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Page 259
divergence between disjunct tetrachords (on the left) and conjunct (on the right). For the upper movable note in each tetrachord two numbers are given, divided by an oblique stroke: the higher one applies to the diatonic genus, the lower one to chromatic or en-harmonic.
This elaborate system is employed with great consistency in the Hellenistic and post-Hellenistic documents. The transcriber of a melody matched its scale with a segment of the Unmodulated System, chose the key in which the said segment appeared at the desired pitch,9 and then used the note-symbols proper to that key until forced, by modulation or chromaticism on the composer's part, to use others. Whenever a new fragment of Greek music is published, therefore, the editor analyses the selection of notes that appear in it with a view to identifying the key. Any note that does not fit the apparent key will merit special comment.
There are a few notes near the top and bottom ends of the repertorynumbers 1-3, 5, 65, 66, 68that have no home in any key. However, 65 is employed in the exotic modal scale of 42 PBerol. 6870, 16-19, and there is no reason why the others should not have been used occasionally, even if they owe their existence primarily to the logic of the notational system itself.
Origins of the pitch notation
Opinions as to the age of this system have varied widely, between the eighth and the third centuries BC. What is fairly clear, and agreed by most investigators, is that it did not come into being all at once but was built up in successive stages. It is also commonly acknowledged that the two parallel series of vocal and instrumental symbols were not invented simultaneously. The instrumental system, or rather its basic core, is generally, and I believe rightly, regarded as the older.
The vocal symbols are perspicuous. The twenty-four letters of the standard Ionic alphabet are assigned to the eight triads of the central octave (f'-f with first and second sharps, notes 48-25), corresponding to the average register of the male voice.10 The series is extended
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9In practice some keys are favoured more than others. Lydian/Hypolydian accounts for over half of the extant fragments, and Ionian/Hyperionian for over half the rest, whereas we have no certain example of the Dorian set. Of those notated in Phrygian, none seems to be a post-Hellenistic composition.
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10 The reader is reminded that 'f'-f' is merely a conventional description of this octave reflecting its interval structure, not its actual pitch, which would have been more like d'-d.

 
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