HANDBOOK OF ACOUSTICS - online book

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210                    HAND-BOOK OF ACOUSTICS.
analysis of the results, arranged in the same way as in the case of the Major Triads.
In comparing La and L6, we may first eliminate the semitone dissonances of a 3rd against a 4th, and 4th against 5th partials, which are common to both; the slight semitone dissonance of a 5th against a 6th still remaining in the case of the latter. Further the two tone dissonances of 2nd against 3rd partials in L6 will be more prominent than the two between 3rd and 4th partials in La. For these reasons La seems slightly more harmonious than ~Lib, and has accordingly been placed first in the Table. It is only right to state, however, that Helmholtz places Tub before La.
About Lc there can be no doubt: it has no fewer than five semitone dissonances, including the prominent one of a 2nd against a 3rd partial; it is decidedly the least harmonious of the six Triads.
It must be recollected that the above results refer only to the lbolated triads; in order to test these conclusions, each chord must be struck separately, unconnected with any others, and judged entirely by its own inherent harmoniousness. Furthermore, they must not be taken too low in the scale, or beats between the fundamentals may occur; and lastly, it must be borne in mind, that the intervals are supposed in the above, to be in just intonation.
On comparing Da with La in the above tables, it will be found that they appear very nearly on an equality with regard to their harmoniousness. The same result is obtained on comparing their constituent intervals; each consisting of a Major and a Minor