Much of my work in acoustics is aimed at improving the way things "sound." How can science be applied to our perceptions?
What relationships are there between the timbre (or spectrum) of a sound and the tunings (or musical scales) in which the sound will appear most consonant to the ear? These papers answer this question via an explicit parameterization of Plomp and Levelt's consonance curve, which leads to a family of optimization problems that can be used to answer two complementary issues: Given a scale, what timbre is most appropriate? Given a timbre, what scale is most appropriate?
W. A. Sethares, Local consonance and the relationship between timbre and scale Journal of the Acoustical Society of America, Vol. 94, No. 3, pp. 1218-1228, Sept. 1993.
See also the December 1993 issue of Experimental Musical Instruments, where I revised the above paper and took away all the math. It's called "Relating Tuning and Timbre" and the complete paper is available online for your browsing pleasure.
W. A. Sethares, Tunings for nonharmonic sounds Synaesthetica Conference, Canberra, Australia, Aug. 1994.
Describes an adaptive, consonance based approach to the problem of forming scales that can match a desired set of intervals and can simultaneously be modulated to all keys. One reviewer stated that this paper "sweeps away about five centuries of useless arguments about scales."
W. A. Sethares, Adaptive tunings for musical scales Journal of the Acoustical Society of America, Vol. 96, No. 1, pg. 10-19, July 1994.
W. A. Sethares, "Local consonance and adaptive tunings: sound demonstrations," 127th Meeting of Acoustical Society of America, Boston, MA, June 1994.
Presents a method of mapping the spectrum of a sound so as to make it consonant with a given specified reference spectrum. One application is to transform nonharmonic sounds into harmonic equivalents. Alternatively, it can be used to create nonharmonic instruments that retain the tonal qualities of familiar (harmonic) instruments. Musical uses of such timbres is discussed, and new forms of (nonharmonic) modulation are introduced. A series of sound examples demonstrate both the breadth and limitations of the method.
W. A. Sethares, Consonance based spectral mappings Computer Music Journal 22:1, pp. 56-72, Spring 1998.
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