Otonality and utonality

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Otonality and utonality are ideas Harry Partch used to describe two ways of building chords from a fixed pitch. Otonality uses harmonic (multiples) of a base tone, while utonality uses subharmonics (divisions) of that same base.

- What they are: An otonality is a set of pitches that can be written as simple ratios with a common denominator and increasing numerators, for example 4/4, 5/4, 6/4, which can also be seen as 4:5:6 (a just major triad). A utonality is the opposite idea, built from a fixed numerator and decreasing denominators, for example 7/4, 7/5, 7/6, 7/7 (1/1).

- How they relate to series: Otonal chords come from the harmonic series. Utonal chords come from the subharmonic series. In practice, otonal chords tend to feel more consonant because the notes share a common “virtual” fundamental. Utonal chords still use the same dyads and roughness but don’t activate that missing fundamental as strongly.

- Narrow versus broad definitions: A narrow definition says only chords whose members are adjacent in their respective series qualify as otonal or utonal (for example, 4:5:6 is an otonality; 10:12:15 is not). Under this view, only a few chords are true otonalities or utonalities: the major triad 4:5:6 and the diminished triad 5:6:7 are otonalities, and the dominant seventh 4:5:6:7 is a tetrad otonality. A broader view allows all just intonation chords to be seen as otonal or utonal, depending on how you stretch the series.

- Odd limit and melodic inversion: In microtonal theory, a chord’s “odd limit” helps classify it. If, when you invert the chord melodically (not just reposition the notes), the odd limit goes up, it’s otonal; if it goes down, it’s utonal; if it stays the same, it’s ambitonal. For example, a major triad 4:5:6 has odd limits 1, 5, and 3; the largest is 5. Its melodic inversion 10:12:15 has an odd limit of 15, which is higher, so it’s otonal. Ambitonal chords can often be heard as either major or minor.

- Examples and uses: The major ninth chord 8:10:12:15:18 is also otonal. Ambitonal chords include the major sixth (12:15:18:20) and the major seventh (8:10:12:15). Partch used otonal and utonal ideas in his music, and other composers have explored expanded tonality using these concepts. The idea that 5-limit otonality equals a major chord and 5-limit utonality equals a minor chord is a starting point, though higher limits can reverse some associations.

- Notable ideas: The terms are part of a broader view where chords in just intonation can be described as otonal, utonal, or ambitonal. Some famous examples discussed in tradition include connections to the Tristan chord and other near-tunings, especially in meantone temperament.

- Extra notes: Partch also coined terms like Monophony to describe his system of intervals from a single starting pitch. The concepts of otonality and utonality have been extended by microtonalists to many chords and tunings.