{ 8 extreme sharp 5ths on C Major mode. { 1 --------------------- D { 1 extreme flat 7th ---- G♯ { 4 extreme sharp 6ths on F Minor mode. { 4 extreme flat 7ths on C♯ { 3 --------------------- G♯ It was thought best to exhibit a complete table of all the consonances which occurred in the 200 scores examined; although (Prop. II.) only the concords in the upper half of the table can be regarded in forming a system of temperament. For the more frequent consonances, this table may be regarded as founded on a sufficiently extensive induction to be tolerably accurate. For the more unfrequent chords, and especially for those which arise from unusual modulations, it expresses the chance of occurrence with very little accuracy; and it is doubtless the fact that a more extensive investigation would include some chords not found at all in this list. But it must be recollected, on the other hand, that the influence of these unusual chords on the resulting system of temperament would be insensible, could their chance of occurrence be determined with the greatest accuracy. But none of the numbers in the foregoing table by any means expresses the chance that a given interval will occur, considering _all_ the keys in which it is found. For example, the Vth CG on the tonic of the natural key, in music written on this key, is the one of most frequent occurrence, its chance being expressed by 1807; but in the key of two flats, it becomes the Vth on the supertonic, and its chance of occurrence is only as 197. Hence the problem can be completed only by finding a set of numbers which shall express, with some degree of accuracy, the relative frequency of different signatures. An examination of 1600 scores, comprising four entire collections of music for the organ and voice, by the best European composers, besides many miscellaneous pieces, afforded the results in the following table: TABLE III. +-------------+-------------+-------------+ | Signatures. | Major Mode. | Minor Mode. | +-------------+-------------+-------------+ |4♯_s_ | 42 | 2 | |3♯_s_ | 95 | 6 | |2♯_s_ | 200 | 13 | |1♯ | 322 | 72 | |♮ | 176 | 121 | |1♭ | 180 | 97 | |2♭_s_ | 70 | 77 | |3♭_s_ | 116 | 8 | |4♭_s_ | 0 | 3 | +-------------+-------------+-------------+ |Ratio of their sums 1201 : 399 | +-----------------------------------------+