- William A. Sethares: Tuning, Timbre, Spectrum, Scale (Second Edition)
William Sethares's curiosity about the relationship between tuning, timbre, spectrum, and scales began after [End Page 92] 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 2 discusses sound quality, particularly the relationship between frequency and pitch, and between the spectrum of a sound and its timbre. Chapter 3, 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 4, in which different scales and tunings are reviewed and historical dimensions examined, and it also explores what makes a good scale. Chapter 5 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 6, "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, which 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 8, 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.
Whereas the previous chapter sought to adjust the pitches of notes during performance to avoid dissonance, chapter 9, "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 10, "The Gamelan," illustrates the relationship between the scales used in gamelan music and the instruments, as western instruments relate to western scales. Chapter 11, on "Consonance-Based Music Analysis," shows how one's sense of consonance and dissonance change during a musical performance.
"From Tuning to Spectrum," chapter 12, 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...