On Musical Temperament. 1 97 



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 nausic 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 II., and those belonging to the 

 major and to the minor signatures, corresponding to the num- 

 bers in Table III., were added, before the products were 

 taken, instead of keeping the modes distinct, which is neces- 

 sary to perfect accuracy. Yet the resulting scheme of tem- 

 perament was essentially the same throughout, with the one 

 which has been just described. It had. the same anomalous 

 temperaments, viz. the Vths on C"*, Eb, and G* ; and the 

 Hid on A ; and these anomalies were similar in degree. The 

 greatest difference between any two corresponding tempera- 

 ments, was between those of the 3d on Eb ; the first computa- 

 tion malting 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 which is described by Rousseau and 

 D'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. VIII., 

 and those products which belong to the several concords of 

 the same name be added, the sums, after the thrp*^ riofht-banr! 

 figures are cut off, will be as follow : 



