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terminate together, the ear has always been accustomed to consider it as a whole. Musical people especially, having been in the habit of directing all their attention to a tone as a whole, are often incapable of recognising the constituent parts, until their attention is directly called to them ; just as a person, after having had a clock ticking in his room for some time,             to notice the ticking unless some-
thing attracts his attention especially to it. Again, when one is thinking deeply, a remark made by another person is often not perceived : the nerves of hearing are doubtless excited, but the attention not being aroused, the sound is not perceived. "When anyone has once become accustomed to listen for overtones, there is no difficulty whatever in hearing them ; in fact, they sometimes force themselves upon the ear of the practised listener when not wanted.
Most of the foregoing facts concerning partials have been known for centuries, but the phenomenon was regarded as little more than a curiosity, until Helmholtz proved that the quality of a musical tone depended upon the occurrence of partials. Before going into this matter, it will be necessary to show more exactly what is meant here by quabty.
Many musical tones are accompanied by more or less noise; thus, the tone of an organ-pipe is adulterated, as it were, more or less, by the noise of the wind striking the sharp edge of its embouchere; the tone from a violin is mingled, more or less, according to the skill of the player, with the scraping noise of the bow against the strings ; the tone from the human voice is accompanied, more or less, with the noise of the breath escaping. Again, the sounds of some instruments differ from those of others, in that their intensities vary in different but regular ways. Thus in the piano and harp, the tones, after the wires are struck, immediately decrease regularly in intensity, till they die away; while on the organ they continue with unvarying intensity, as long as they sound at all. All such peculiarities as the above are not included under the term quatity, as we use it here. The following may be taken as a formal definition of the term quality, as employed below. If two tones perfectly free from noises, of precisely the same pitch, and of equal intensities, differ in any way from one another, then all those respects in which they differ are comprised under the term quality. Using the term quaHty in this sense, Helmholtz has shown that: The Quality of a compound tone depends upon the number, order, and relative intensities of its constituent partials.