Westphal (_Harmonik und Melopöie_, 1863, p. 255) supposes a much deeper corruption. He would restore [Greek: ta de lydia [kai iastia hoi tou migmatos tou syntonou diatonou tou ... ta de ...] hoi tou toniaiou diatonou tou Dôriou]. This introduces a serious discrepancy between the two passages, as the number of scales in the second list is raised to eight (Westphal making [Greek: iastia] and [Greek: iastiaioliaia] distinct scales, and furthermore inserting a new scale, of unknown name). Moreover the (unknown) scale of unmixed [Greek: diatonon toniaion] is out of its place at the end of the list. Westphal's objection to [Greek: lydia] as the name of a scale of the _Dorian_ species of course only holds good on his theory of the Modes. The only other differences between the two passages are: (1) In the scales of the lyre called [Greek: malaka] the admixture, according to i. 16, is one of [Greek: chrômatikon syntonon], according to ii. 16 of [Greek: chr. malakon]. But, as Westphal shows, Soft Chromatic is not admitted by Ptolemy as in practical use. It would seem that in the second passage the copyist was led astray by the word [Greek: malaka] just before. (2) The [Greek: iastia] of i. 16 is called [Greek: iastiaioliaia] in ii. 16. We need not suppose the text to be faulty, since the two forms may have been both in use. Another point overlooked in Westphal's treatment is that [Greek: diatonon syntonon] and [Greek: d. ditoniaion] are not really distinguished by Ptolemy. In one passage (i. 16) he gives his [Greek: lydia] and [Greek: iastia] as a mixture with [Greek: d. syntonon], adding that in practice it was [Greek: d. ditoniaion]. In the other (ii. 16) he speaks at once of [Greek: d. ditoniaion]. This consideration brings the two places into such close agreement that any hypothesis involving discrepancy is most improbable. In practice it appears that musicians tuned the tetrachord _b-e_ of this scale with the Pythagorean two Major tones and [Greek: leimma]. Of the remaining scales one, called [Greek: hypertropa], is Phrygian in species (_d-d_), and of the standard genus: _d_ 9/8 _e_ 28/27 _f_ 8/7 _g_ 9/8 _a_ 9/8 _b_ 28/27 _c_ 8/7 _d_ One, called [Greek: iastia], or [Greek: iastiaioliaia], is of the Hypo-phrygian or _g_-species, the tetrachord _b-e_ being 'highly strung' Diatonic or (in practice) Pythagorean, viz.: _g_ 9/8 _a_ 9/8 _b_ 256/243 _c_ 9/8 _d_ 9/8 _e_ 28/27 _f_ 8/7 _g_