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The first two of these, we recall (p. 166), Ptolemy describes as being not widely current. The last, the 'even' diatonic, is his own invention. He has tried it out, and reports that the effect is 'rather foreign and rustic, but exceptionally gentle'. The rest must be taken as mathematical idealizations of tunings actually to be heard. |
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In two cases Ptolemy observes that citharodes do not tune exactly as they should. In the tense diatonic, while they sing with the correct intonation, they tune their instruments with two full tones as the upper intervals of the tetrachord (90 + 204 + 204 cents); and similarly in the enharmonic they use a full ditone (408 cents) as the major interval. These 204-cent tones were easily obtained by tuning down a fifth and up a fourth, and this was no doubt the citharodes' procedure. But Ptolemy allows that the discrepancies are too small to be noticeable.38 He proceeds to admit the 'ditonic' as another variety of diatonic. |
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Aristoxenus lays down rules about concord between corresponding notes in neighbouring tetrachords which appear to exclude the combination in one scale of tetrachords tuned with different series of intervals.39 Ptolemy, on the other hand, treats the tonic diatonic as the only form of tuning, of those in common use, that is employed in successive tetrachords; the rest are coupled with tonic diatonic tetra-chords, with the tenser form of tetrachord above the disjunctive tone and the less tense below, or vice versa in the case of conjunct tetra-chords. He provides details of six specific kithara attunements embodying these arrangements, with their technical names, and two generic lyra ones.40 Rendered in modern notation on the octave e-e', which is probably about a tone too high, the kithara tunings appear as follows: |
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Parhypatai (soft + tonic diat.) |
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Tropoi (tonic diat. + tense chr.) |
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Iastiaiolia (ditonic + tonic diat.) |
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Lydia (tonic + ditonic diat.) |
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38Harm. 1. 16 p. 39. 14-40.8, cf. 2. 1 p. 44.1-5; Barker, GMW ii. 312f., 317f. The 90: 204: 204 division had long been established (Philolaus, Plato. Euclid). |
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39Harm. 1.29, 2.54. At 1.7, however, he recognizes some kind of mixture of genera, and at 2.44 (cf. Cleon. Harm. p. 189. 11-18) their combination (by modulation) in the course of a melody. |
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40Harm. 2. 15-16, cf. 1. 16, 2. 1; Barker, GMW ii. 312f., 350f., 356-61. The names are somewhat obscure: see Barker's discussion. p. 360. |
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