(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' (diatonon toniaion) [34]. The other was a 'mixture' of this Diatonic with the standard Chromatic (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 [35]. 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 [36]. Of the six scales two are of the Hypo-dorian or Common species (a-a). One of these, called 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 tropoi or 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♯ | 7/6 | e | 28/27 | f | 8/7 | g | 9/8 | a |