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Otonality and 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,....
== Definition ==
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. 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. 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.
Utonality is the opposite, corresponding to a subharmonic series of frequencies, or an arithmetic series of wavelengths (the inverse of frequency). The ''arithmetical proportion'' "may be considered as a demonstration of Utonality ('minor tonality')."〔Partch, Harry. ''Genesis of a Music'', p.69. 2nd ed. Da Capo Press, 1974. ISBN 0-306-80106-X.〕
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