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note, fg, to g: this alteration being external compression (c'd'-fg to c'd'-g) in the case of the upper fifth and internal repair in the case of the lower (b-g-fg-e to b-g-f); both tracts nevertheless existing as fifths (d'-g; e'-f) by the penumbral extension from which the change arose. There remains only to resolve this novel kind of discord — this untenable figure not within a framework but of a framework — by proceeding to the suggested fifths, d'-g, c'-f. This the singer does in the B's and C with a vigor and iteration that recall the long felicitations of the close of " Fidelio." The upper fifth, d'-g, is exhibited in all its possibilities of charm, divided all ways by thirds and fourths, the initial descent of B1 already anticipating most. The lower, c-f, is gradually dismounted interval by interval, the octave echo of its upper limit becoming the close of C1 and of the song, within a fourteenth tone of the pitch at which it was first announced in A1 and at the identical pitch with which it closed A2.
Surprising and even hardly credible as this intricacy sounds, the interpretation does not depend on the evidence of this song alone. It is a link in a chain of evidence of an instinctive preference for elasticity of form to which nearly every song of the series contributes. Separately the inferences to the use of this device as an artistic motive seem doubtful; collectively they seem to present under the aspect of a deliberate plan which really was the spontaneous choice of the singer.
The diagram on the following page shows the relation between two chief means of effect in European music, discord and modulation, and the mutation of figure illustrated again in Sumyacoli. The continuum of tone is represented as a circle, in which the octaves of any given pitch alternately occupy opposite ends of a certain diameter, movement against the hands of a clock being upward. As in the previous diagrams of the modes, the diatonic scale is represented by three brackets in contact signifying any combination of seven pitches spanning three fifths, chosen from the alternate octaves represented by the points on which the ends and medial points of the brackets fall, and standing for the tonic, dominant, and subdominant chords in the order in which the European musical consciousness finds them balanced.