Share page  Visit Us On FB 
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 semiTone 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 partialtones, 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 
