Tuning Timbre Spectrum Scale:

To seek out new tonalities, new timbres... To boldly listen to what no one has heard before.

Several years ago I purchased a musical synthesizer with an intriguing feature - each note of the keyboard could be assigned to any desired pitch. This freedom to arbitrarily specify the tuning removed a constraint from my music that I had never noticed or questioned - playing in twelve tone equal temperament. (This is the way modern pianos are tuned. The seven white keys form the major scale and the five black keys fill in the missing tones so that the perceived distance between adjacent notes is (roughly) equal.) Suddenly, new musical worlds opened and I eagerly explored some of the possibilities: unequal divisions of the octave, n equal divisions, and even some tunings not based on the octave at all.

Somehow the timbre, or tone quality of the sounds seemed to be interfering.

Interestingly, it was much easier to play in some tunings than in others. For instance, 19-tone equal temperament (19-tet) with its 19 equal divisions of the octave, is easy. Almost any kind of sampled or synthesized instrument plays well: piano sounds, horn samples, and synthesized flutes all mesh and flow. 16-tet is harder, but still quite feasible. I had to audition hundreds of sounds, but finally found a few good sounds for my 16-tet chords. In 10-tet, though, none of the tones in the synthesizers seemed right on sustained harmonic passages. It was hard to find pairs of notes that sounded reasonable together, and triads were nearly impossible. Everything appeared somewhat out-of-tune, even though the tuning was precisely ten tones per octave. Somehow the timbre, or tone quality of the sounds seemed to be interfering.

The more I experimented with alternative tunings, the more it appeared that certain kinds of scales sound good with some timbres and not with others. Certain kinds of timbres sound good in some scales and not in others. This raised a host of questions: What is the relationship between the timbre of a sound and the intervals, scale, or tuning in which the sound appears "in tune"? Can this relationship be expressed in precise terms? Is there an underlying pattern?

Psychoacoustic studies (scientific studies of how the ear and brain work) can tell us something about music!

Tuning Timbre Spectrum Scale answers these questions by drawing on recent results in psychoacoustics, which allow the relationship between timbre and tuning to be explored in a clear and unambiguous way. Think of these answers as a model of musical perception that makes predictions about what you hear: about what kinds of timbres are appropriate in a given musical context, and what kind of musical context is suitable for a given timbre.

Tuning Timbre Spectrum Scale begins by explaining the relevant terms from the psychoacoustic literature. For instance, the perception of "timbre" is closely related to (but also quite distinct from) the physical notion of the spectrum of a sound. Similarly, the perception of "in-tuneness" parallels the measurable idea of sensory consonance. The key idea is that consonance and dissonance are not inherent qualities of intervals, but are dependent on the spectrum, timbre, or tonal quality of the sound. To demonstrate this, the first audio track on the accompanying CD plays an example where the octave has been made dissonant by devious choice of timbre, even though other, non-octave intervals remain consonant. In fact, almost any interval can be made dissonant or consonant by proper sculpting of the timbre.

Consonance and dissonance depend on the tonal quality of the sound.

Dissonance curves provide a straightforward way to predict the most consonant intervals for a given sound, and the set of most-consonant intervals defines a scale related to the specified spectrum. These allow musicians and composers to design sounds according to the needs of their music, rather than having to create music around the sounds of a few common instruments. The spectrum/scale relationship provides a map for the exploration of nonharmonic musical worlds.

The same kinds of relationships are found in the music of many cultures: the gamelans of Indonesia, Thai classical music, as well as in the western traditions.

To the extent that the spectrum/scale connection is based on properties of the human auditory system, it is relevant to other musical cultures. Two important independent musical traditions are the gamelan ensembles of Indonesia (known for their metallophones and unusual five and seven note scales) and the percussion orchestras of classical Thai music (known for their xylophone-like idiophones and seven tone equal tempered scale). In the same way that instrumental sounds with harmonic partials (for instance, those caused by vibrating strings and air columns) are closely related to the scales of the West, so the scales of the gamelans are related to the spectrum, or tonal quality, of the instruments used in the gamelan. Similarly, the unusual scales of Thai classical music are related to the spectrum of the xylophone-like renat.

Immediate control over consonance and dissonance

But there's more. The ability to measure sensory consonance in a reliable and perceptually relevant manner has several implications for the design of audio signal processing devices and for musical theory and analysis. Perhaps the most exciting of these is a new method of adaptive tuning that can automatically adjust the tuning of a piece based on the timbral character of the music so as to minimize dissonance. Of course, one might cunningly seek to maximize dissonance; the point is that the composer or performer can now directly control this perceptually relevant parameter.

The effects are not subtle.

Fortunately, you can listen to the sounds and the tunings, and verify for yourself that the predictions of the model correspond to what you hear. This is the purpose of the accompanying CD which contains over three hours of sound. Some tracks contain simple examples that help your ear focus on the appropriate aspects of a sound to understand the psychoacoustic definitions and terms. Other tracks contain musical compositions. Some tracks are desgined to fulfill the predictions of the model, and some are designed to violate them; it is not hard to tell the difference. The effects are not subtle.

For more information, there is the overview, the first chapter and table of contents, the full text of the paper Relating Tuning and Timbre, and don't forget to check out the CDs XENTONALITY and EXOMUSICOLOGY, where you'll also find links to download mp3 pieces that show that the effects are very real.

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