161 THE APPLICATIONS OF PHYSICAL FORCES. [BOOK 11. 



1* s 



system, or approximately just intonation. Of cyclical systems, the 

 most important, besides the equal temperament, are the divisions of 

 the octave into 53 and 31 equal intervals respectively. 



Systems have to be divided into two classes in another way, viz., 

 with resgect to the nature of the relation between their fifths and 

 thirds. Systems of the one class have properties analogous to those 

 assumed in technical music, those of the other require treatment dif- 

 fering in many important respects ; these latter present the more per- 

 fect concords, but the J and ^ notation becomes unmeaning with 

 reference to them. Helmholtz's system and the system of 53 are of 

 this latter class. 



The sharp thirds of the equal temperament do not appear to offend 

 ears accustomed only to them ; and with soft qualities of tone they 

 are but little offensive to any ears. But the stronger and sharper 

 the tone the worse is the effect. The harmonium derives the greater 

 part of its unpleasant character from the prominence which its 

 peculiar tone gives to the effect of temperament. Instruments with 

 sustained tones suffer more from temperament than percussion instru- 

 ments, such as the piano. There can be no doubt that the equal 

 temperament must be retained in practice so long as the ordinary 

 key-board is employed, other key-boards have been proposed from time 

 to time ; and Mr. Bosanquet has constructed a " generalised key- 

 board/' by means of which all temperaments can be dealt with in a 

 complete form, within certain limits. 1 



Let us suppose the operation of temperament to have been 

 accomplished ; the piano is said to be tuned, and the whole series of 

 successive strings are stretched so as to vibrate in unison with notes 

 which compose the six or seven octaves of its key-board with their 

 sharps and flats. Now how is each string or several strings put into 

 vibration at once ? 



It is generally known that this is accomplished by placing the 

 fingers of the two hands on the ivory and ebony keys arranged 

 horizontally, and by holding them down for a certain time. But the 

 mechanism by which this is actually accomplished is not so clearly 



1 For historical references on systems generally, see Ellis, Proc. R. 8. 1864 ; and 

 App. to Ellis's translation of Helmholtz on the Sensations of Sound. For the 

 general treatment by Mr. Bosanquet, see Proc. R. S. 1875 ; and the article 

 "Temperament" in Novello's Dictionary of Musical Terms. 



