplete, yielded the character C . The crooked iota (iota) appears as iota2. The two forms of lambda serve for different notes, thus bringing the number of symbols up to fifteen. Besides these there are two characters, reclining_pand epsilon01, which cannot be derived in the same way from any alphabet. As they stand for the lowest notes of the scale, they are probably an addition, later than the rest of the system. At the upper end, again, the scale is extended by the simple device of using the same characters for notes an octave higher, distinguishing them in this use by an accent. The original fifteen characters, with the letters from which they are derived, and the corresponding notes in the modern musical scale, are as follows:

15-characters

These notes, it will be seen, compose two octaves of the Diatonic scale, identical with the two octaves of the Greater Perfect System. They may be regarded as answering to the white notes of the modern keyboard,—those which form the complete scale in the so-called 'natural' key.

The other notes, viz. those which are required not only in different keys of the Diatonic scale, but also in all Enharmonic and Chromatic scales, are represented by the same characters modified in some simple way. Usually a character is turned half round backwards to raise it by one small interval (as from HypatÊ to ParhypatÊ), and reversed to raise it by both (HypatÊ to Lichanos). Thus the letter epsilon, epsilon02, stands for our c: and accordingly epsilon04 (epsilon02 anestrammenon or hyption) stands for c*, and epsilon03 (epsilon02 apestrammenon) for c?. The Enharmonic scale c-c*-c?-f is therefore written enharmonicscale, the two modifications of the letter epsilon02 representing the two 'moveable' notes of the tetrachord. Similarly we have the triads triad01, triad02, triad03, triad04, triad05, triad06, triad07. As some letters do not admit of this kind of differentiation, other methods are employed. Thus ? is made to yield the forms delta1 (for delta2) delta3 ?: from H (or B) are obtained the forms capalpha1 and capalpha2: and from Z (or I]) the forms lambda3 and lambda4. The modifications of N are / and \: those of alpha1 are alpha2 and alpha3.

The method of writing a Chromatic tetrachord is the same, except that the higher of the two moveable notes is marked by a bar or accent. Thus the tetrachord c c? d f is written enharmonicscale.

In the Diatonic genus we should have expected that the original characters would have been used for the tetrachords b c d e and e f g a; and that in other tetrachords the second note, being a semitone above the first, would have been represented by a reversed letter (gramma apestrammenon). In fact, however, the Diatonic ParhypatÊ and TritÊ are written with the same character as the Enharmonic. That is to say, the tetrachord b c d e is not written tetrachord01, but tetrachord02: and d e? f g is not tetrachord03, but tetrachord04.

Let us now consider how this scheme of symbols is related to the Systems already described and the Keys in which those Systems may be set (tonoi eph' hÔn tithemena ta systÊmata melÔdeitai).

The fifteen characters, it has been noticed, form two diatonic octaves. It will appear on a little further examination that the scheme must have been constructed with a view to these two octaves. The successive notes are not expressed by the letters of the alphabet in their usual order (as is done in the case of the vocal notes). The highest note is represented by the first letter, A: and then the remaining fourteen notes are taken in pairs, each with its octave: and each of the pairs of notes is represented by two successive letters—the two forms of lambda counting as one such pair of letters. Thus:

The Greek notes

On this plan the alphabetical order of the letters serves as a series of links connecting the highest and lowest notes of every one of the seven octaves that can be taken on the scale. It is evident that the scheme cannot have grown up by degrees, but is the work of an inventor who contrived it for the practical requirements of the music of his time.

Two questions now arise, which it is impossible to separate. What is the scale or System for which the notation was originally devised? And how and when was the notation adapted to exhibit the several keys in which any such System might be set?

The enquiry must start from the remarkable fact that the two octaves represented by the fifteen original letters are in the Hypo-lydian key—the key which down to the time of Aristoxenus was called the Hypo-dorian. Are we to suppose that the scheme was devised in the first instance for that key only? This assumption forms the basis of the ingenious and elaborate theory by which M. Gevaert explains the development of the notation (Musique de l'AntiquitÉ, t. I. pp. 244 ff.). It is open to the obvious objection that the Hypo-lydian (or Hypo-dorian) cannot have been the oldest key. M. Gevaert meets this difficulty by supposing that the original scale was in the Dorian key, and that subsequently, from some cause the nature of which we cannot guess, a change of pitch took place by which the Dorian scale became a semitone higher. It is perhaps simpler to conjecture that the original Dorian became split up, so to speak, into two keys by difference of local usage, and that the lower of the two came to be called Hypo-dorian, but kept the original notation. A more serious difficulty is raised by the high antiquity which M. Gevaert assigns to the Perfect System. He supposes that the inventor of the notation made use of an instrument (the magadis) which 'magadised' or repeated the notes an octave higher. But this would give us a repetition of the primitive octave e-e, rather than an enlargement by the addition of tetrachords at both ends.

M. Gevaert regards the adaptation of the scheme to the other keys as the result of a gradual process of extension. Here we may distinguish between the recourse to the modified characters—which served essentially the same purpose as the 'sharps' and 'flats' in the signature of a modern key—and the additional notes obtained either by means of new characters (reclining_p and epsilon01), or by the use of accents (GammaPrime, &c.). The Hypo-dorian and Hypo-phrygian, which employ the new characters reclining_p and epsilon01, are known to be comparatively recent. The Phrygian and Lydian, it is true, employ the accented notes; but they do so only in the highest tetrachord (HyperbolaiÔn), which may not have been originally used in these high keys. The modified characters doubtless belong to an earlier period. They are needed for the three oldest keys—Dorian, Phrygian, Lydian—and also for the Enharmonic and Chromatic genera. If they are not part of the original scheme, the musician who devised them may fairly be counted as the second inventor of the instrumental notation.

In setting out the scales of the several keys it will be unnecessary to give more than the standing notes (phthongoi hestÔtes), which are nearly all represented by original or unmodified letters—the moveable notes being represented by the modified forms described above. The following list includes the standing notes, viz. Proslambanomenos, HypatÊ HypatÔn, HypatÊ MesÔn, MesÊ, ParamesÊ, NÊtÊ DiezeugmenÔn and NÊtÊ HyperbolaiÔn in the seven oldest keys: the two lowest are marked as doubtful:—

Greek symbols

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 digamma for digamma, iota for iota, and lambda4 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 (iota), 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 iota in the fifth century was confined to localities of which we have no complete epigraphic record, or (2) that iota 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 iota.

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 lambda for lambda, which is distinctive of the alphabet of Argos, along with the commoner form lambda. Westphal indeed asserts that both these forms are found in the Argive alphabet. But the inscription (C. I. 1) which he quotes [27] for lambda really contains only lambda 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 iota 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.

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, [28] and doubtless Argos was one of the first cities to share in the advance which Pronomus made in the technique of his art.