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B8 ANALYSIS BY RESONANCE. [IV. § 45.
cessively heard. The reader should apply the method of proof here adopted to notes in various regions of the key-board. He will find considerable differences, even between consecutive notes, in the number and relative intensities of the separate tones into which he is thus able to resolve them. The higher the pitch of the fundamental tone, the fewer will the recognisable associated tones become, until, in the region above
the notes are themselves approximately
single tones. The causes of these differences will be explained in detail in a subsequent chapter; it is sufficient here to indicate their existence. The result arrived at, thus far, is that the sounds of the pianoforte are in general composite, the number of constituent tones into which they are resolvable being largest in the lower half of the instrument, and diminishing in its upper half, until at last no analysis is called for.
45. The above resolution has been effected by means of the principle of resonance. It can, however, be performed by the ear directly, though only to a small extent and with less ease. In applying the direct analysis to the sounds of a musical instrument, it is best first to produce gently the note corresponding in pitch to the tone which it is wished to isolate, and then to develope the compound sound containing