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110 PITCH OF STRING SOUND [V. § 55.
to strengthen the fundamental-tone. The material of the string itself produces its effect chiefly by limiting the number of partial-tones. Its stiffness resists division into very short segments, and this implies, for every string, a fixed limit beyond which further subdivision ceases and where, therefore, the series of overtones is cut off. Hence very thin mobile strings are favourable, thick weighty strings unfavourable, to the production of a large number of partial-tones.
55. Having examined what determines the quality of the sound of a vibrating string, we have next to enquire on what its pitch depends. This term is indeed, strictly speaking, inappropriate to a composite sound containing a series of different tones each having its own vibration-number and independent position in the musical scale. If, however, we use the phrase 'pitch of a sound' as equivalent to 'pitch of the fundamental-tone of the sound/ we shall avoid any confusion arising from this circumstance. The pitch of a string-sound depends of course on the rate at which the string is vibrating. We have seen that when the material, thickness and tension of a string remain the same, its rate of vibration varies inversely as the length of the string. Accordingly, the vibration-number of a string varies inversely
as the length of the string It follows hence that the