3 CO On difft^rent Tempera^mtnts 



because (savs the professor), since other chords beside these 

 must necessarily occur in diflerent parts of every piece of 

 music, the ideal system now objected to cannot be adopted, 

 any more than lol"d Stanhope's, witliout doing mischief, and 

 particularly by occasioning transitions, during performance, 

 from a belter to a worse harmonv." iJovv, [ ask, are loga- 

 rithms to be applied to determine ihe best system of tem- 

 perament, but on some principle, previously settled, as to 

 wherein the pt-r/'ecl ion oi' a tempered system consists? In 

 the letter alliidod to (vol. xxvi. p. 1 76) I mentioned the 

 principle, quoted above, which I have endeavoured more 

 fully to explain in the previous part of this letter, and which, 

 it may not be irrelevant to state, was the result of many con- 

 versations with the late justly celebrated Dr. Arnold, and 

 with other musicians, as well as of much observation and 

 thought on the subject; and wherein I meant to include, the 

 consideration of every conchord or harmonic interval (less 

 than an octave) which can occur upon each finger-key as a 

 bass or lower note, as a 3d, III, 4th, V, 6th, and Vf, above 

 each note, or JiJ conchords in the whole; and my inquiry 

 goes to the finding, bv a very extensive experiment, a series 

 of 72 numbers, expressing the order of frequency, in which 

 the several chords above named arise in the music in use, 

 or likelv to be in use, if the exjjeriuient can be so far ex- 

 tended : these obtained, we should, I think, (if possible,) at- 

 temper the douzeavc so, that the ini perfections of ihe conchords 

 shrill h in the inverse ratio of their frecjiiency of occurrence. 

 What other chords, besides those included above, can arise? 

 For I speak not cA'dischords, begause their c()nsiderati(>n would 

 so involve the subject as to render all success hopeless ; an-d 

 after all, the absence of any sensible phajnomena, like the 

 beutins^s which attend conchords wlien tempered, renders it, 

 perhaps, impossible to fix any priuciplc chi which their tem- 

 peraments cau be regulattd ; and they may therefore, I think 

 safely, be left,io receive such temperaments, as the fixing of 

 the ctJhchords may happen to give them. Does the learned 

 Professor rest his objection, on the supposed inconsistency 

 of that sound maxim, which 1 quoted frofn Dr. Smith (as 

 to worse harmony succeeding belter), with the principle I 



have 



