442 



REPORT OF NATIONAL MUSEUM, 1900. 



As illustrations of the use of the table, find the successive intervals of the scale of 

 the Hindu Sitar, the string being stopped successively at 36, 35, 34, . . 27; the corre- 

 sponding differences in column 4 of the table are 0.49, .50, .52, . . . .63 E. S., the 

 sum being 4.98 E. S., as required by Tagore's rule (j). 425 above). To complete the 

 octave, the space 27 to 18 is to be divided into 13 equal parts; substitute for the ratio 

 27:18, or 3:2, 39:26, and use the table again; the differences are now 0.45, .46, . . . 

 .65, the sum being 7.02 E. S., which added to 4.98 gives 12 E. S., or the octave. 



If the law be that of the square roots, as with resonators, the table is to be used in 

 precisely the same way, but the final results are to be divided by 2; for example, in 

 the type resonator, calling the equivalent radius of the mouth hole 1.0, that of the 

 finger holes is 0.6 (more accurately, 0.<)2); the series of terms will therefore be 1.0, 

 1.6, 2.2, 2.8, 3.4; multiply all by 10, and take the corresponding numl)ers from column 

 3 of the table; divide the differences by 2, and add the quotients to the fundamental 

 pitch. The results are as follows: 



E. S. 



10 39.86 F 



16 48.00 8.14 4.07 A + -07 E. S. 



22 53.51 13.65 6.83 - .17. 



28 57.69 17.83 8.92 D - .08. 



34 61.05 21.19 10.60 E - .40. 



If 0.62 had been taken the results would have been slightly higher in pitch. 



Plate 10 has been plotted to give directly the intervals of resonator scales for any 

 number of open holes up to 5, and for ratios of radii between and 1. The dotted 

 line corresponds to the type resonator. 



The table may also be used for bars; the only change is that the differences are to 

 be doubled instead of halved. Thus, with a series of uniform bars whose lengths are 

 24, 23, etc., to 17, the compass will be 2 X (.55.02 — 49.05) = 11.94 E. S., which is 

 practically an octave, as stated on page 436. 



Table for computing musical intcrrdls. 



N. 



1 



2 

 3 

 4 

 5 

 6 

 7 

 8 

 9 

 10 

 11 

 12 

 13 

 14 

 15 

 If. 

 17 

 18 



ly 



20 



N. 



21 

 22 

 23 

 24 

 25 

 26 

 27 

 28 

 29 

 30 

 31 

 32 

 33 

 34 

 35 

 36 

 37 

 38 

 39 

 40 



Log.N. E. S. 



Dif. 



