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FLUE-PIPES AND REEDS.                       109
harmonics; the terms "partials" and "overtones" being used when they are simultaneously produced. For example, if the air in a stopped pipe were simultaneously vibrating in the forms (A), (B), and (C), fig. 56, we should obtain from it a compound tone con­sisting of the first three odd partials, that is, the 1st, 3rd, and 5th.
With regard to the open organ pipe, the fundamental is never produced alone; according to the dimensions and shape of the pipe, it is accompanied by, from two to five, or more overtones. As a rule, the overtones are more prominent in narrow than in wide pipes, and in conical, than in cylindrical ones. The shape of the pipe has a great influence on the production of partials. The conically narrowed pipes found in some organ stops, which have their upper opening about half the diameter of the lower, have the 4th, 5th, and 6th overtones proportionally more distinct than their lower ones. Stopped wooden pipes of large diameter, when softly blown, produce sounds which are nearly simple. Such tones are sweet and gentle, but tame and monotonous. A greater pressure of wind, or a reduction in the diameter of the pipe, developes the 3rd and 5th partials.
The great body of tone in the organ is produced by wide open pipes, forming the "principal stops." The tones they produce, owing to the deficiency of upper partial tones, are somewhat dull; they lack character, richness, and brilliancy. Long before Helm-holtz had shown that richness of tone is due to the occurrence of well-developed upper partial tones, organ builders had learnt how to supply such tones artificially, by means of smaller pipes, tuned to the pitch of these partials, forming what are termed mixture stops. As an example of such mixture stops, the " sesquialtera " may be mentioned, which originally consisted of three pipes to each digital, the smaller two producing tones, a twelfth and a seventeenth, above the fundamental of the larger one, thus reinforcing the 3rd and 5th partials. The sesquialtera is now often made with from three to six ranks of open metal pipes. The smaller ranks are usually discontinued above middle 0 as they become too shrill and prominent, larger pipes sounding an octave lower, being sometimes substituted.
In the flute, the tone is produced, as in the organ pipe, by directing a current of air against a thin edge, the edge in this case being the side of a lateral aperture near the end of the tube. In the older form, that of the flageolet, there is an arrangement very similar to that of the ordinary organ pipe, and the air is simply blown in. Variations in pitch are effected, in the first place, by