1 96 'On Musical Temperament. 



quent occurrence. Although the beats of these 3ds g:row 

 slower as their temperaments are increased, yet they are losing 

 their character in melody ; and become, in this respect, morci 

 and more offensive, the more they are tempered. Hence the 

 harmony and melody of the several intervals, jointly consi- 

 dered, are to be judged of rather from their temperaments, in 

 the three first columns, than from their beats, in the three last, 



Scholium 1. 



It will be perceived, from a comparison of the tempera- 

 ments in Table XII. with the corresponding numbers in Table 

 IX., that the harshness of the several concords, especially of 

 the Illds and 3ds, is, in general, nearly in the inverse ratio of 

 their frequency. The contending cleiims of the different con- 

 cords render it impossible that *this ratio should hold exactly. 

 Including the Vths, the harmony of the concords is much more 

 nearly equal, than the principle of rendering the temperament 

 qf each inversely as its frequency, could it be caTried into 

 complete effect, would require. 



Scholium 2. 



The foregoing system may be put in practice, on the organ, 

 by making the Vths beat flat, with the exception of those on 

 Q-^, Eb, and G*, which must beat sharp, at the rate required in 

 the table ; proving the correctness of the temperaments of the 

 Vths, by comparing the beats of the lllds, as they rise, with 

 those required by column two. Should less ar.curacy be re- 

 quired, the Illds on C, D, and A, might be made perfect, with- 

 out producing any essential change in the system. This would 

 reduce the labour of counting the beats to eight degrees only. 



Scholium 3. 



To sliow that the computations of the different frequency of 

 occurrence of the different concords, on which this system of 

 temperament is founded, may be relied on as practically cor- 



