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VIII. § 84.] MAJOR THIRD AND MAJOR SIXTH. 173
note too sharp, we have the interval CF#, which is treated in the last figure but one. Slight flattening of the F will set the pair 4—3 beating slowly ; the disappearance of their beats thus secures the accurate tuning of the interval. On the other hand, lowering F weakens the beats of 3—2 by widening the dis­tance between those tones, and therefore tends to lessen the whole amount of roughness. These con­siderations go far to explain the fact that a long dispute runs through the history of Music, as to whether the Fourth ought to be treated as a concord or as a discord. The decision ultimately arrived at in favour of the first of these alternatives was per­haps, as Helmholtz suggests, due more to the fact that the Fourth is the inversion1 of the Fifth than to the inherent smoothness of the former interval.
84. Next come the intervals of the Major Third and Major Sixth, which shall be taken together, as they are very nearly equally consonant.
The dissonance due to the pair 3—2, separated by a Tone in the Sixth, is perhaps about equal" to
1 See § 97 post.
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