a. 
PL Ce ee ee 
On Musical Temperament. $3 
with regard to their successive tonics, as these have with regard 
toC. Whenever an interval occurs, affected with a new flat 
or sharp, it is to be considered as the commencement of a new 
succession of products. The IlId CHE4, for example, does 
not occur at all till we come to the key of two sharps, and even 
then only in occasional modulations, corresponding to the IfId 
on B in the natural key, whose multiplier is 10. In the key of 
3 sharps it becomes another accidental chord, answering to the 
{lid on E in the key of C, and consequently has 40 for its 
multiplier. It is only in the key of 6 sharps, that it becomes 
a constituent chord of the key; when, if that key were ever 
used, it would correspond to the IL[d GB on the dominant of 
the natural key. 
After all the products have been taken and reduced to their 
proper places, in the manner exemplified above, a similar opera- 
tion must be repeated with the numbers in the second column, 
of Table III, and those in the second columns in the three first 
divisions of Tablé Ef. 
The necessity of keeping the major, and its relative minor 
key, distinct, will be evident, when we consider that the 
several keys in the minor mode do not follow the same law of 
frequency as in the major; as is manifest from the observations 
in Schol. Prop. III, and as clearly appears from an inspection 
of Table IIT. 
But in order to discover the relative frequency of the dif- 
_ ferent chords on every account, the results of the two forego- 
ing Operations must be united, Now, as the numbers in the 
two columns of Table II, ata medium, are as 3: 1, and’ those 
in Table IT] are in the same ratio, although the factors are te 
each other in only the simple ratio of the relative frequency 
‘of the two modes, yet their products will, at a medium, be in 
the duplicate ratio of that frequency. Hence, to render the 
two sets of results homologous, so that those which correspond 
to the same interval may be properly added, to express the 
general chance of occurrence for that interval in all the major 
and minor keys in which it is found, this duplicate ratio must 
be reduced to a simple one, either by dividing the first, or by 
multiplying the last Series of results, by 8. We will do the 
OLwwd. No. 1, 5 
