HANDBOOK OF ACOUSTICS - online book

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ON DISSONANCE.
167
If we limit ourselves to intervals not greater than an octave, we shall find, that the only interval entirely free from these partial beats, is the Octave itself, thus :
In all intervals smaller than the Octave, it will be found that two or more of the first six partials beat with one another. To take a couple of examples: In the Perfect Fifth a 3rd partial beats against 4th and 5th partials; and in the Diminished Fifth 2nd, 3rd and 4th partials come within beating distance of 3rd, 4th, 5th and 6th.; thus: