of the Muslcat Scale. 321_ 



have assumed ? In this case, let him reflect on what I said 

 above, and consider, that chords very differently attem- 

 pered* are nol, according to the law ot" chance?, very likely 

 to succeed each other, because the whole atten;pering must 

 lie within small limits, and one of the most frequent chords 

 in occurrence, is not very likely to be preceded or followed 

 by one of those the fnost rare of occurrence, and vice versa. 

 ft is the want of agreement with Dr. Smith's maxim, on 

 which my chief objection to the isoto?iJc sys'.cm (which the 

 learned Professor thinks th.e best) is founded, and for ex- 

 plainintr which T beg to refer him to Emerjon's Algebra, 

 prob. ccii, and to request of him to consider, what the efFect 

 must be of hearing a Vth (above the bass, or F clidT note), 

 beating only once in a second of time, quickly succeeded by 

 a III beating 1 1 times per second, a VI 13 times, a 3d 15 

 times, or perhaps, a 6th beating is times per second, and 

 these perhaps intermixed with 4ths, which beat but i-L times 

 per second? It is my fear that lord Stanhope's sys'em will 

 furnish frequent instances, of transitions from perfect Vths 

 to those beating very considerably, and from the former to 

 other chords, beating faster perhaps than those stated above; 

 which induces me to withhold my approbation of it, until a 

 complete table of all its temperaments and beats is before 

 us, and which I heartily wish that some person, with mure 

 leisure to spare for lliese pursuits than myself, would under- 

 take. In the remarks at the top of p. 421, a similar over- 

 sight is, if I mistake not, observable, as in lord Stanhope's 

 essay, in first fixing the notes by means of a regular series 

 oi' fifths (tempered in this case), and iifterwards talking of 

 adjusting the same notes, to suit the temperaments of the 

 thirds. The temperaments of no one conchord ought to be 

 exactly the same, throughout the octave, norou^rht anyone 

 interval above the key to be attempered, without takin"- into 

 consideration, the effect which the same will have upon all 

 the conchords above and below its upper note, accord;ng to 

 the view which I have taken of this matter. I be ;, to be 



• 1 h.ivc not yet attempted to d*cidc, whether d.U artemperlnj should be 

 regulated, witliout takin;^ into tonsiderjilion, ilie degree of Ismpcramcnt wliich 

 di.Tcrent cunchords will bear. 



X 2 permitted, 



