.pdf papers

Here are links to a number of the original technical articles that make up the core of the ideas presented in Tuning, Timbre, Spectrum, Scale. These can be found in the pdf/ directory on the CD. In addition, there is a .html version of an article that originally appeared in Experimental Musical Instruments that considers many of the basic ideas. It's called Relating Tuning and Timbre.

"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. [An explicit parameterization of Plomp and Levelt's consonance curve leads to a family of optimization problems which are used to answer two complementary issues: Given a scale, what timbre is most appropriate? Given a timbre, what scale is most appropriate?]

"Adaptive tunings for musical scales", Journal of the Acoustical Society of America, vol. 96, no. 1, pg. 10-19, July 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."]

"Specifying Spectra for Musical Scales", J. of the Acoustical Society of America in 102(4), Oct. 1997. [Presents a method of specifying the spectrum of a sound so as to maximize a measure of consonance with a given desired scale.]

(with John Sankey) "A consonance-based approach to the harpsichord tuning of Domenico Scarlatti", J. of the Acoustical Society of America, April, 1997. [Applies psychoacoustic measure of "total dissonance" to the problem of reconstructing musical scales that best fit the extant work of Scarlatti.]

"Consonance based spectral mappings", Computer Music Journal 22:1, 56-72, Spring 1998. [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]

"Real-time adaptive tunings using MAX", Journal of New Music Research, Vol. 31, No. 4, Dec 2002. [Details the simplifications needed to implement an adaptive tuning algorithm in real time. Introduces the notion of a "context", which imparts a kind of memory to the adaptation.]

"The Forms of Tonality", by Paul Erlich. [Illustrates the concepts of tone-lattices, scales, periodicity and notational systems for 5-limit and 7-limit music.]

"Tuning, Tonality, and Twenty-Two-Tone Temperament", by Paul Erlich. [Considers notions of generalized diatonic scales, with great figures and comparisons of a number of tunings.]

"The Hermode Tuning System", by Werner Mohrlok. [Detailed discussion of the inner workings of the hermode system of adaptive tuning.]