■336 On the Vibrations of Musical Strings. 



224, for those of equal harmony, mean tones, and Mr, 

 Huy^ens ; I therefore siibjohi one, and will here show the 

 steps of the calculation. 



The Doctor correctly states, p. 219, that the tempera- 

 ment of the 5th, when the beats are to be equally quick 

 with those of the 3d, to the same base, is 5-23ds of a 

 comma. Hence, if from the logarithmic ratio of the per- 

 fect 5lh 2 : 3 0-1760913 



5-23ds of the logarithmic ratio of 80 : 8l\ ^.^^^ j^gg 

 (0-0053950) be subtracted / "_ 



There remains the log. ratio of the tempered 1 q. 1749 135 

 5th 3 



This subtracted from the log. ratio of thel ^.^^j^^^^ 

 perfect octave 3 



Leaves the log. ratio of the tempered 4th... 0' 1261 115 

 The difference between the log. ratios of the^ 

 • tempered 5th and 4th, gives the log. V 0-0488070 



ratio of the tone J 



Log. ratio of two tones, being the tempered \ o.oq76140- 



3d major — j 



Which taken from log. ratio of tempered ^ 



4th, leaves the limma major, or greater >0-02S497^ 



half tone J 



Which taken from the tone, leaves the ''"^"l o-0203095 



jna minor, or the less half tone J 



These two last logarithms successively subtracted, accord- 

 in<T to the proper order, from the logarithms 5-0000000 

 an"^ 1-2916574, and added to 2-4014005, (beginning at the 

 bottom) will give the logarithms found in the 3d, 4th, and 

 5th columns of the Table; of which those in columns 6lh, 

 7th, and 8th, are respectively the natural numbers. The 

 above logarithms are respectively those of the whole pro- 

 portional string, of the whole length of the monochord 

 strintr, and o*^' the number of vibrations in a second of the 

 latter". 



I am, sir. 



Your most obedient servant, 



Soho, in Birmingham, JoHN SOUTHERN. 



Nov. Iti, 1812. 



TABLfi 



