i906 On Musical Temperament 
quent occurrence. Although the beats of these 3ds grow 
slower as their temperaments are increased, yet they are losing 
their character in melody; and become, in this respect, more 
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 colamns, than from their beats, in the three last, 
Scholium 1. 
It will be perceived, from a comparison of the tempera: 
ments in Table XIL. with the corresponding numbers in Table 
1X., that the harshness of the several concords, especially of 
the IIIds and Sds, is, in general, nearly in the inverse ratio of 
their frequency. The contending claims 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 
of each inversely as iis frequency, could it be carried into 
complete effect, would require. | 
Scholium 2. 
The foregoing system may be put in practice, on the orgau, 
by making the Vths beat flat, with the exception of those om 
Cc, Eb, and G#, which must beat sharp, at the rate required 18 
the table; proving the correctness of the temperaments of the 
Vths, by comparing the beats of the IIIds, as they rise, with 
those required by column two. Should less accuracy aa@ 
quired, the IlIds on C, D, and A, might be made perfect, with: 
out producing any essential change in the system. his would 
reduce the labour of counting the beats to eight degrees only ‘ 
Scholium 3. 
To show that the computations of the different frequency d 
occurrence of the different concords, on which this system 4 
tempqgament is founded, may be relied on as practically -. 
a amaearee 
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