[ 164 ] 



XXL On Temperament, or the Division of the Octave. — No. II. 

 By R. H. M. Bosanquet, Esq.* 



[Continued from vol. xlviii. p. 511.] 



BEFORE continuing the discussion of the subject in the 

 form proposed at the end of my last communication, I 

 have to say a few words on the general purpose of the investiga- 

 tions contained in these papers. 



Some time ago, in tuning an organ, my attention was di- 

 rected, for the first time in a practical manner, to the effect of 

 temperament. Since that time I have perceived the effect con- 

 stantly in all musical instruments, in some more, in some less. 

 I do not say that the effect is always tormenting or intolerable ; 

 but it is there. This was the inducement to study the subject 

 in the first instance. 



The following passage from Stainer's f Harmony founded on 

 the Tempered Scale/ pointed out a defect in our knowledge 

 with a directness rarely found in the writings of any one not 

 specially devoted to science. 



" When musical mathematicians shall have agreed amongst 

 themselves upon the exact number of divisions necessary in the 

 octave, when mechanists shall have constructed instruments 

 upon which the new scale can be played, when practical musi- 

 cians shall have framed a new notation," &c. 



Without entering into detailed criticism, I may observe that 

 this passage first pointed out to me the division of the octave as 

 a subject of study : it was clear that musicians in general knew 

 nothing about it, and scientific men but little more, and that 

 any knowledge that did exist was perfectly useless regarded from 

 any point of view whatever. 



Two principles are regarded as axioms, or perhaps postu- 

 lates, drawn from practical music, especially that of Bach : — 



(1) Similarity of all keys. 



(2) Unlimited facility of modulation. 



The first requirement is met by the property which I have 

 expressed by the word regular — i. e. that the notes of a system 

 admit of arrangement in a series of fifths, all of which have the 

 same value. The second requirement can only be completely 

 met by the property to which the name cyclical has been com- 

 monly applied. 



All will acknowledge that the notes of the ordinary equal 

 temperament are first approximations to the notes intended to 

 be discussed ; and it is in strict analogy to the practice of other 



* Communicated by the Author, being the substance of a second paper 

 read before the Musical Association, May 3, 1875. 



