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On Musical Temperament. ae 
the same mode, whatever be their signature, is much the same. 
‘There is scarcely more difference, for example, in the relative 
frequency of different chords in the natural key, and in that of 
two sharps, or two flats, than there is in different pieces on the 
same key. If the Vth CG on the tonic has to the Vth EB on 
the mediant in the natural key, any given ratio of frequency 
m:n, the relative frequency of the Vth DA on the tonic, and 
the Vth Fi CH on the mediant in the key of two sharps, will 
not sensibly differ from that of m:n. Hence, if we examine a 
sufficient number of pieces to establish the relative frequency 
of the different consonances in one major and its relative minor 
key, and, by a much more extensive investigation, ascertain the 
relative frequency of occurrence of the different signatures, it 
is evident, that by multiplying this last series of numbers into 
the first, and adding those products which belong to chords ter- 
minated by the same letters, we shall have a series of numbers 
expressing the chance of occurrence in favour of each of the 
consonances of the scale, when all the keys are taken into 
view. 
It was judged that 200 scores, taken promiscuousl¥ from all 
the varieties of music for the organ,* would afford a set of 
numbers expressing, with sufficient accuracy, the chance that 
a given consonance will occur in a single major, and its relative 
minor key. Accordingly 200 scores were examined, 150 in 
the major, and 50 in the minor mode, (as it will appear here- 
after that this is nearly the ratio of their frequency,) of the 
various species of music for the organ, comprising a proper 
share both of the simpler and of the more rapid and chromatic 
movements. As the selecting and reducing to their proper 
keys all the occasional modulations which occur in the same 
_ * The propriety of this limitation will be manifest, when we se gan that 
m organ music, the chords are generally played more full, and are more 
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adapted to different instruments. If, as is probable, such an examination 
a te give essentially the same results, to introduce them would be super: 
