436 



REPOKT OF NATIONAL MUSEUM, 190(). 



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 Twelfth of bar No. 8. The sim- 

 plicity of the rule, however, frequently disappears, either because of 

 variations in the thickness, as when a savage splits a bamboo stem and 

 then cuts his bars so that the shorter ones are also thinner, or because 

 of the attachment of lumps of wax or clay to the bars to tune them to 

 some other instrument; or because of the hollowing of the center, as 

 is done by modern Japanese; so at present one can not affirm that this 



Fig. 8. 

 XYLOPHONES. 

 After Kraus. 



