Utonality

Otonality and utonality are terms introduced by Harry Partch to describe chords whose pitch classes are the harmonics or subharmonics of a given fixed tone (identity), respectively. For example: 1/1, 2/1, 3/1,... or 1/1, 1/2, 1/3,....

An otonality is a collection of pitches which can be expressed in ratios, expressing their relationship to the fixed tone, that have equal denominators. For example, 1/1, 5/4, and 3/2 (just major chord) form an otonality because they can be written as 4/4, 5/4, 6/4. This in turn can be written as an extended ratio 4:5:6. Every otonality is therefore composed of members of a harmonic series. Similarly, the ratios of a utonality share the same numerator. 7/4, 7/5, 7/6, and 1/1 (7/7) form a utonality, sometimes written as 1/(4:5:6:7), or as 7/(7:6:5:4). Every utonality is therefore composed of members of a subharmonic series.

An otonality corresponds to an arithmetic series of frequencies, or lengths of a vibrating string. Brass instruments naturally produce otonalities, and indeed otonalities are inherent in the harmonics of a single fundamental tone. Tuvan Khoomei singers produce otonalities with their vocal tracts.

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