(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.