Bauhaus-Universität Weimar

Titel:
Sound and Music. A Non-Mathematical Treatise on the Physical Constitution of Musical Sounds and Harmony
Person:
Taylor, Sedley
PURL:
https://digitalesammlungen.uni-weimar.de/viewer/image/lit38360/156/
VI. § 73.] 
FOURIERS THEOREM. 
145 
versely as the numbers 1,2, 3, 4, &c. He has fur¬ 
ther shown that each individual wave-form admits 
of being thus compounded in only one way, and has 
provided the means of calculating, in any given case, 
how many, and what, members of the partial series 
will appear, their relative amplitudes and their 
differences of phase. 
When translated from the language of Mechanics 
into that of Acoustics, the theorem of Fourier asserts 
that every regular musical sound is resolvable into 
a definite number of simple tones whose relative 
pitch follows the law of the partial-tone series. It 
thus supplies a theoretical basis for the analysis and 
synthesis of composite sounds which have been ex¬ 
perimentally effected in chapters iv. and v. 
When we are listening to a sustained clang, 
the air, at any one point within the orifice of the 
ear, can have only one definite mode of particle-vi¬ 
bration at any one moment. How does the ear 
behave towards any such given vibration ? It pro¬ 
ceeds as follows. If the vibration is simple, it leaves 
it alone. If composite, it analyzes it into a series of 
simple vibrations whose rates are once, twice, three 
times &c. that of the given vibration, in accordance 
with Fourier’s theorem. In the former event, the 
ear perceives only a simple tone. In the latter, it 
is able to recognize, by suitably directed and assisted 
T. 10
        

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