HANDBOOK OF ACOUSTICS - online book

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182                      HAND-BOOK OF ACOUSTICS.
in the former case 5 beats and in the latter 6 beats per second will be produced.
As the intonation of the Thirds is guarded by such high, and therefore weak partials, a slight error in their tuning is much less evident, than in the case of the Fifth. Thus Thirds tuned in equal temperament are, as we shall see later on, mistuned to an extent, which if adopted with the Fifth, would render this latter interval unbearable.
Major and Minor Sixths. By pursuing the method adopted above, the student will find that the former of these two intervals between Compound Tones, is defined by the coincidence of the 3rd and 5th, and the latter by the coincidence of 5th and 8th partials. Inasmuch as the 8th partial is generally exceedingly weak, the Minor Sixth can scarcely be said to be defined at all.
In all the above intervals, we have only considered the lowest pair of coincident partials, as these are by far the most important; but it must not be forgotten, especially in the case of the Octave, and Fifth, that there are coincident pairs above those given. If the interval be not quite true, not only will beats be produced by this lowest pair, but by the higher also, and at a more rapid rate. Thus, let di = 101 and d = 200 : then,