Tuning Timbre
Spectrum Scale

by William A. Sethares

Here is a brief guide to Tuning Timbre Spectrum Scale. Click for a quick rundown of the central ideas or for an overview, go to the complete table of contents by clicking on the appropriate chapter, or click to download the first chapter. The book includes a set of sound examples on CD, and the full text of one of the early seminal articles is now available on-line. Several pieces of music that exploit the sound techniques are also available for download in mp3 format.

The Octave is Dead... Long Live the Octave

Introducing a dissonant octave--almost any interval can be made consonant or dissonant by proper choice of timbre.

The Science of Sound

Some basic ideas from psychoacoustics are required to understand the interaction between timbre (or spectrum) and sensory consonance and dissonance.

Sound on Sound

Pairs of sine waves interact to produce interference, beating, roughness, and the simplest setting in which (sensory) dissonance occurs.

Musical Scales

Many scales have been used throughout the centuries.

Consonance and Dissonance of Harmonic Sounds

The words `consonance' and `dissonance' have had many meanings. Tuning Timbre Spectrum Scale focuses primarily on sensory consonance and dissonance.

Related Spectra and Scales

The relationship between spectra and tunings is made precise using dissonance curves. See also the paper Relating Tuning and Timbre.

A Bell, A Rock, A Crystal

Three concrete examples demonstrate the usefulnes of related scales and spectra in musical composition.

Adaptive Tunings

Adaptive tunings modify the pitches of notes as the music evolves in response to the intervals played and the spectra of the sounds employed. You can hear adaptive tuning at work by downloading the piece Three Ears, which is available in mp3 format.

A Wing, An Anomaly, A Recollection

Adaptation: tools for retuning, techniques for composition, strategies for listening.

The Gamelan

In the same way that Western harmonic instruments are related to Western scales, so the nonharmonic spectrum of gamelan instruments are related to the gamelan scales.

Consonance-Based Musical Analysis

The dissonance score demonstrates how sensory consonance and dissonance change over the course of a musical performance. What can be said about tunings used by Domenico Scarlatti using only the extant sonatas?

From Tuning to Spectrum

How to find related spectra given a desired scale.

Spectral Mappings

How to relocate the partials of a sound for compatibility with a given spectrum, while preserving the richness and character of the sound.

A "Music Theory" for 10-tet

Each related spectrum and scale has its own "music theory".

Classical Music of Thailand and 7-tet

Seven-tone equal temperament and the relationship between spectrum and scale in Thai classical music.

Speculation, Correlation, Interpretation, Conclusion




Sound Examples

Follow links for mp3 downloads that explore the relationship between tuning and timbre. 

Tuning Timbre Spectrum Scale is published by Springer-Verlag, and is available in fine college and technical bookstores everywhere. If your bookseller doesn't have it in stock, it's easy to order from your friendly web book seller such as Amazon.com. If you're short on cash, you might check out your local library. They ought to have a copy. If not, tell your librarian.

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