434 PHYSIOLOGICAL PHYSICS, tchap. xxxn. 



produced. Again, the fifth, f , would be produced by 

 one note of 264 vibrations, and another of 396, the 

 difference being 132, the number at which roughness 

 disappears. The fourth, -|, gives the following : 



352 264 = 88; 



and here the roughness will be perceptible. This will 

 be more marked with the major third, |-, viz. : 



330 264=66. 



With the interval of" a second, |^ the roughness is very 

 great, namely, 



297 --264 = 33; 



for here, according to Helmholtz, the number of beats 

 is the most discordant. 



Thus, it is seen that in their results, the physical 

 theory and the physiological sensation agree remark- 

 ably. It is to be noted that where the difference 

 between the fundamental tones is too great to occasion 

 beats, their overtones may beat, and so produce dis- 

 sonance. (See page 438.) 



Quality of musical sounds. The third feature 

 of musical sounds is their quality. Every one knows 

 that there is a marked difference between the note of 

 a pianoforte and a note of the same pitch produced 011 

 a violin, and between these two and a note of the 

 same pitch produced by the human voice, a marked 

 difference also between a note of the same pitch pro- 

 duced by two voices. This distinction between notes 

 of the same pitch as produced by different instruments 

 is signified by saying that they differ in quality, that, 

 for instance, one produces rich tones and another thin, 

 one produces mellow tones and another harsh, and so 

 on. It is apparent that neither the amplitude of the 

 vibrations nor their frequency can account for this 

 feature. The difference in character is said to depend 

 on the quality of the note. The Germans use the 



