178 SPECIAL SENSES. 



and 8th, as well as the intermediate notes. If we diminish 

 the 3d by half a tone, which is formed by a string J- the 

 length of the tonic, instead of f, we have, the key converted 

 into the minor. The minor chord, consisting of the 1st, the 

 diminished 3d, the 5th, and the 8th, is perfectly harmonious, 

 but has a quality quite different from that of the major 

 chord. The notes of a melody may progress in the minor 

 key as well as in the major. Taking the small numbers of 

 vibrations merely for convenience, the following is the mode 

 of progression in the natural scale of C major : 



1st. 2d. 3d. 4th. 5th. 6th. 7th. 8th. 



Note, . . . CDEFGABC 



Lengths of the string, 1 f i t f T V * 

 Number of vibrations, 24 27 30 32 36 40 45 48 



The intervals between the notes of the scale, it is seen, 

 are not equal. The smallest, between the 3d and 4th and the 

 7th and 8th, are called semitones. The other intervals are 

 either full perfect tones or small perfect tones. 1 Although 

 there are semitones, not belonging to the key of C, between 

 C and D, D and E, F and G, G and A, and A and B, these 

 intervals are not all composed of exactly the same number of 

 vibrations ; so that, taking the notes on a piano, if we have 

 D as the tonic, its 5th would be A. "We assume that D has 

 27 vibrations, and A, 40, giving a difference of 13. With C 

 as the tonic and G as the 5th, we have a difference of 12. It 

 is on account of these differences in the intervals, that each 

 key in music has a peculiar and an individual character. 



In tuning a piano, which is the single instrument most 

 commonly used for. accompaniment and the general interpre- 

 tation of musical compositions, the ordinary method is by 



1 Although a tone and a semitone do not have an absolutely-fixed value, they 

 are usually defined as above ; but a maximum tone is the interval between the 

 4th and 5th, equal, in the scale we have given, to four vibrations. A minimum 

 tone is the interval between the 3d and 4th, or the 7th and 8th, equal to two or 

 three vibrations. (LA.UGEL, La voix, Voreille et la musique, Paris, 1867, p. 121, 

 .note.) 



