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Page 187
tonic on the third degree (E mode), the Nemesis hymn has it on the fifth (G mode).
Actually the lowest note in the Nemesis hymn is the least used, and it might be maintained that it is the other eight notes that should be taken as defining the octave species, which will then be D. There will always be this kind of ambiguity with pieces which have an ambitus of more or less than an octave, and this further diminishes the usefulness of the species-names as a basis for classification.
A tonic, on the other hand, is regularly identifiable. This is not to say that the music always stays in thrall to one and the same tonal focus. The notes a fourth below the tonic and a fourth or a fifth above itif the ambitus of the pieces reaches so farfunction as secondary foci (analogous to the 'dominant' in the Western tonal system), and they take over whenever the melody is in their region, like planets capturing a roving satellite in their gravitational fields. There are also cases of true modulation within a piece, where either the focus shifts to a different note (normally a tone higher or lower) or it remains on the same note but the interval-pattern made by other notes changes. This will be discussed further in the next chapter.
The Hellenistic material (insofar as it is diatonic) is predominantly in the E or A mode. Sometimes there was a secondary focus a fourth below the tonic, and this might become the melody's final resting-place. Limenius' Paean (13) is well enough preserved for us to see that overall it was in the A mode; after a shift of focus from a to b, and several alternations between b and the e below, there was a return to a, but at the end the melody subsided to the e.
The later texts are nearly all in the E, G, or C modes. Two pieces descend a fourth from the tonic to reach their finals, like the Limenius;101 others end on the tonic. We find modulation between E and C modes, and between C and G. One piece, the Berlin Paean (40), may be assigned to the D mode, though it has a secondary focus a fifth higher (A mode) which bears much of the work.
Within these groupings we might attempt further distinctions according to ambitus. The interval-structure of the tonal nucleus by itself may not be enough to define a mode. For example, in the parts of 30 POsl. 1413. 1-15 which are in the C mode the melody ranges freely over an octave, from the fourth below the tonic to the fifth above it. This hardly seems to belong in the same category as the
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101 The Seikilos epitaph; 30 POsl. 1413. 15; cf. 51 POxy. 1786.

 
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