On Musical Temperament. 197 
rect for music in general, it may be proper to state, that a 
similar series of calculations had been before made, from an - 
enumeration of the concords in fifty scores of music entirely 
different from that made use of in Prop. IV. They were not, 
indeed, made with the same accuracy, for the music of which 
the chords were counted, was too generally of the simpler kind, 
and the numbers corresponding to those in the two columns 
under each concord in Table IL., and those belonging to the 
_ ihajor and to the minor signatures, corresponding to the num- 
bers in Table II1., were added, before the products were taken, 
instead of keeping the modes distinct, which is necessary to 
perfect accuracy. Yet the resulting scheme of temperament 
Was éssentially the same throughout, with the one which has 
heen just described. It had the same anomalous temperaments, 
viz. the Vths on C#, Ep, and G# ; and the Iffd on A; and 
these anomalies were similar in degree. The greatest differ- 
ence between any two corresponding temperaments, was be- 
tween those of the 3d on Ep; the first computation making it 
only 702, while the last has it 818. 
Proposition XI. 
The aggregate of dissonance, heard in a given time, in the sys- 
tem of temperament unfolded in the last Proposition, will 
be less than in either of the systems generally practised. 
In order to compare the foregoing system with those which 
have been most generally approved, the temperaments of all 
the concords have been calculated, in the system of equal semi- 
tones; in that of Earl Stanhope, which has had considerable 
celebrity ; in that of Dr. T. Young; in that of Mr. Hawkes ; 
in that of Kirnberger, which has been extensively adopted in 
Germany; and in that whichis described by Rosseau and 
"Alembert as generally practised in France. If these tem- 
Peraments be multiplied into the corresponding numbers of 
Table IX, agreeably to what was shown under Prop. VILL, 
and those products which belong to the several concords of 
the same name be added, the sums after the three right-hand 
Figures are cut off, will be as follows : 
