172 Mr. R. H. M. Bosanquet on Temperament, 



The view to which I have been driven is that the appreciation 

 of melodic sequences is purely the result of custom. This com- 

 pletely explains how an eminent violinist may play diatonic 

 scales, while other musicians, educated at a keyed instrument, 

 cannot endure any marked deviation from the equal tempe- 

 rament. 



The harmonic seventh is an interesting example of the general 

 point. If we flatten the tempered minor seventh by about one 

 third of a semitone, we get a pure chord free from beats. The 

 ordinary musician cannot at first endure it. The consonance of 

 a full chord of the dominant seventh containing this note is of 

 the most magnificent quality ; and if its introduction is properly 

 managed, so that the interval made by the flattened note with 

 the preceding and following notes of the same part is not out- 

 rageous, most musicians appreciate its beauty after a time. But 

 it is necessary to be very careful about the context. Though by 

 dint of custom I like the chord much now, yet if I introduce it 

 so as to give rise to any melodic interval widely different from 

 its usual value, the effect is still bad to my ear. 



I am clear that a general certainty on this and similar points 

 can be attained only by a wider diffusion of actual knowledge 

 (not reading) on the subject. One might suppose that an edu- 

 cated musician would have some right to speak with authority 

 on such questions as intervals, consonance, dissonance, and the 

 like. It is hard to believe, but it is nevertheless true, that 

 scarcely any musician has ever heard a perfect consonance, or 

 has any idea of the sound of any intervals except those formed 

 by the equal-temperament scale. But until a person has become 

 tolerably familiar with the effects of any system, his opinion as 

 to its merits cannot command any confidence. Smith, in his 

 ' Harmonics/ makes this same observation. These systems can 

 all be thoroughly studied by means of my key-board ; whether 

 they ever will be so studied remains to be seen. 



Intervals. 



Intervals are always expressed in terms of equal-temperameut 

 (E.T.) semitones. The following rules are employed for trans- 

 formation of vibration-ratios into E.T. semitones as far as five 

 places of the latter, and vice versa. The rationale is obvious. 



I. To find the value of a given vibration -ratio in E.T. semi- 

 tones. 



From the logarithm of the ratio subtract ^ n of itself; call 

 this the first improved value. From the logarithm subtract Y ho 

 of the first improved value, and , * 00 - of the first improved 

 value. Multiply the result by 40. The product is the value 

 in E.T. semitones correct to five places. 



