COMPOSITION OF SOUND WAVES. 295 



arbitrary tone or absolute pitch, the voice rises or falls in 

 a manner very pleasing to the ear, by eight steps or inter- 

 vals. The whole series of musical tones may be divided 

 into octaves, or groups of eight tones each, the relation 

 between any two members of one group being the same as 

 the relation between the corresponding members of any 

 other group. The eighth of the first group becomes the 

 first of the second. The intervals between the successive 

 tones are not precisely the same, as will be seen from the 

 next paragraph. 



457. Relative Numbers of Vibrations. A 



string vibrating half as rapidly as a given string, will give 

 its octave below ; one vibrating twice as rapidly, its octave 

 above. The ratio of the number of vibrations correspond- 

 ing to the interval of an octave is, therefore, 1:2. The 

 relative number of vibrations corresponding to the tones 

 which constitute the major diatonic scale (gamut) are as 

 follows : 



Relative Names, - : , ^, 1, 2, 3, 4, 5, 6, 7, 8. 



Absolute Names, - - - C, D, E, F, G, A, B, C. 



Syllables, - -do, re, mi, fa, sol, la, si, do. 



Relative Numbers of Vibrations, I, f, , f, f, f, - 1 /, 2. 



24, 27, 30, 32, 36, 40, 45, 48. 



458. Absolute Numbers of Vibrations. 



Knowing the number of vibrations which constitute the 

 tone called do, the absolute number of vibrations of any 

 of the other tones of the scale may be obtained by multi- 

 plying the number of vibrations of do by the ratio between 

 it and that of the given tone as shown above. Thus, if C 

 have 256 vibrations per second, G will have 256 x f 384 



