HISTORY OF MUSICAL SCALES. 429 



bearing- the catalogue number 59970 (Plate T, tig. 1) has served as the 

 type speciuieii. and is the instrument which led to this investigation. 

 It has a glol)ular body with bird's head, a mouthpiece aljout in the 

 position of a bird's tiiil, and four tinger-holes on the liack symmetri- 

 cally placed; these holes seem to be precisely equal in diameter, and 

 equivalent in nuisical effect, so the order of lingering is a matter of 

 indifference, and all the tones are clear and distinct; in Dr. Wilson's 

 paper.^ Mr. Upham, who is a violinist, notes them as F. A, C, D, E. 

 On measurement the volume was found to be 36,0 cc, the equivalent 

 diameter of the trapezoidal mouth hole 1 cm., and the diameter of the 

 iinger holes .65 cm.; these diameters, however, need a correction on 

 account of the thickness of the walls, since the air can not pass freely 

 through the rather thick wall. The tinal result of the calculation is 

 to give, with all tinger-holes closed, the note F on the highest line of 

 the tre})le staff', to within half a semitone, and on opening the finger- 

 holds in any order to give the succession of intervals 4, 3, 2, and 2 

 equal semitones, with a mean error of only one-eighth E. S. Accord- 

 ing to the theory the series of intervals depends onh' on the ratio 

 between the diameters of the holes and the mouth hole, in this case 1 

 to 1.62; so the series of tones has vibration frequencies approximately 

 as the square roots of 1.6, '2J), 3.6, 4.6, 5.6, or of 1, 1.62, 2.24, 2.86, 

 3.48; but the pitch of all depends on the quotient of the radius of the 

 mouth-hole b}^ the volume. Although the theoretical correction for 

 thickness of wall can not be quite precise, it affects all the holes to 

 nearly the same extent, and the greatest probable error that can be 

 assumed will not change the whole compass more than half a semitone; 

 so the calculated scale would still be substantially what the ear con- 

 firms — F, A, C. D, E, or in syllables do, mi, sol, la, si. 



The Museum has several other Costa Rican instruments also of 

 pottery quite similar in appearance to this, but not capable of giv- 

 ing such clear tones, or quite so perfect in the equality of the holes. 

 If the holes are unequal in diameter, in thickness of wall, or in loca 

 tion with reference to the vibrating mass of air, the order of pitch will 

 depend on which holes are opened instead of merely on how many; 

 with five holes sixteen combinations are possible; but of the eleven 

 instrimients in the Museum eight give only five notes each, two give 

 seven notes, and one gives nine notes. If the finger-holes are small 

 relatively to the mouth hole, the compass is small, so one high-pitched 

 whistle has a compass of only six semitones — G to C4f — and another runs 

 from B to E; three hav^e a compass of seven E. S., that is, a musical 

 fifth, and tw^o each have, respectively, eight, nine, and eleven semitones. 



Still other National Museum instruments, similar in principle, but 

 ruder in workmanship and more grotesque in form, have come from 

 Chiriqui, Columbia, and are figured in Dr. Wilson's report, pages 628 



1 Report of United States National Museum for 1896, p. 617. 



