HANDBOOK OF ACOUSTICS - online book

A complete view of Acoustical Science & its bearings on music, for musicians & music students.

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184
HAND-BOOK OF ACOUSTICS.
the number of beats per second will be 602 600 = 2, which is the smaller of the two numbers, in the ratio, 3 : 2.
When the two Compound Tones forming an interval do not possess all the first six partial Tones, the above results require to be modified.
Thus for example, in wide open organ pipes, the tones of which consist of only the first two partials, the Octave is the only Interval which is defined by the coincidence of partials ; the other Intervals being guarded merely by Differentials.
Again, in stopped organ pipes the tones of which only consist of the 1st and 3rd partials, the Twelfth is the only interval defined by the coincidence of the partials; the other intervals, even the Octave, being guarded by Differentials only.
In such cases as these, however, the definition is better than it would be if the tones were simple, more Differentials and those of a higher order being produced. For example, take the mistimed Major Third d = 400 and n = 501, and suppose each of these tones to consist of the first three partials only. Then the 1st horizontal line of the following table shows the partials of the one tone, and the 1st vertical line those of the other, the differentials of the 1st order being at the intersections.