QUALITY OF MUSICAL SOUNDS. 179 



the 5ths. We bring the 5th of C in exact accord with the 

 tonic ; then the 5th of D ; then the 5th of E, and finally the 

 5th of F. The 5th of F should be the octave of C, but, by 

 progressing in this way, the last note, C, is too sharp, and is 

 not the octave of the lower C. If this progression were con- 

 tinued higher and higher, the octaves would become more 

 and more out of tune ; and, to avoid this, the octaves are 

 made perfect and the 5ths and 3ds are tuned down, so that 

 the inequality is distributed throughout the scale. This is 

 called tempering the scale, and, with this " temperament," the 

 notes are not exactly true ; still, musicians are accustomed to 

 this, and fail to recognize the mathematical defect. 1 



Even in melody, and still more in harmony, in long com- 

 positions, 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 af- 

 terward to the original key. 



Quality of Musical Sounds. By appropriate means, we 

 can analyze or decompose white light into prismatic colors ; 

 and, in the same way, nearly all musical tones, which seem at 

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

 constituents. There are few absolutely simple sounds used 

 in music. We may take, an example, however, in the tones 

 of great stopped-pipes in the organ. These are simple, but 

 are of an unsatisfactory quality, and wanting in richness. 

 Almost all other tones, however, have a fundamental note, 

 which we recognize at once ; but this note is accompanied by 

 harmonics caused by secondary vibrations of subdivisions of 

 the sonorous body. 



The number, pitch, and intensity of these harmonic, or 

 partial vibrations affect what is called the quality, or timbre 

 of musical tones, by modifying the form of the sonorous 



1 Helmholtz, in the great work we have so often quoted, discusses the faults 

 and inaccuracies of the temperament very fully. ( Theorie physiologique de la 

 musique, Paris, 1868, p. 411, et seq.) 



