v THE SENSE OF HEAKING 227 



meiits in which the partial notes are so weak that they have no 

 musical value. Such are tuning-forks, organ-pipes of the highest 

 tones, and flutes. These instruments may be used to distinguish 

 the quality of the respective fundamental tones. 



The timbre or quality of musical tones i.e. of compound 

 masses of sound expresses the particular character by which the 

 different orchestral instruments, including the human voice, are 

 easily distinguished from one another, even when they give out 

 the same note with uniform intensity (see Vol. III. Chap. III.). 

 When a certain musical note is sung and the same note is sounded 

 on the violin, clarinet, flute, piano, and organ, every tone is composed 

 of the same number of vibrations. Yet they can be distinguished 

 by an ear that is but slightly musical, and referred to the instru- 

 ments which produce them, because the larynx and the various 

 musical instruments give the note a peculiar quality or colour, 

 independently of the number and amplitude of the vibrations. 



The attempt to explain the different qualities of tone leads to 

 the idea that these depend on the different form of the vibrations 

 produced by the different instruments, which in its turn depends 

 on the number, position, and intensity of the over-tones which 

 summate algebraically with the fundamental tone. 



It has long been known to musicians that the separate tones 

 of musical instruments are accompanied by a series of higher 

 tones, known as the harmonics or partial tones of the fundamental 

 tone, which is the lowest of them. When the string of a double 

 bass is made to vibrate over its entire length, a note is obtained 

 in which the trained ear at once recognises complexity, and is 

 able to distinguish a fundamental tone, and that of the octave 

 next above it, which contains double the number of vibrations. 

 This means that while the whole string makes a single vibration, 

 each of its two halves makes two. The proof is given by the 

 fact that if, while the string is vibrating over its entire length, 

 the fundamental note is suppressed by placing the finger in the 

 middle of the string, the octave composed of the vibrations of its 

 two halves, which were not suppressed and which necessarily pre- 

 existed, is distinctly heard. 



But when the string vibrates over its whole length, not only 

 the two halves, but also the three thirds, four fourths, five fifths, 

 etc., of the string vibrate synchronously, producing partial tones 

 that are increasingly higher and weaker, and thus less easy to" 

 distinguish. The pitch of the partials is determined by the 

 fundamental tone. In proportion as this has one vibration, the 

 first harmonic has two, the second three, the third four, the fourth 

 five, etc. If, e.g., the fundamental tone is a c, the series of 

 harmonics will be c 1 , g l , c 2 , e 2 , g 2 , etc. Fig. 90 shows in musical 

 notes the series of harmonic overtones or partials of c. 



It is seen from this that the intervals between the successive 



