On Musical Temperament. 87 



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 F* C« on the mediant in the key of two sharps, will 

 not sensibly differ from that of 7n ; 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 promiscuously 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, 160 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 consider that in 

 organ music, the chords are generally played more full, and are more protracted, 

 than in music for other keyed instruments. It is harmony which constitutes its 

 character, in a higher degree than in music for other instruments. Hence the 

 harmony of the organ ought not to be impaired by including in our computations 

 any music not adapted to it. If a similar examination of music for the piano-forte 

 would afford a set of results essentially different from those of this proposition, this 

 is no proof that it ought to have any concern in a system of temperament designed 

 primarily for the organ, but merely that the same temperament cannot Le equally 

 adapted to different instruments. If, as is probable, such an examination would 

 give essentially the same results, to introduce them Tould be superfluous. 



