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IV. § 47.] THEORY OF QUALITY. 91
are used as nearly synonymous. It will be convenient to restrict the meaning of the latter so that it shall denote a sound which does not admit of resolution into simpler elements. A single sound of deter-. minate pitch will accordingly, in what follows, be called a tone, or simple tone. For a compound sound the word clang will be a serviceable term. The series of elementary sounds into which a clang can be resolved we shall call its partial-tones, sometimes distinguishing among these, the lowest, or fundamental tone, from the others, or overtones of the clang. This nomenclature is a direct adaptation of the German terms employed by Helmholtz. Its introduction is due to Professor Tyndall.
47. This long discussion has paved the way for the complete explanation of musical quality which is contained in the following proposition. The quality of a clang depends on the number, orders and relative intensities of the partial-tones into which it can be resolved. We have here three different causes to which variations in the quality of composite sounds are assigned.
1. A clang may contain only two or three, or it may contain half-a-dozen, or even as many as fifteen or twenty, well developed partial-tones.
2. The number of partial-tones present remaining the same, the quality of the resulting sound will