Bauhaus-Universität Weimar

Sound and Music. A Non-Mathematical Treatise on the Physical Constitution of Musical Sounds and Harmony
Taylor, Sedley
two co-existing sounds are no longer simple tones, 
but composite clangs, eacb consisting of a series of 
well developed partial-tones, the case becomes alto¬ 
gether different. Let us examine the state of things 
which then presents itself. 
The sounds of most musical instruments do not 
contain more than the first six partial-tones ; we 
will, therefore, assume this to be the case with the 
clangs before us. No beats can then arise between 
partial-tones of the same clang for the reason as¬ 
signed on p. 164. Dissonance due to beats will, 
however, be produced if a partial-tone belonging 
to one clang is within the specified distance of a 
partial-tone belonging to the other clang. Several 
pairs of tones may be thus situated, and, if so, each 
will contribute its share of roughness to the general 
effect. The intensity of the roughness due to any 
such pair will depend chiefly on the respective 
orders to which the beating partial-tones belong, 
and on the interval between them. The lowest 
partial-tones being the loudest, produce the most 
powerful beats, and half-tone beats are, in general, 
harsher than those of a whole tone. In determining 
the general effect of a combination of two clangs, we 
have to ascertain what pairs of partial-tones come 
within beating-distance, and to estimate the amount 
of roughness due to each pair. The sum of all these


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