SS 
SS eee Te ee eT T_T 
ae eS ee eee 
ee ee PURE ee aes ee UE et RE ee eae eee eee 
On Musical Temperumert. $1 
Besides the following chromatic intervals : 
é extreme sharp 5ths on C 
Major mode. 
i extreme flat 7th -G 
4 extreme sharp 6ths on F 
Minor mode. < 4 extreme flat 7ths on C4 
3 
It was thought best to exhibit a complete table of all the 
consonances which occurred in the 200 scores examined; al- 
though (Prop. EI.) 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, consi- 
dering 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 be- 
comes 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 col- 
lections of music for the organ and voice, by the best Euro- 
pean composers, besides many miscellaneous pieces, afforded: 
the results in the following table : 
