29 L A Reply to Earl Stanhope, on his Defence of 



3d, Wh et her four or jive columns are to be found in page* 



7 and 22 of the Stereotype pamphlet ? 

 4th, Whether the intervals called the four tierce wolves are of 



the same or different magnitudes ? 

 3th, Whether equal temperaments of successive concords 

 of the same kind, produce equality in the rates of their 

 heating P 

 43th, Whether the notation of musical intervals generally, 

 by S, f and m, rather than by their most simple ratios, be 

 analogous to substituting a notation by scores } dozens, and 

 odd, in place of the universally received decimal nota- 

 tion $ 



I. — In addition to the reasons I have given at page U)2 of 

 vol. xxvii., for preferring a decimal division of the mono- 

 chord, I have further to remark, on what has fallen from 

 His Lordship (page 144 of vol. xxviii.) that those :J impor- 

 tant lengths" which His Lordship's scale is calculated to 

 show in round numlers, are perfectly unimportant ; for, 

 what person using a monochord, other than as a play-thing, 

 wants to use the scale attached to the string at all, in tuning 

 a. perfect concord of any kind ? And does not the use of its 

 ocale as a tuning apparatus wholly consist, in either setting 

 or taking oft tempered intervals P And whether is it easiest, 

 to set a triequal quint for instance, on a decimal scale by my 

 number '6694329, or on His Lordship's scale of 120, by 



means of his vulgar tractions y^^^o - (Stereotype page 



71,70,247,502 -f /A \l_ 



^° f i0 7 ,10,92728o + ( D P- 21 ) ? 



II. — I have maintained (and am backed by all mathema- 

 tical writers) that it is ratios only, and not lengths, except 

 of such things as in their nature measure ratios, as logarithm 

 scales 8cc. do, that can define musical intervals. And 

 though His Lordship expressly asserts (p. 145, vol. xxviii.) 

 that " deviations from perfect intervals are concisely, as 

 well as accurately and conveniently expressed, by means of 

 ihe difference of the lengths of wires," I shall take the very 

 example which he alludes to, (Stereotype p. 8,) wherein it 

 is said, that 1*44 the difference o*i two strings, of which the 



octave 



