34 



On Musical Temperament. 



latter, as it will give the ratios in the largest, and, <if course, 

 the most accurate terms. Then adding those results in each 

 which belong to the same interval, and cutting off the three 

 right hand figures, (expressing in the nearest small fractions 

 those results which are under 1000) which will leave a set of 

 ratios abundantly accurate for every purpose ; the numbers 

 constituting the final solution of the problem will stand as 

 follows : 



TABLE IV. 



Note. In this table, as well as the last, the Vths, Illds, and 

 3ds are to be taken above, and the 4ths, 6ths, and Vlths, their 

 complements to the octave, below the corresponding degrees ia 

 the first column. And, in general, whenever the Vths, Illds, 

 and 3ds are hereafter treated as different classes of concords, 

 each will be understood to include its complement to the octave 

 and its compounds with octaves. 



Scholium. 



The foregoing table exhibits, with sufficient accuracy, the 

 ratio of the whole number of times which the different chords 

 would occur, were the 1600 scores, whose signatures were 

 examined, actually played in succession, on the keys to which 

 they are set, and with an instrument having distinct sounds for 



