Vol. 30 Issue 2 Reviews
William A. Sethares: Tuning, Timbre, Spectrum, Scale (Second Edition)

Hardcover, 2005, ISBN 1-85233-797-4, 425 pages, 149 figures, appendices, bibliography, discography; CD-ROM with sound and video examples, research papers, software, online references; Springer London Ltd., Ashbourne House, The Guildway, Old Portsmouth Road, Guildford, Surrey, GU3 1LP, UK; telephone (+44) 1483-734431; fax (+44) 1483-734411; World Wide Web www.springer.com/.

Reviewed by Ian Whalley
Hamilton, New Zealand

William Sethares’ curiosity about the relationship between tuning, timbre, spectrum, and scales began after he bought a music synthesizer allowing him to assign different notes to any pitch, and then realizing that some divisions of the octave sounded better than others, and that certain timbres sounded good with some scales but not others. His subsequent research set out to explain, given that a musical work sounded in tune, the connection between the structure of a scale and the structure of the sound used.

The case put forward in Tuning, Timbre, Spectrum, Scale  is that one’s sense of musical consonance or dissonance does not depend on set intervals, but on aligning tuning with the spectrum and timbre of the sound. Further, Mr. Sethares argues that once this relationship is understood, composers can make consonant music using alternate tunings other than twelve-tone equal temperament (12-tet).

Readers without an extensive acoustics background might not warm to the title, and the text’s appeal may largely be to engineers in the first instance. However, the book also provides something of an introduction to alternative tunings and timbre for musician/composers, with extensive appendices and reference sections allowing different pathways into the topic.
Although not a book for the novice, one is led gently through the subject matter that is dealt with in a clear and engaging manner. The introductory chapter surmises that musical intervals can be made to sound consonant by the correct choice of timbre, and proposes a dissonance meter to accurately measure this.  

Chapter two discusses sound quality, particularly the relationship between frequency and pitch, and between the spectrum of a sound and its timbre.  Chapter three, titled “Sound on Sound,” notes that “pairs of sine waves interact to produce interference, beating and roughness, and the simplest setting in the (sensory) dissonance occurs” (p. xi).

Musicians will feel more at home with chapter four, in which different scales and tunings are reviewed and historical dimensions examined, and it also explores what makes a good scale.  Chapter five shows how consonance and dissonance have both perceptual and physical aspects. Different past notions of consonance and dissonance are reviewed and sensory consonance placed in this historical perspective. Chapter six, “Related Spectra and Scales,” illustrates how “the relationship between spectra and tunings is made precise using dissonance curves” (p xii).

“A Bell, A Rock, A Crystal” is the charming title of the next chapter that demonstrates how scales and spectra can be applied in musical composition. The resonant rock from Chaco Canyon is an intriguing idea here. “Adaptive Tuning” is covered in chapter eight, putting forward how composers can change the pitch of notes in real time in response to the intervals played and the spectra of the sounds used. An adaptive algorithm is proposed that can dynamically alter tunings to keep sensory consonance when modulating to other keys within a work.

While the previous chapter sought to adjust the pitches of notes during performance to avoid dissonance, chapter nine,  “A Wing, An Anomaly, A Recollection,” presents the real-time Max program Adaptun, that can be applied to timbre adjustments. Various techniques for the compositional application of timbre adaptation are also outlined.

Chapter ten, “The Gamelan,” illustrates the relationship between the scales used in gamelan music and the instruments, as western instruments relate to western scales. Chapter eleven on “Consonance-Based Music Analysis” shows how one’s sense of consonance and dissonance change during a musical performance.

“From Tuning to Spectrum,” chapter twelve, describes a method of finding related spectra once a desirable scale is found. The following chapter on “Spectral Mappings” shows “how to relocate the partials of a sound for compatibility with a given spectrum, while preserving the richness an character of the sound” (p. xiv).

The next two sections look at the application of two different tunings. Chapter fourteen is focused on 10-tet, noting that “each related spectrum and scale has its own musical theory” (p. xiv); and chapter fifteen deals with the “Classical Music of Thailand and the 7-tet,” particularly examining the tuning in relationship to the spectrum and scale used in this music.

The final chapter, “Speculation, Correlation, Interpretation, Conclusion,” closes the book with philosophical considerations and possible directions. Extensive appendices range from how to use and interpret the FFT, to miscellaneous tunings and tables. The bibliography is broad, and a range of compositional work in the field is presented in the discography.

The CD-ROM contains sound and video files related to the text: ample to get lost in with over three and a half hours of sound examples. These certainly help to come to terms with the text.  Also included on the disc are software programs, Web references, associated technical papers, and extracts from two of Mr. Sethares’ collected works released on the CDs  Xentonality and Exomusicology.

One might be seduced into thinking that this work presents part of a new grand theory of music, as a reviewer on amazon.com claims; but music history reflects a dialectic between new algorithms/technology, exceptional musicians/composers, social conditions/needs, and the intersection of personal and shared musical narratives. Mr. Sethares’ work is a prospective part of this nexus. J. S. Bach’s work with equal temperament in his forty-eight preludes and fugues illustrates what happens when each part of the paradigm comes together.

This book/CD-ROM is a substantial continuing contribution to the future of digital music, presented with a passion rarely encountered in academic writing. The idea that consonance within a scale/tuning can be controlled, in combination with timbre/spectra chosen by computer music composer-musicians, holds out the promise of digital instrument-building becoming a greater part of the creative process, particularly in systematically exploring inharmonic timbres. As such, this approach might provide alternatives to soundscape, acousmatic, and algorithmic idioms that dominate academic and art music. It could also offer different ways to incorporate inharmonic sounds into commercial musical genres.

The proof of the pudding, however, is in the eating. Musical composition, technically and artistically, is more than a treatise on consonance and dissonance; and the reliance on a single idea has led to many technically interesting but artistically impoverished moments in music history.

One of the great strengths of the remarkably robust western 12-tet tuning and major/minor scale system is its inherent potential for dramatic contrast to express the human condition. This is particular so when aptly manipulated in combination with a broad range of other elements one can use to compose. By contrast, many of the musical works on the CD-ROM, apart from the culturally specific examples, left me wondering if the algorithms proposed are solutions in search of an artistic problem that has yet to be widely pondered on, defined, or understood. Of course, there is always room for experimentation, and Mr. Sethares’ work is a labyrinth to revel in for the curious, and presents many avenues to explore.

This updated and expanded second edition of the text first published in 1998 gets us beyond thinking that we are stuck in simple harmonic ratios that have dominated Western music and instrument making for some time. It reminds us to think about music in material terms rather than formally: that things once considered absolute are largely based on perception and convention. Consequently, the book deserves a wide audience, including the intended engineers, instrument/effects manufacturers, and electronic composer-musicians, but hopefully also extending to musicologists and music historians.