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By Makhmudov O. I.

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Pont added to data from Parsons' working tapes corresponding information for five monophonic repertorieschants from ancient Greece, chants from the Liber Usualis, Gaelic melodies, Peyote Indian songs, and Aboriginal songs. The three kinds of directional motion tracked produce nine logical combinations. The results of their comparison were reported by the percentage of occurrence of each of the nine intervallic-direction patterns. The results are simplified in the rank-order lists given in Figure 6.

The two problems solved were interval invariance and discrete accommodation of enharmonic pitches through all double sharps and flats. ), but 40 is the lowest common denominator for tonal music through the nineteenth century. Interval invariance guarantees that there is always consistency between an interval and its numerical mapping. All of the systems mentioned have some degree of invertibility, but none guarantees complementarity for all conceivable interval combinations. All systems accommodate perfect-interval combinations, provided that the tones involved regularly occur in the scale and are not altered.

Repeated notes are ignored in Lincoln's meta-data (1988; 1993), which is sorted by intervallic size and direction based on the first nine discrete pitches. Durations, although undoubtedly included in the original DARMS code and although obviously necessary for printing, were excluded from the indexes in his two important finding aids (each based on several tens of thousands of incipits). When the intervallic index of the madrigal volumes was used to seek matches to unattributed works, the absence of repeated notes proved to have an insidious effect (SelfridgeField, 1990).

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