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VIII. §§ 86, 87.] DISSONANT INTERVALS.                 175
pianoforte, and other instruments of fixed sounds, the same notes (CAb) which represent the Minor Sixth have also to do duty as one of the harshest discords, the Sharp Fifth, (CG#). The extremely defective consonance of the Minor Sixth could hardly be more conclusively shown than by the fact just mentioned. 86. As regards the dissonant intervals of the scale, we have, in addition to those incidentally examined above, the semi-Tone, Tone and Minor Seventh. The first two need not be examined, since obviously each pair of corresponding overtones are brought within the same beating intervals as the two fundamentals. The dissonance resulting is, of course, harsher for the half than for the whole Tone. The Minor Seventh is constituted thus :
It is the mildest of the discords, in fact in mere smoothness it decidedly surpasses the Minor Sixth.
87. In order that the reader may see at a glance the whole result of this somewhat laborious discussion, we subjoin a graphical representation of the amount of dissonance contained in the several intervals of the scale. The figure is taken, with some slight altera-
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