[34] 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.
[35] Ptol. Harm. ii. 16 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 tonou tinos evidently means 'of any given key,' and 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.
[36] 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.—
sterea, of the lyre.
tritai } of the cithara.
hypertropa }
Mixture of Chromatic, viz.—
malaka, of the lyre.
tropika, of the cithara.
Mixture of Soft Diatonic, viz.—
parypatai, of the cithara.
Mixture of diatonon syntonon, viz.—
lydia } of the cithara.
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 leimma (called 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 parypatai comes before tropika (now called tropoi), and lydia is placed last. The words ta de lydia hoi tou toniaiou diatonou [sc. arithmoi periechousi tou dôriou cannot be correct, not merely because they contradict the statement of the earlier passage that lydia denoted a mixture with diatonon syntonon (or in practice 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 ta de lydia hoi [tou migmatos] tou [di]toniaiou diatonou tou Dôriou.]
[37] Harm. i. 16 plên kathoson adousi men akolouthôs tô dedeigmenô syntonô diatonikô, kathaper exestai skopein apo tês tôn oikeiôn autou logôn parabolês, harmozontai de heteron ti genos (sc. the Pythagorean), xynengizon men ekeinô, k.t.l.