The Alphabetic Notation Invented By William of Volpiano
One of William's innovations as a cantor and notator was an alphabetic pitch notation. Its point of reference was the Boethian diagramm, which displayed the double octave of the systema teleion in the diatonic (semitonium-tonus-tonus), the chromatic (semitonium-semitonium-trihemitonium), and the enharmonic tetrachord (diesis-diesis-ditonus). The different positions were represented by alphabetical letters, except the dieses which had special signs not unlike the tyronic letters used by Boethius:
This alphabetic pitch notation does not only offer insights into microtonal shifts used by the cantors of this local school, it also proves that the common projection of the piano keyboard on the medieval tone system is inadequate. Like many other letter systems used since the 8th century, also the system of William of Volpiano represented the positions of the Boethian diagramm, and the enharmonic signs used for the dieses represented not a change into another genus, but microtonal attractions within the diatonic melos of a certain mode.
Concerning the diesis Guido of Arezzo wrote about 1026 in his treatise Micrologus that the diesis sharpens the usual tonus between re-mi (a-b; d-e; g-h or h-i) with the proportion 9:8 by a proportion of 7:6 (a-˫; d-˧; g-Γ or h-˥). Guido's explanation, how to find this intervall at the monochord, made it already evident that the diesis, taken from the "enharmonic" division of the tetrachord, was used here as a microtonal shift in different melodic modes of the diatonic genus.
Read more about this topic: Antiphonary Of St. Benigne
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