To show that the computations of the different frequency of occurrence of the different concords, on which this system of temperament is founded, may be relied on as practically correct, 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 II., and those belonging to the major and to the minor signatures, corresponding to the numbers in Table III., 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 essentially the same throughout, with the one which has been just described. It had the same anomalous temperaments, viz. the Vths on C♯, E♭, and G♯; and the IIId on A; and these anomalies were similar in degree. The greatest difference between any two corresponding temperaments, was between those of the 3d on E♭; 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 system 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 semitones; 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 temperaments 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 three right-hand figures are cut off, will be as follows: TABLE XIII.