Just intonation: Difference between revisions
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'''Just intonation''' ('''JI''') is an approach to [[ | '''Just intonation''' ('''JI''') is an approach to [[musical tuning]] where [[pitch]]es are chosen in a way such that every [[interval]] can be expressed as a whole-number [[ratio]] of the [[frequencies]] of pitches. '''Just intervals''' naturally occur in the [[harmonic series]] as intervals between any two [[harmonic]]s of a fundamental tone produced with a harmonic [[timbre]]. For instance, an interval with a frequency ratio of [[3/2]] appears between the 2nd and 3rd harmonics of a harmonic sound. Just intonation is particularly efficient when used with harmonic instruments, because it allows the tuning and the timbre to reinforce each other. | ||
In theory, there are infinitely many just intervals, because each possible [[Wikipedia:Fraction|fraction]] corresponds to a just interval. In practice, however, additional constraints are used to reduce the number of intervals to a reasonable amount, but also in many cases to prioritize [[consonant]] intervals. Usual constraints include [[subgroup]]s of [[generator]]s (including [prime limit]]s), common denominators or numerators (as used in [[primodality]]), and [[complexity]] limits (usually [[height]] limits). Multiple constraints can be applied at the same time as well, such as the intersection of a prime limit and an [[odd limit]]. | |||
In the context of Western music theory prior to the 20th century, the term ''just intonation'' used alone usually refers to [[5-limit]] tuning. ''Extended just intonation'', a term coined by [[Ben Johnston]], usually refers to higher prime limits,<ref>[https://marsbat.space/pdfs/EJItext.pdf Sabat, Marc. ''On Ben Johnston’s Notation and the Performance Practice of Extended Just Intonation'']</ref> such as the [[7-limit]], the [[11-limit]] and the [[13-limit]]. The practice of just intonation without any particular constraint is sometimes referred to as '''rational intonation''' ('''RI''') or as [[free style JI]]. | |||
The structure of just intonation has several implications on music composition. [[Wolf intervals]] and [[commas]], two kinds of dissonant intervals, may appear between distantly-related pitches. In addition, certain chord progressions are [[comma pump]]s, which may cause the tonal center of a piece to drift up or down in pitch over time. These effects can be treated either as features or as problems to be solved. The first approach leads mainly to [[adaptive just intonation]], while the second leads to [[temperament]]. | |||
== Just intonation explained == | == Just intonation explained == | ||
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# ''While related to the above, the use of recurrent sequences is by some included under JI as it involves whole numbers. Wilson's [http://anaphoria.com/wilsonintroMERU.html Meru scales] are a good example.'' | # ''While related to the above, the use of recurrent sequences is by some included under JI as it involves whole numbers. Wilson's [http://anaphoria.com/wilsonintroMERU.html Meru scales] are a good example.'' | ||
# ''Choosing some set of relatively high overtones (disregarding prime limit or subgroups), and using each overtone as a root for extended harmony within the set ([[primodality]], [[neji]]s).'' | # ''Choosing some set of relatively high overtones (disregarding prime limit or subgroups), and using each overtone as a root for extended harmony within the set ([[primodality]], [[neji]]s).'' | ||
== Music == | == Music == | ||
{{ | {{Main|Music in just intonation}} | ||
== See also == | == See also == | ||
* [[List of approaches to musical tuning]] | |||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[Gallery of 12-tone just intonation scales]] | * [[Gallery of 12-tone just intonation scales]] | ||
* [[Gallery of pentatonics]] | * [[Gallery of pentatonics]] | ||
* [[Families of scales]] | * [[Families of scales]] | ||
* [[List of root-3rd-P5 triads in JI]] | * [[List of root-3rd-P5 triads in JI]] | ||
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* [[Hypergenesis58.scl|58 note 11 limit JI scale - hyper-Partchian!]] | * [[Hypergenesis58.scl|58 note 11 limit JI scale - hyper-Partchian!]] | ||
* [[boogiewoogiescale|Boogie woogie scale]] | * [[boogiewoogiescale|Boogie woogie scale]] | ||
* [[:Category:Just intonation | * [[:Category:Just intonation]] | ||
== References == | == References == | ||
<references /> | <references /> | ||
== | == Further reading == | ||
* [http:// | * [http://www.tonalsoft.com/enc/j/just.aspx Just intonation] on the [[Tonalsoft Encyclopedia]] | ||
* [http://www.kylegann.com/tuning.html Just Intonation Explained] by Kyle Gann | * [http://nowitzky.hostwebs.com/justint/ Just Intonation] by Mark Nowitzky | ||
* [http://www.kylegann.com/Octave.html Anatomy of an Octave] by Kyle Gann | * [http://www.kylegann.com/tuning.html Just Intonation Explained] by Kyle Gann | ||
* [http://www.dbdoty.com/Words/What-is-Just-Intonation.html What is Just Intonation?] by David B. Doty | * [http://www.kylegann.com/Octave.html Anatomy of an Octave] by Kyle Gann | ||
* [http://lumma.org/tuning/faq/#whatisJI What is "just intonation"?] by Carl Lumma | * [http://www.dbdoty.com/Words/What-is-Just-Intonation.html What is Just Intonation?] by David B. Doty | ||
* [http://www.dbdoty.com/Words/werntz.html A Response to Julia Werntz] by David B. Doty | * [http://lumma.org/tuning/faq/#whatisJI What is "just intonation"?] by Carl Lumma | ||
* [http://lumma.org/tuning/gws/commaseq.htm Comma Sequences] by Gene Ward Smith | * [http://www.dbdoty.com/Words/werntz.html A Response to Julia Werntz] by David B. Doty | ||
* [http://lumma.org/tuning/gws/commaseq.htm Comma Sequences] by Gene Ward Smith | |||
* [https://casfaculty.case.edu/ross-duffin/just-intonation-in-renaissance-theory-practice/ Just Intonation in Renaissance Theory & Practice] by Ross W. Duffin | * [https://casfaculty.case.edu/ross-duffin/just-intonation-in-renaissance-theory-practice/ Just Intonation in Renaissance Theory & Practice] by Ross W. Duffin | ||
[[Category:Just intonation| ]] <!-- main article --> | [[Category:Just intonation| ]] <!-- main article --> | ||
[[Category:Terms]] | [[Category:Terms]] | ||