Auditory roughness estimation of complex spectra—Roughness degrees and dissonance ratings of harmonic intervals revisited
Pantelis N. Vassilakis · The Journal of the Acoustical Society of America · 2001
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 (Springer-Verlag, London, 1998)] and introduces an additional term to account for: (a) the contribution of the amplitudes of interferring 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.