On Musical Temperament. \ 35 



ratio of the aggregate dissonance of the systems under which 

 they stand. The last has decidedly the advantage over the 

 first, both in regard to the aggregate dissonance, and the 

 equality of its distribution among the different classes of con- 

 cords. It has nearly an equal advantage over the second in 

 regard to the first of these considerations ; although tn regard 

 to the equality of distribution, the latter has slightly the advan- 

 tage. It has, in a small degree, the advantage over the third, 

 in regard to the aggregate dissonance 5 while, as it respects the 

 equahty of its distribution, it has the decided preference. It is 

 true that the temperaments of the concords of the same name, 

 in the new scale, are not as in the others, absolutely equal ; 

 but no one of them is so large as to give any offence to the 

 nicest ear. The largest in the whole scale exceeds the uniform 

 temperament of Dr. Smith's Vths by only j\ of a comma. 



Scholium 1. 



The above system may be put in practice on the organ, by 

 making the successive Vths CG, GD, DE, &c. beat flat at the 

 rate contained in Table VII., descending an octave, where 

 accessary, and doubling the number of beats belonging to any 

 degree in the table, when the Vth to be tuned has its base in 

 the octave above the treble G. The tenor C must first be 

 made to vibrate 240 in a second, the methods of doing which 

 are detailed at length in various authors. Whenever a Illd 

 results from the Vths tuned, its beats ought to be compared 

 with those required in the table, and the correctness of the 

 Vths thus proved. This system is as easy, in practice, as any 

 ether ; for no one can be tuned correctly except by counting 

 the beats, and rendering them conformable to what that sys- 

 tem requires. The intervals of the first octave tuned ought 

 to be adjusted with the utmost accuracy, by a table of beats. 

 When this is done, the labour of making perfect the other 

 octaves of the same stop, and the unisons, octaves, Vths, &lc. 

 ©f the other stops, is the same in every system. This last, 

 indeed, is so much the most laborious part of the tuning of 

 the organ, that if even much more labour were required than 



Vol. I,. ..No. ?. 1^^ 



