176' On Musical 2'empefament. 



FINE ARTS. 



Art. XXI. Essay on Musical Temperament. By Pro- 

 fessor Fisher, of Yale College. 



[Concluded from page 35.} 



Proposition V. 



To determine that position of any degree in the scale, which 

 will render all the concords terminated by it, at a me- 

 dium, the most harmonious ; supposing their relative 

 frequency given, and all the other degrees fixed. 



JL HE best scheme of temperament for the changeable scale, 

 on supposition that all the concords were of equally frequent 

 occurrence, is investigated in Prop. III. But it is shown, in 

 the last Proposition, that some chords occur in practice far 

 more frequently than others. Hence it becomes necessary to 

 ascertain what changes in the scale above referred to, this 

 different frequency requires. Any given degree, as C, termi- 

 nates six different concords ; a Vth, llld, and 3d above, and 

 the same intervals below it. Let the numbers denoting the 

 frequency of these chords below C be denoted by a, b, and c, 

 and their temperaments, before the position of C is changed, 

 by OT, n, and p : and let the frequency of the chords above C 

 be denoted by a, b', and c, and their temperaments by m, n\ 

 and p', respectively. If, now, we regard any two of these 6 

 chords, whose temperaments would be diminished by moving 

 C opposite ways, and of which the sum of the temperaments is 

 consequently fixed, it is manifest that the more frequent the 

 occurrence, the less ought to be the temperaments Were 

 we guided only by the consideration of making the aggregate 

 of dissonance heard in them in a given time, the least possible, 

 we should make the one of most frequent occurrence perfect, 

 and throw the whole of the temperament upon the other; 



