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172                       FIFTH AND FOURTH.           [VIII. § 83.
Octave. The tuning must be perfectly accurate, the Fifth being closely bounded by harsh discords. The result of an error of a semi-Tone is as follows :—
For every single vibration per second by which the higher clang is out, there will be two beats per second from the pair 3—2, with others of greater rapidity, but less intensity, from the higher pairs.
83. For the Fourth we have
The amount of dissonance is greater than in the case of the Fifth, since 3 and 2 are usually both powerful tones, and therefore produce louder beats than those of 4—3 and 5—3. There are, in addi­tion, the beating pairs 5—4, 6—4 and 6—5. More­over the first pair of coincident partial-tones, 4—3, are in general weaker than the beating pair below them, 3—2. The Fourth is bounded only on one side by a harsh discord. If its upper clang is half a
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E-Book - An Annotated Compendium of Old Time American Songs by James Alverson III