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Berlin Ajax fragment (42), also a tragic song in the C mode, where the compass is only a fifth (a third on each side of the tonic), and moreover the major third is divided unusually into 1 1/4 + 3/4 tones, the whole scale being a' b' c'' 0188-001.gife".102
We can neatly indicate structure and ambitus together by writing for the Oslo fragment '3C4' (i.e. the three degrees below the tonic C and the four above), and for the Berlin one '2C2'. If we had many more texts than we have, and in a more complete state, it might be instructive to sort them on this principle, to see how many distinct groups emerged. As it is, many of our fragments are too small for us to be sure that all the notes of the scale are represented, and the rest are too few for clear groupings to be established. We can see that this piece is quite unlike that one, but not how many different modalities were current. It might turn out, if we had an abundance of evidence, that there was no definite number, and that to a certain extent any song might create its own modality. There might be endless dispute over criteria for classification, and over whether four or four dozen modes were to be distinguished.
It is a separate question to what extent modal categorization continued to be significant to practising musicians. Did they retain a concept of a Dorian or Phrygian mode as something distinct from the keys or octave-species of those names? Authors who refer to the ethical effects of these modes may simply be parroting old dogmas and supposing them to apply to the keys. We certainly find the view argued that the keys differ from one another in ethos, or represent distinct harmoniai, only to the extent that they yield different octave-species.103 But did someone like Mesomedes, who composed one song in the E mode and another in the G, but notated them both in the Lydian key, consciously think of them as belonging to different modal categories?
It might depend whether he needed to change the tuning of his kithara. We know from Ptolemy (above, p. 171) that various accordaturas had agreed names. Each of them is linked to a particular key and presents a particular octave-speciessometimes the
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102 In general we must remember that diatonic scales in different texts, though identically notated, may have differed perceptibly in their schemes of attunement'soft' or 'tonic' diatonic, etc. We can, however, identify a soft diatonic tuning in certain of the Hellenistic fragments (7. 10).
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103 Ptol. Harm. 2. 8-11; Ath. 625d; cf. Aristid. Quint. p. 15. 15-19, 80. 6-81. 31. Plutarch believes harmonia to be simply a musicians' equivalent of tonos or tropos (An seni 793 a, cf. De E apud Delphos 389e).

 
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