EXPLANATION OF PLATE 10. 



SCALES GIVEN BY RESONATORS. 



The construction of this chart has been explained in the appendix. To use it, find 

 in the base Hne the number which expresses the radius of the finger holes, that 

 of the mouth hole being considered 1.0, and erect a perpendicular therefrom; 

 the heights of the points of intersection with the successive curves, measured on 

 the left-hand scale, give the pitch of the successive notes produced as the holes 

 1, 2, 3, etc., are opened, expressed in equally tempered semitones, E. S. The 

 dotted line corresponds to tlie position on the chart of the type resonator. The 

 chart shows clearly how the successive intervals become smaller as the number of 

 open holes increases, and how the total compass is small if the finger holes are 

 relatively small. 



Use may be made of the chart for many ready calculations of intervals other than 

 those due to equal differences, and by doubling the readings in E. S. the result 

 may be applied to string ratios; e. g., find the interval corresi:)onding to the ratio 

 5 : 4, or 1+0.25; the chart gives directly 1.9; the double of which is 3.8 E. S. The 

 table in the appendix gives more accurately 3.86 E. S., showing that the just 

 Third is 0.14 E. S. flatter than the piano Third. 



462 



