513 



Musical Intonation and Temperament. 



easily influenced by sounds than pipes. A wonderful illustration of 

 this is furnished by an attempt of a performer, at the commemoration 

 of Handel at Westminster Abbey, to produce a discord on his violon- 

 cello during a grand chorus. He could not do it ! Wherever he 

 stopped it, it would produce perfect harmony with the other instru- 

 ments. As he slided his finger on the string it would jump from har- 

 monic to harmonic. This consideration tells in favor of Equal Tem- 

 perament, but is far from settling the question. The extremes must 

 be Professor Fisher's scheme on the one hand and Equal Tempera- 

 ment on the other. The tuner has ample liberty between them to 

 consult his own judgment and the taste of the musical world. 



The annexed table gives the comparative length of string to pro- 

 duce the 12 pitches of an octave tuned to Equal Temperament, and by 

 Professor Fisher's scheme. By means of a monochord the pitches can 

 be taken from the table and transferred to an instrument. 





Equal Temperament. 



Fisher's 



Scheme. 



Untemp'd. 

 Vibrations 



Length, 



Vibrations 



Length. 



Vibrations 



I).. 1 , 



5000 



256.0 



5000 



250.0 



256.0 



Si*, 



5297 



241.6 



5345 



239.5 



240.0 



Lan 4 , Sir*, 



5012 



228.1 



5595 



228.8 



227.6 



La*, 



5946 



215.3 



5979 



214.1 



213.3 



Son 4 , Lar 4 , 



6300 



203.2 



6371 



200.9 



200.0 



Sol 4 , 



6674 



191.8 



6687 



191.4 



192.0 



Fan 4 , Sor 4 , 



7071 



181.0 



7150 



179.0 



177.7 



Fa 4 , 



7492 



170.9 



7479 



171.1 



170.7 



Mi 4 , 



7937 



161.3 



7997 



160.1 



160.0 



Ren 4 , Mir 4 , 



8409 



152.2 



8419 



152.0 





Re 4 , 



8909 



143.7 



8938 



143.2 



144.0 



Don 4 , Rer 4 , 



9439 



135.6 



9568 



133.8 





Do 4 , 



10000 



128.0 



10000 



128.0 



128.0 



The next class of imperfect instruments is of the Trumpet class. 

 These, if fixed in length, will give one fundamental note and its har 

 monies. Its intonation is perfect in the key of which its fundamen- 

 tal is tonic, but it is limited to the harmonic notes. Some are fur- 

 nished with contrivances for instantaneously varying their length and 

 so producing other fundamentals and other setts of harmonics — thus 

 multiplying the resources of the instrument, but leaving them wholly 



