Otonality and utonality
Otonality[1] and utonality[2] are terms introduced by Harry Partch to describe chords whose pitch classes are the harmonics or subharmonics of a given fixed tone (identity[3]), respectively.
[3] An otonality corresponds to an arithmetic series of frequencies, or lengths of a vibrating string.
For example, the minor triad in root position is made up of the 10th, 12th and 15th harmonics, and 10/10, 12/10 and 15/10 meets the definition of otonal.
A better, narrower definition requires that the harmonic (or subharmonic) series members be adjacent.
Microtonalists have extended the concept of otonal and utonal to apply to all just intonation chords.
Its melodic inverse 10:12:15 has an odd limit of 15, which is greater, therefore the major triad is otonal.
Partch coined the term "Monophony" (not to be confused with monohpony) to describe a system of just intervals deriving from a single starting pitch.
[8] Partch said that his 1931 coinage of "otonality" and "utonality" was "hastened" by having read Henry Cowell's discussion of undertones in New Musical Resources (1930).
Thus otonality and utonality can be viewed as extensions of major and minor tonality respectively.
However, whereas standard music theory views a minor chord as being built up from the root with a minor third and a perfect fifth, a utonality is viewed as descending from what's normally considered the "fifth" of the chord,[9] so the correspondence is not perfect.
Though Partch presents otonality and utonality as being equal and symmetric concepts, when played on most physical instruments an otonality sounds much more consonant than a similar utonality, due to the presence of the missing fundamental phenomenon.
Ben Johnston[10] often uses the otonal as an expanded tonic chord: 4:5:6:7:11:13 (C:E:G:B♭:F↑:A♭) and bases the opening of the third movement of his String Quartet No.
