726 SPECIAL SENSES 



chord, consisting of the ist, the minor 3d, the 5th and the 8th, is harmo- 

 nious, but it 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, which may 

 be assumed to be the scale of C major : 



ist 2d 3d 4th 5th 6th yth 8th 



Note CDEFGABC 



Lengths of the strings . , . ,. I f i f f f ^ \ 

 Number of vibrations . . . 48 54 60 64 72 80 90 96 



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. 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, with D as the tonic, 

 the 5th would be A. It is assumed that D has 54 vibrations, and A, 

 80, giving a difference of 26. With C as the tonic and G as the fifth, 

 there is a difference of 24. It is on account of these differences in the 

 intervals, that each key in music has a more or less peculiar and dis- 

 tinctive character. 



Even in melody, and still more in harmony, in long compositions, 

 the ear becomes fatigued by a single key, and it is necessary in order to 

 produce the most pleasing effects to change the tonic, by what is called 

 modulation, returning afterward to the original key. 



Quality of Musical Sounds. Nearly all musical sounds, which 

 seem at first to be simple, can be resolved into certain well-defined con- 

 stituents ; but with the exception of the notes of great stopped pipes in 

 the organ, there are few absolutely simple sounds used in music. These 

 simple sounds are pure, but are of unsatisfactory quality and wanting 

 in richness. Almost all other musical sounds have a fundamental tone 

 which is at once recognized ; but this tone is accompanied by harmonics 

 caused by secondary vibrations of subdivisions of the sonorous body. 

 The number, pitch and intensity of these harmonic, or aliquot vibra- 

 tions affect what is called the quality, or timbre of musical notes, by 

 modifying the form of the sonorous waves. A string vibrating a certain 

 number of times in a second, if the vibrations were absolutely simple, 

 would produce, according to the laws of vibrating bodies, a simple musi- 

 cal tone ; but as the string subdivides itself into different portions, one 

 of which gives the 3d, another, the 5th, and so on, of the fundamental, 

 it is evident that the form of the vibrations must be considerably modi- 



