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Otonality and Utonality are terms introduced by Harry Partch to describe chords whose notes are the overtones (multiples) or "undertones" (divisors) of a given fixed tone. Harry Partch (June 24, 1901 – September 3, 1974) was an American composer. ...
Definition An Otonality is a collection of pitches which can be expressed in ratios which have equal denominators. For example, 1/1, 5/4, and 3/2 form an Otonality because they can be written as 4/4, 5/4, 6/4. Every Otonality is therefore part of the harmonic series. Similarly, the ratios of an Utonality share the same numerator. 7/4, 7/5, 7/6, and 1/1 (7/7) form an Utonality. Pitched musical instruments are usually based on a harmonic oscillator such as a string or a column of air. ...
An Otonality corresponds to an arithmetic series of frequencies or a harmonic series of wavelengths or distances on a string instrument. 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. // Definition In mathematics, an arithmetic series is the sum of the components of an arithmetic progression. ...
See harmonic series (music) for the (related) musical concept. ...
A string instrument (or stringed instrument) is a musical instrument that produces sound by means of vibrating strings. ...
A brass instrument is a musical instrument whose tone is produced by vibration of the lips as the player blows into a tubular resonator (mouthpiece). ...
The Tuva Republic (Russian: ; Tuvan: Тыва РеÑпублика) is a federal subject of Russia (a republic). ...
Khoomei (Tuvan language: Хөөмей, Mongolian:Khöömii, Simplified Chinese:呼麦, Traditional Chinese:呼麥), also spelled Xoomii, Xöömei, Xöömej, Khöömei, or Höömey, is a type of throat singing used in folk music from Tuva and Mongolia. ...
Utonality is the opposite, corresponding to a harmonic series of frequencies or an arithmetic series of wavelengths. If a string such as that of a monochord is divided into equal parts, it will produce an Utonality. A monochord is an ancient musical and scientific laboratory instrument. ...
Relationship to standard Western music theory The 5-limit Otonality is simply a just major chord, and the 5-limit Utonality is a just minor chord. 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, an Utonality is viewed as descending downwards from what's normally considered the "fifth" of the chord, so the correspondence is not perfect. Just intonation tunings and scales can be described by giving an upper bound on the complexity of the harmonies admitted by the tuning or scale. ...
Just intonation is any musical tuning in which the frequencies of notes are related by whole number ratios. ...
Generally speaking, a major chord is any chord which has a major third above its root, as opposed to a minor chord which has a minor third. ...
Generally speaking, a minor chord is any chord which has a minor third above its root, as opposed to a major chord which has a major third. ...
A minor third is the smaller of two commonly occurring musical intervals that span three diatonic scale degrees. ...
The perfect fifth or diapente is one of three musical intervals that span five diatonic scale degrees; the others being the diminished fifth, which is one semitone smaller, and the augmented fifth, which is one semitone larger. ...
In the era of meantone temperament, augmented sixth chords of the kind known as the German (or depending on how it resolves, the English) sixth were close in tuning and sound to the 7-limit Otonality, called the tetrad. This chord might be, for example, Ab-C-Eb-F#, where the F# replaces Gb, which would have made it a dominant seventh. Standing alone, it has something of the sound of a dominant seventh, but considerably less dissonant. It has also been suggested that the Tristan chord, for example, F-B-D#-G# can be considered a Utonality, or 7-limit utonal tetrad, which it closely approximates if the tuning is meantone, though presumably less well in the tuning of a Wagnerian orchestra. Meantone temperament is a system of musical tuning. ...
An augmented sixth chord is a chord which has the interval of an augmented sixth between its highest and lowest notes and also a major third above the lowest note. ...
A seventh chord is a chord or triad which has a note the seventh above the tonic in it. ...
The Tristan chord is a chord made up of the notes F, B, D# and G#. More generally, it can be any chord that consists of these same intervals (from the bottom up, an augmented fourth, a major third, and a perfect fourth). ...
Criticism 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 difference tones. In an Otonality all the difference tones are elements of the same harmonic series, so they reinforce the tonality, but in an Utonality the difference tones are all different and they tend to destabilize the tonality. Consonance is a stylistic device, often used in poetry. ...
Also called a Tartini tone, a combination tone is a usually lower pitch produced inside the inner ear by the presence of two external pitches. ...
Pitched musical instruments are usually based on a harmonic oscillator such as a string or a column of air. ...
It could be argued that Otonality and Utonality are equally consonant simply because they have the same sets of intervals between pairs of pitches, but in that case there are other pitch collections that must be considered. For example, the chord 9:10:12:15 is not part of any Otonality or Utonality below the 15 limit, but all its intervals are consonant within the 9 limit. Just intonation tunings and scales can be described by giving an upper bound on the complexity of the harmonies admitted by the tuning or scale. ...
See also
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