C J75 ] 



XXIX. O?! M. Bemetzrteder's erroneous Calculaihm 

 of the Matmkudks of certain musical Mtervals, By 

 Mr, John Farkv. 



To Mr. Tilloch. 



55"iR, VV HEN r some time ago took up my pen*, to combat 

 the erroneous principles advanced by Earl Stanhope, re- 

 specting: the accuracy of expressing musical intervals \^y 

 the difference oF tht lengths of strings producing the sounds, 

 I thought that his lordship had an exclusive claim to this, 

 and other similar and '^ important musical truths,** which" 

 he has advanced ; but a folio work opening the long- way- 

 was this day put into my hand)?, entitled, '* General In- 

 structions in Music/' by M. Bemetzrieder, printed at Lon- 

 don, about the year 1780 (as I have been told j, price one 

 guinea. Who ailer statmg, at page 92, that a major tone 



u ~ 3 3 9 27 



— taken from a minor fourth ~, ov '— x -^ produces — 

 (which he calls a minor third) and which taken from a fifth 



2 

 3~ 



-, or — X — produces — (which he calls a major third), 



tmd mentioning, that -^ and -.- are ratios usually as^xgntdi 



to the 3**. and III'^., thereon subjoins these remarks : ^' It i$ 

 '^ probable, that \.\\q facilhy of arithmetical calculation has 

 ^^ been preferred to geometrical exactitude ; besides, the 



4 64 



" difference of the two (major) thirds -- and — - is no more 



*^ than — ^ (being the difference o^ ^^ and ^-_) the 90th 



*^ part of a tone (because — ^— - = ^ = --7 which is let- 

 *^ ter perceived by the understanding than by the ear ; the 

 *^ (major) third - is a 90Th part of a tone lower than the 



^^ third --> The difference of the two minor thirds — 



ol 6 



" and -~ is -—; the (minor) third—, is —too acute;*' 



32 96 ' ^ ' 6 96 



for as above, -[^ - -^ = -L = -L, and still proceeding as 



>Above, ~— = — 5 or, — is more than — by an 83} part 



of the same tone (~) as above. Now, if instead of taking 

 jhe numerical differences of the thirds, in Mr. B.'s erroneous 



* See our 27th Volume, pr;<je 108^ and 33d Volume, page 294 and 5, — 



method^ 



