438 REPORT OF NATIONAL MUSEUM, 1900. 



From these it is evident that whichev^er type of instrument one ma}^ 

 take, there will be some intervals that verj^ closely agree with inter- 

 vals of our familiar scale. In a few cases this comes about because 

 our scale is prin(;ipally derived from the Greek theorists, who based 

 their scales on proportional string-lengths; so, if the unit of equal 

 distance on a simple guitar chances to be an aliquot part of the length 

 of the string from the bridge to the nut, some of the resulting notes 

 will belong to our scale. (However, the divisor nuist not have a prime 

 factor greater than live.) But whatever the instrimient, on any doc- 

 trine of chances, there will be some approximate coincidences; and 

 these coincidences, as judged ))3"tho ear, will be found nuich closer and 

 more numerous than when judged mathematically or graphically; for 

 the training of modern musicians, as has often been recognized, not 

 only allows but compels theiu to ignore deviations from their standard 

 scale — deviations amounting sometimes to more than half a semitone. 

 So one is forced to conclude that the recognition, even by a musically 

 educated ear, of a series of notes as agreeing substantially with our 

 diatonic scale or with any other known scale, does not afford any ade- 

 quate ground for judging of the principles underlying the series; in 

 fact, the failure to note the deviation may prevent the recognition of 

 the underlying principle. 



The type Costa Rican four-hole whistle is the most striking example 

 of a series agreeing closely with notes of our scale, yet based on an 

 absolutely different principle; for the mean computed deviation from 

 the piano intervals is only one-eighth of a semitone. 



Further, the whole discussion makes it evident that the people who 

 made and used these instruments, or any single type of them, had not 

 that idea of a scale which underlies all our thinking on the subject, 

 nameh" A series either of tones or of intervals recognized as a stand- 

 ard, independent of any particular instrument, but to which every 

 instrument nuist conform. Modern Europeans for the sake of har- 

 mony have nearl}^ ])anished all scales but one, and seldom know by what 

 rules the instruments are tuned to furnish this. But for these people 

 the instrument is the primary thing, and to it the rule is applied, while 

 the scale is a result, or a secondary thing; and the same rule applied a 

 himdred times may possibl}^ give a hundred different scales. Natur- 

 ally one does not expect to find much concerted music among people 

 in this stage of development. 



The various rules discussed jibove may be united in a generic one, 

 namely : 



The 2)rmiary pri7iciple in the making of musical instruments that 

 yield a scale is the repetition of elements similar to the eye; the size, 

 number^ and location of these elements heing dependent (m the size of 

 the hand and the digital expertness of the J)<'rf^''^''^^^'''' 

 T\nB principle shows itself in the occasional equal spaces on the neck 



