248 



PHYSIOLOGY 



CHAP. 



correspond to f of d. In harmony it is, however, necessary to be 

 able to begin the scale on any note desired, giving it the value of 

 the keynote, or tonic, and the octave has therefore been divided 

 into twelve intervals of perfectly equal semitones (in the ratio of 

 1 '05946 to 1) : so that all the intervals except the octave have to 



m 



H c d e f g a h c' d' e' f g' a' h' c' d" e" f" g' 



I 





< | 1 



Si do re mi fa sol la si doi rel mil f a l soil lai sil do2 re2 mi2 f a 2 so!2 



FIG. 101. The upper figure shows part of the keys of a piano or harmonium with the symbols for 

 notes used in Germany ; the lower, the single notes corresponding to the white keys (scale of 

 C major) in the key of the violin or double bass, with the international nomenclature. 

 (Roiti.) 



be slightly altered. This is the tempered scale followed by all 

 instruments with fixed notes (pianoforte, organ, flute, etc.) and by 

 the orchestra in general, while the former is the so-called natural 

 scale. The following table brings out the differences in the two 

 scales : 



" The force of education and of habit is so great," writes Eoiti, 

 " that musicians usually follow the tempered scale, even in 

 singing without accompaniment. But well-established experi- 

 ments have proved beyond a doubt that in celebrated string 

 quartets the great performers (using instruments without fixed 

 notes) play by ear alone, and follow the natural scale, which 

 science did not invent, but has only discovered." 



In music, the intervals between two notes given out simul- 





