. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. VI. COMPOSITE INSTRUMENTS. Each of the instruments thus far examined is capable of furnishing several notes of approximately constant pitch, but the general princi- ple before us may be embodied in composite instruments, where each note has its own vibrating body; thus 1. Various forms of harps and dulcimers show strings of regularly decreasing length; here, of course, difference of tension may nullifj^ the scale due to the lengths. One for
. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. VI. COMPOSITE INSTRUMENTS. Each of the instruments thus far examined is capable of furnishing several notes of approximately constant pitch, but the general princi- ple before us may be embodied in composite instruments, where each note has its own vibrating body; thus 1. Various forms of harps and dulcimers show strings of regularly decreasing length; here, of course, difference of tension may nullifj^ the scale due to the lengths. One form is shown on Plate 8. 2. Pan's pipes are sometimes seen with regularh^ decreasing lengths; it is true that this regularity is not very common, but it is the only principle of scale building (except the Chinese cycle of fifths) yet recog- nizable in these primitive instru- ments. (Plate 9.) 3. Instruments of the bar type are found frequently in our orchestras and l)ands under various names, as ityJophone; they are familiar in children's toja and are widely dis- tributed in savage and half-civilized lands under the names of 7nari7nha^ haJdfong^ harmonicon, etc. (Plate 8 and fig. 8.) The law of the uni- form bar is that the frequencies of vibration of a series of bars of the same material are proportional to the quotients of the thickness divid- ed l)y the square of the length; the breadth is immaterial if it is uni- form. So if one takes a series of uniform bars of the same thickness and regularly decreasing length he may o})tain a series of ascending notes. Thus, let the first bar be 24 units long (for example 24 cm.), the successive bars decreasing b}^ one unit; the eighth bar will be 17 units long, and the fifteenth bar 10 units; the series of frequencies would then be as the reciprocals of the squares of 24, 23, etc., so giving to the ear a series of increasing inter- vals; with these proportions bar No. 8 would give the Octave of the first, but bar No. 15 would give the Twe
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