. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. THE PHYSICAL BASIS OF MUSICAL HARMONY. 353 recourse to the wave-siren, an earlier invention of his own, and of which the wave-disks which have already been showo are examples. In the first place, Dr. Keeni^ proceeded synthetically to constructthe wave-forms for tones consisting of the resultant of a set of pure har- monics of g^radnally decreasing intensity. The curves of these, up to the tenth member of the series, were carefully compounde
. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. THE PHYSICAL BASIS OF MUSICAL HARMONY. 353 recourse to the wave-siren, an earlier invention of his own, and of which the wave-disks which have already been showo are examples. In the first place, Dr. Keeni^ proceeded synthetically to constructthe wave-forms for tones consisting of the resultant of a set of pure har- monics of g^radnally decreasing intensity. The curves of these, up to the tenth member of the series, were carefully compounded graphically : first with zero difference of phase, then with all the upper members shifted on one quarter, then with a difference of a half-wave, then with a difference of three-quarters. The results are shown in the top line of curves in Fig. 6, wherein it will be noticed that the curve for difference. Fig. 6. of phase = ^ is like that for zero difference, but reversed, left for right; and that the curve for difference of phase = | is like that for difference = ^, but inverted. Now, according to von Helmholtz, the sounds of all these four curves should be precisely alike, in spite of their differ- ences of form and position. To test the matter, these carefully plotted curves were set out upon the circumference of a cylindrical band of thin metal, the edge being then cut away, leaving the unshaded portion, the curve being repeated half a dozen times, and meeting itself after passing round the circumference. For convenience, the four curves to be compared are set out upon the separate rims of two such metallic ^cylindrical hoops, which are mounted upon one axis, to which a rapid motion of rotation can be imparted, as shown in Fig. 7. Against the dentilated edges of these rims, wind can be blown through narrow slits connected to the wind chamber of an organ table. In the appara- tus (Fig. 7) the four curves in question are the four lowest of the set of .six. It will be obvious
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