

BROADWOOD'S TEMPERAMENT. 



wants. It is ri;;ht here also to explain, that the lo- 



749 



garithm of the vibrations of the note A, at the begin- 

 "'"' aild in tlu- middle of the lin.t column of the 

 table, lias been assumed by previous trial, or work- 

 i:i;j backwards, such, that the note C may have a 

 log. of 2.3802112,4, answering to the number 'J 10 of 

 vibrations, which is understood to be the present 

 CONCERT Piti/t, (see that article,) and to which the 

 pitch of the instrument to be tuned, must be care- 

 fully adapted, according to the rules that will there 

 be given, (see also Dr R. Smith's Harmonics, prop. 

 xviii.) otherwise the beats here calculated will not 

 apply. 



Notes. Logs, of Vib. Vibrations-. 

 A 2.6053528,6 = 403.0443 



Beats of 



the Fifths. 



.3010300,0 

 2. 3043228,6 A 



.1753905,4 



H-2 



201.52215 A 

 _ X3 



604.56645 .. . . 

 603.5920 - a9 <**& 



X2 



2.4797134,0 = 301.7960 

 X3 



+ .1753905,4 = 



903.9282 



. .- 







B 



X2 

 2.655 1 039,4 = 45 1 .964 1 



.3010300,0 

 .3.540739.4 B 



-j-2 



225.98205 B 

 X3 



677.91615, 



~ 



F # 



+ .17.3390.5,4 676.8532 



X2 

 2.5294644,8 = 838.4266 



.3010300,0 



2.2284344, 



.1753905,4 



-:-2 



1 69.21 33 F^: 

 3 



507.6399_ nft , R , 

 506.8216- UB1 



X2 



2.4038250,2 = 253.4108 

 3 



+ 1753905,4 



760.232 4 

 759.0066 ' 



X2 



G% 2.5792155,6 = 379.5033 

 3010300,0 2 



2.2781855,6 G# 189.75165 G $ 

 X3 



569.25495 



A 



. ib. Vilj, 

 2.'i0.j:>52, = 403.0443 

 X2 

 .1753905,4 806.( 



Halof 



= J.3017b 



D 2.4299623,2 = 



.1753905,1 



538. 



=0.86V 



G 



2.2545717,8= 179.70-J8 

 + .3010300,0 x2 



2.55560I7T8 G 359.4196 G 



X2 

 .1753905,4 



718.8392_ 

 720.0000-' - 1 '' 1 *' 



2.38021 12,4 = 240.0000 

 + 3010300,0 2 



2.68 1241 2, tC 480.0000C 



2 



.1753905,4 960.0000 



961.5501 



" X3 



2.5058507,0 = 320.5167 

 .1753905,4 x2 



= 1.5501 



641.0334 

 642.0684- 1 



~X3 



2.3304601,6= 2140.228 

 + .3010300,0 2 



2.6314901,6B|? 04S6Bi> 

 .1753905,4 x2 



856.091 2_ 

 857-4738- l 



El) 



XS 



2.4560996,2= 285.82 Mi 



X2 



571.G492 



= 1.3943^ 



The first column in the above Table or process, 

 had better be calculated through, as above directed, 

 and written wide, before proceeding to the second, 

 and let the resulting log. of G% be deducted from 

 that of El), which, in the present case, will give 

 .1779140,6 for this bearing or resulting fifth, from 

 which, taking the perfect fifth .1760912,6, we get 

 .0018228,0, the recig. log. of the quint wolf or sharp 

 and fifth in Mr Broadwood's system, =3.7191062 ; 

 and by reference to Mr Farey's 15th corollary in the 

 Philosophical Magazine, vol. xxxvi. p. 374, or to our 

 article TEMPERAMENT, we find, that 1 1 X temp, of 

 V ct, ought to give this same Vth wolf; or, 

 11 X .0007007,2 0058851,4=.0018227,8 ; which 

 differing only 2 in the eighth place of logarithm*, 

 hews that all the several operations in this column . 

 have been correctly performed ; otherwise they mutt 



. : : 



