HANDBOOK OF ACOUSTICS - online book

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208                    HAND-BOOK OF ACOUSTICS.
corresponding partials which beat at a semitone distance; and the remaining lines, those that beat at a tone distance. It has not been thought necessary to discriminate between the 16:15 and the 25 : 24 beats, nor between the 9 : 8 and 10 : 9.
Comparing, in the first place, Dc with Da : after eliminating the semitone dissonance between the 3rd and 4th partial, which is common to both, there remains in the latter, a semitone dissonance between a 4th and 5th partial, which is absent in the former. On the other hand, among the tone dissonances, Dc has two, between the 2nd and 3rd partials, as against the two between 3rd and 4th partials in Da: the former being of course the more prominent. The two dissonances of 4th against 6th partials are so slight, that they may be disregarded. It is difficult, on the whole, to decide between these two Triads; there is probably not much difference between them. Helmholtz gives the preference to Dc, which we have therefore put first in the table.
If there be any doubt concerning the relative harmoniousness of Dc and Da, there can be none with respect to Db. Comparing it with Da: after discarding the semitone dissonance of a 4th against a 5th partial, which is common to both, there remains in Db the two semitone dissonances of a 2nd against a 3rd and a 3rd against a 5th partial, while in Da there is only that of a 3rd against a 4th. Again, among the tone dissonances, after throwing out that of a 3rd against a 4th partial from both, there remains in Db the dissonance of a 2nd against a 3rd, while in Da there is the less prominent dissonance of a 3rd against a 4th. Thus Db is decidedly the least harmonious of the Major Triads.
Coming now to the Minor Triads : fig. 86 shows them drawn out on the same plan as in fig. 85, and the following table contains an