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That identity of partial tones is not a sufficient explanation of consonance as Helmholtz thought it to be is proved by the fact that simple tones, which have no partials, may still be consonant.
If vibration arises from imperfectly elastic wood, we hear a dull wooden thud; if it comes from metal, partials of the strings are re-enforced that should be left undeveloped, which give a false ring to the tone, and an after ring that blurs legato playing, and nullifies the staccato.
I do not pose as the obstinate advocate of parallel stringing, although I believe that, so far, it is the most logical and the best; the best, because the left hand division of the instrument is free from a preponderance of dissonant high partials, and we hear the light and shade, as well as the cantabile of that part, better than by any overstrung scale that I have yet met with.
Each lower note struck of the undamped instrument, by excitement from the sound-board carried through the bridge, sets vibrating higher strings, which, by measurement, are primes to its partials; and each higher string struck calls out equivalent partials in the lower strings. Even partials above the primes will excite their equivalents up to the twelfth and double octave.
I say these things impressively and take the opportunity to tell him some interesting scientific facts about fundamental and upper partials, and how different combinations produce different vowels, also how these combinations are affected by different forms of the vocal cavities, leading up to the great scientific truth that he must hold the tongue down and the throat open in order that these great laws of acoustics may become operative.
The pleasure in the single tone is similar, in its causes, to the pleasure in the consonance of two tones. As we should expect from this analogy, the pleasure is greater in rich tones, which contain many partials, than in thin tones, which are relatively uninteresting. But the feeling of tones is something more than mere pleasantness; it is also a mood.
Has any one the hardihood to assert that such knowledge prepares one for the responsible work of training voices? One may know all of this and still be as ignorant of voice training as a Hottentot is of Calvinism. Further, who shall decide which particular combination of fundamental and upper partials constitutes the perfect singing tone?
If the hammer is hard, and impelled with force, the string breaks into shorter sections, and the discordant upper partials of the string, thus brought into prominence, make the tone harsh. If the hammer is soft, and the force employed is moderated, the harmonious partials of the longer sections strike the ear, and the tone is full and round.
There is no record of a great voice teacher having been trained in a physics laboratory. It is possible to analyze a tone and learn how fundamental and upper partials are combined and how these combinations affect quality. Does this constitute scientific voice production? This knowledge may all be gained from the various hand books on acoustics.
For the chords have in part merely the significance of highly enriched tones, the harmonized tones of the chords taking the place of the partials of the single notes and imparting a more voluminous color, which may have its own beauty as such; and, in addition, they simply confer upon the melody another dimension, as it were, the tonal relations of harmony and contrast operating between the tones of the chords simultaneously, as well as temporally between the successive elements of the melody.
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