184 - On Musical Temperament: 
Proposition Vill. 
To compare the harmoniousness of the foregoing system with 
that of several others which have been most known and 
approved. beg 
The aggregate of dissonance, heard in any tempered con 
cord, is as its temperanient (Prop. I.) when its frequency of oc- 
currence is given, and as its frequency of occurrence, when 
its temperament is given: hence, universally, it is as the pro- 
duct of both. “Fhe whole amount of dissonance heard in all 
the concords of the same name, must consequently be as the sum 
of the products of the numbers denoting their iemperamentseach: 
~ jnto the number in Tab. IV. denoting its freqaency. ‘These pr 
ducts, for the scale of Huygens, which divides the octave into 
$1 equal parts, of which the tone is 5 and the semitone 3; for 
the system of mean tones, and for Dr. Smith’s system of equal 
harmony, compared with the scale of the last proposition, (cut: 
ting off the three right hand figures,) stand as follows: 
TABLE VIIL. : 
I eninge 
Systems. Huygeas’s. | Dr. Smiths. | Mean Tones New Seales | 
Disso- ( Vths 825 945 850 786 
nance < [Ilds 121 $82 0 240 
of the { 3ds 1049 629 944 683 
Total i995 | 1956 | 1794 } 17091 
Were we to adhere to Dr. Smith’s measure of equal bar- 
mony, the rows of products belonging to’ the Vths, [Ids, and 
3ds, must be divided respectively, by 4, #5, and is (the Te 
ciprocals of half the products of the terms of their perf 
ratios,) before they could be properly added to express the 
whole amount of dissonance heard in all the cone but, 
according to Prop. I. the simple products ought to 
and the sums at the bottom of the table will expres 
ords 5 mee fi 
