INTRODUCTION 3 



sensations very near to one another in the scale, but these need 

 not detain us at present. It may be regarded as in the main 

 fully established, chiefly in consequence of the labours of 

 Helmholtz*. The sensation corresponding to a simple-harmonic 

 vibration is called a " simple tone " or a " pure tone," or merely 

 a "tone." The sound emitted by a tuning fork fitted with 

 a suitable resonator, or by a wide stopped organ pipe, gives the 

 best approach to it. 



Since the form of the vibration -curve is fixed, the distinction 

 between one simple tone and another can only be due to 

 difference of frequency or of amplitude. The " frequency," i.e. 

 the number of complete vibrations per second, determines the 

 " pitch," greater frequency corresponding to higher pitch. The 

 lower and upper limits of frequency for tones audible to the 

 human ear are put at about 24 and 24,000 respectively; the 

 range employed in music is much narrower, and extends only 

 from about 40 to 4000. As between tones of the same pitch, 

 the amplitude, or rather its square, determines the rate of 

 supply of energy to the ear and so the relative "intensity," 

 but it will be understood that it is physical rather than 

 subjective intensity that is here involved. Between tones of 

 different pitch only a vague comparison of loudness is possible, 

 and this may have little relation to the supply of energy. Near 

 the limits of audibility the sensation may be feeble, even though 

 the energy-supply be relatively considerable. 



2. Musical Notes. 



From the chaos of more complex sounds there stands out a 

 special class, viz. that of musical "notes." The characteristic of 

 such sounds is that the sensation is smooth, continuous, and 

 capable (at least in imagination) of indefinite prolongation 

 without perceptible change. The nature of the corresponding 

 vibrations is well ascertained. If we investigate any contrivance 



* Hermann Helmholtz (1821 94), successively professor of physiology 

 (Konigsberg 1849), anatomy (Bonn 1855), physiology (Heidelberg 1858) and 

 physics (Berlin 1871). Reference will often be made to his classical work : Die 

 Lehre von den Tonempfindungen als physiologische Grundlage filr die Theorie der 

 Musik, Brunswick, 1862. An English translation from the third edition (1870) 

 was published by A. J. Ellis under the title Sensations of Tone, London, 1875. 



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