Musical Intonation and Temperament. 517 



corresponding notes in the table of Equal Temperament, we shall see 

 that all the pitches are too sharp except Sol, but all so slightly, that 

 no perceptible injury to the melody results. It is not so with the har- 

 mony. As it is harmony that fixes the precise intervals in intonation, 

 so must considerations of harmony alone decide every question of 

 temperament. And because the Illrds, the 3rds, and the Vths, are so 

 much more important than IVths, the Vlths, and the Gths, the former 

 alone are to be taken into consideration. We find the Vths of mean 

 temperament flat, by an interval of about 499 : 500, and the Illrds 

 sharp, by an interval of about 99 : 100 ; and as a IHrd and a 3rd 

 make a Vth, the 3rd must, therefore, be quite flat. So Mean Tem- 

 perament furnishes us no good chords, though none of them are abso- 

 lutely intolerable. Some of these chords occur much more frequently 

 than others. Son, for instance, is Vth to Don, and Ulrd to Mi, but in 

 the latter relation it occurs more than 12 times as often as the former. 

 If flattened more than in Equal Temperament, so as to make a worse 

 Vth but a better IHrd, the ear is pleased with the change a dozen 

 times to where it is annoyed once. Considerations like this have led 

 to various schemes of Unequal Temperament. The best probably of 

 these is that of Professor Fisher. 



Musicians are not agreed what temperament is best. In Unequal 

 Temperament some of the chords are very good, while the aggravated 

 dissonance of others, called by tuners the Wolf, imparts a peculiarity 

 to the keys in which it occurs, much admired by certain musicians. 

 Science hardly justifies these predilections, which must be chiefly at- 

 tributed to fancy and prejudice. Some inequality of temperament 

 may be preferable, but no key ought to be made so bad as to give it 

 a character for harshness. 



One argument for Equa. Temperament seems strangely to have 

 been overlooked by every one who has discussed the subject. This 

 arises from the influence, before alluded to, which musical bodies 

 nearly in harmony have on each other. Two organ pipes, differing 

 nearly -^ of an octave, when sounded together may sound in unison. 

 In full chords this influence is stronger than with two sounds only. 

 But for this principle, what is called "the furniture stop," opening at 

 the same time perfect thirds, perfect fourths and perfect fifths to each 

 note played, would produce the most frightful discords if each pipe 

 sounded its own note. Influenced by each other, and by the other 

 stops, they produce the most sublimo harmony. Strings are mora 



