On Musical Temperament. 



193 



Three successive applications of this theorem to each degree 

 in the scale, in the manner described Prop. VI., will bring 

 them very near to the required position, as appears by the 

 smallness of the corrections in the 3d column below, where 

 the results of the several operations are exhibited at one 

 view. 



TABLE X. 



Cor. Hence we may deduce, in the same manner as in 

 Prop. VII., the diatonic and chromatic intervals, the lengths 

 of a string and their vibrations in a second, and the tempera- 

 ments and beats of all the concords for the scale which results 

 from the foregoing computations. They may be seen in the 

 two following tables : 



