PITCH OF MUSICAL SOUNDS. 173 



rapidity of the regular vibrations ; and quality, upon the 

 combinations of different notes in harmony, the character of 

 the harmonics of fundamental tones, and the form of the vi- 

 brations. 



Pitch of Musical Sounds. In discussing the pitch of 

 musical sounds, we shall leave out of the question, for the 

 present, the harmonics, which exist in nearly all musical 

 tones and affect their quality, and confine ourselves to the 

 study of simple vibrations. Such tones 'are those of great 

 organ-pipes, which are deficient in harmonics and in over- 

 tones, and are almost entirely pure. 



Pitch depends upon the number of vibrations. A musical 

 sound may be of greater or less intensity ; it may at first be 

 quite loud and gradually die away ; but the number of vibra- 

 tions in a definite tone is invariable, be it weak or powerful. 

 The rapidity of the conduction of sound does not vary with 

 its intensity or pitch, and, in the harmonious combination 

 of the sounds of different instruments, be they high or low 

 in pitch, intense or feeble, it is always the same in the same 

 conducting medium. Distinct musical tones may present an 

 immense variety of qualities, but all tones of the same pitch 

 have absolutely equal rates of vibration. Tones equal in 

 pitch are said to be in unison. This fact, though simple, has 

 a most important physiological bearing. In the first place, 

 an educated ear can, without difficulty, distinguish slight dif- 

 ferences in pitch, in ordinary musical tones. 1 Again, we as- 

 certain by experiment that this power of appreciation of 

 tones is restricted within well-defined limits, which vary 

 slightly in different individuals. Without citing all of the 

 numerous observations upon this point, we may state that 

 Helmholtz, whose authority is the very highest, gives, as the 



1 Helmholtz states, on the authority of E. H. Weber, that " experienced mu- 

 sicians can appreciate a difference in pitch corresponding to a relation of vibra- 

 tions of 1,000 to 1,001. This would equal about ^ of a semitone." (HELM- 

 HOLTZ, Theorie. physiologique de ia musique, Paris, 1868, p. 183.) 



