Abstract
Examination of musical
instrument construction and performance practice indicates that sound
variations involving the sensation of roughness are found in most musical
traditions. A new roughness estimation model is proposed
that better represents the theoretical knowledge and experimental results on
sensory roughness. The model is based on
previous studies [E. Terhardt, Acoustica 30, 201-213
(1974) - W. A. Sethares: Tuning,
Timbre, Spectrum, Scale. London: Springer-Verlag (1998)]
and introduces an additional term to account for: a) the contribution of the amplitudes of
interfering sines to the roughness of a sine-pair and b) the difference between amplitude
modulation depth and degree of amplitude fluctuation. Compared to earlier roughness estimation
models, the proposed model demonstrates the best agreement between estimated
and observed roughness. Possibilities
for further improvement are discussed. A
hypothesis linking dissonance and roughness ratings of harmonic intervals
within the chromatic scale is tested. Clear presence or absence of roughness appears to dominate dissonance
ratings. In other cases, decisions on
dissonance often ignore roughness and are culturally and historically
mediated. The results suggest that, in
the Western musical tradition, the consonance hierarchy of harmonic intervals
corresponds to variations in roughness degrees. Further study should include cross-cultural empirical investigations.
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