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164                    HAND-BOOK OF ACOUSTICS.
The harshness of the beats between each pair of overtones in the above, must be estimated, from the conclusions we arrived at before, in the case of simple tones, for these overtones are simple tones; but in estimating the total harshness of the whole combination, it should be remembered that for ordinary qualities of tone, the intensity of the partials becomes less and less, as we go farther from the Fundamentals (a fact roughly indicated in the above by the use of smaller type for the upper partials); and therefore the intensity of the beats in the above, will become less and less as we ascend.
(2) Beats arising betiveen the Fundamental of one tone and an overtone of the other. As an example, we may take the common dissonance—
This interval, when sounded between simple tones, is quite free from harshness ; the tones are far beyond beating distance, and no differential is near enough to produce beats. When, however, it is sounded between ordinary compound tones, beats are generated by the fundamental f and the 2nd partial of S|, thus :—
The following dissonances, between compound tones, although often called by the same name, are very different indeed in their degree of dissonance.
To render this evident, it is only necessary to set forth the partiaJs of each tone, thus:—