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the shift, but we miss the lusty adiatonic d'e' of A1. The triads of £ span approximate fifths in C2 and consist of two major thirds spanning a minor sixth in Helmholtz speaks of the latter discordant com-
bination (compare Snake Songs Nos. 2 and 3) as " sehr lehrreich fur die Theorie der Musik" (Tonempfindungen, p. 352) because consisting wholly of intervals accepted as consonances in the
tempered scale, and explains the anomaly by an unconscious memory of the diminished and hence dissonant fourth that in true intonation combines with a major third to make a minor sixth. The disagreeable effect of the combination may also be explained diatonically, according to the diagram, as the union of parts of two triads of the minor mode, C-E-GA, demanding resolution into one or other; either C becoming B and giving the dominant triad, or GA becoming A and giving the tonic. In so far as this latter motive enters, the freedom with which the combination is executed in the present songs argues against a diatonic sense in the singers.
It is a constant temptation to neglect the anomalies of this music. Yet they contain its secret, as zero and infinity values that of a function.