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and the tone-interval that it makes with the e are not matched at the top end. This d, which also appears in the Phrygian scale, can be characterized as an 'infrafix' attached to the tetrachord e-a, providing the concord of a fifth with a and also a note useful for circling about the e at the bottom of the tetrachord. The arrangement is replicated a fifth higher, in the Dorian, by the disjunctive tone a-b and the upper tetrachord b-e'. In the Phrygian, on the other hand, the top note is d', making a fourth with the presumptive 'tonic' a and giving the upper part of the scale a more diatonic character.49 |
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The Mixolydian scale presents a diatonic aspect in its lower section, with the g intruding into the enharmonic tetrachord e  f a; but it has an exceptionally wide gap at the top, between  and e'. Probably it represents a combination of two mini-scales between which the melody alternated: the usual tetrachord e  f a,and an open fifth erected on the a with infixes of the enharmonic type and an infrafix a tone below: |
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The name 'Mixolydian' ought to denote something that is a cross between Lydian and some other type, but it is hard to see what the Mixolydian and Lydian of this Damonian set have in common. The Lydian contains one regular tetrachord, b-e'; we can also find in it two overlapping fifths, f-c' and a-e', or from another viewpoint a chain of thirds, f-a-c'-e', but whether they were used as such in melody we cannot tell.50 The two extreme degrees,  (or  ) and  , look like ornamental affixes serving as leading notes to their immediate neighbours. |
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Taken together, these six Damonian scales and the Spondeion scale reflect a corresponding number of melodic types with an ambitus |
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49 This may have something to do with a remark by Aristoxenus (fr. 84) that 'the enharmonic genus is very well suited to the Dorian tuning, and the diatonic to the Phrygian'. Elsewhere (ap. ps.-Plut. De mus. 1137d) he referred to Olympus and his followers using a scale containing the notes a b c' d' in some of their Phrygian melodies. Cf. Winnington-Ingram, Mode, 27. The nine-note Dorian scale reappears in a chromatic form (d e f  a b c'  ' e') in Pliny, HN 2.84 from a Hellenistic Pythagorean source. See W. Burkert, Philol. 105 (1961 ). 28-43. |
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50 Possibly the connection between this Lydian and the Tense Lydian is that both emphasized a note making a fifth with the note at the top of the pyknon, below it in the Lydian (f (-b  ) c', above it in the Tense Lydian ((e  )f-c'. |
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