Just intonation: Difference between revisions

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Other approaches include [http://anaphoria.com/wilsonintroMERU.html Meru scales], [[tritriadic scale]]s, and [[combination product set]]s.
Other approaches include [http://anaphoria.com/wilsonintroMERU.html Meru scales], [[tritriadic scale]]s, and [[combination product set]]s.


==Approximating JI with temperaments==
== Approximating JI with temperaments ==
There are a lot of JI intervals, and it's difficult to keep track of all of them. As such, people often use simpler systems to approximate JI intervals, known as [[temperament]]s. A popular choice is [[equal temperament]]s; for example the predominant [[12edo|12et]], which is widely used to approximate [[5-limit]] JI. Other equal temperaments exist, for example [[19edo|19et]], [[22edo|22et]], and [[31edo|31et]]. Besides equal temperaments, other temperaments exist, such as [[regular temperament]]s and [[well temperament]]s.
There are a lot of JI intervals, and it's difficult to keep track of all of them. As such, people often use simpler systems to approximate JI intervals, known as [[temperament]]s. A popular choice is [[equal temperament]]s; for example the predominant [[12edo|12et]], which is widely used to approximate [[5-limit]] JI. Other equal temperaments exist, for example [[19edo|19et]], [[22edo|22et]], and [[31edo|31et]]. Besides equal temperaments, other temperaments exist, such as [[regular temperament]]s and [[well temperament]]s.


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[[Microtemperaments]] are very accurate and temper out [[unnoticeable comma]]s, and add minimal damage to the intervals of JI, while also simplifying its structure. For example, [[schismic]] flattens the fifth by around 0.2 cents to equate the [[Pythagorean comma]] with the syntonic comma. Microtemperaments are also very useful in higher prime limits, where JI itself becomes too complex.
[[Microtemperaments]] are very accurate and temper out [[unnoticeable comma]]s, and add minimal damage to the intervals of JI, while also simplifying its structure. For example, [[schismic]] flattens the fifth by around 0.2 cents to equate the [[Pythagorean comma]] with the syntonic comma. Microtemperaments are also very useful in higher prime limits, where JI itself becomes too complex.


==Instruments==
== Instruments ==
{{todo|expand|comment=Expand the instruments section with more examples}}
{{Todo|expand|comment=Expand the instruments section with more examples}}
*The [[Kalimba#Array mbira|array mbira]] was designed by [[Bill Wesley]] as a versatile just intonation instrument, covering a 5 octave range.
 
*Most of [[Harry Partch]]'s instruments were designed to be for just intonation.
* The [[Kalimba #Array mbira|array mbira]] was designed by [[Bill Wesley]] as a versatile just intonation instrument, covering a 5 octave range.
==Music==
* Most of [[Harry Partch]]'s instruments were designed to be for just intonation.
 
== Music ==
{{Main|Music in just intonation}}
{{Main|Music in just intonation}}


== Notation ==
== Notation ==
There are various [[Musical notation|notation systems]] for just intonation, for example [[Helmholtz-Ellis notation]] and the [[Functional Just System]].
There are various [[musical notation|notation systems]] for just intonation, for example [[Helmholtz–Ellis notation]] and the [[Functional Just System]].
{{Todo|expand|inline=1}}
{{Todo|expand|inline=1}}


==See also==
== See also ==
{{todo|cleanup|inline=1}}
{{Todo|cleanup|inline=1}}
*[[List of approaches to musical tuning]]
 
*[[Gallery of just intervals]]
* [[List of approaches to musical tuning]]
*[[Families of scales]]
* [[Gallery of just intervals]]
*[[:Category:Just intonation]]
* [[Families of scales]]


==References==
== References ==
<references />
<references />


==Further reading==
== Further reading ==
*[http://www.tonalsoft.com/enc/j/just.aspx Just intonation] on the [[Tonalsoft Encyclopedia]]
* [http://www.tonalsoft.com/enc/j/just.aspx Just intonation] on the [[Tonalsoft Encyclopedia]]
*[http://nowitzky.hostwebs.com/justint/ Just Intonation] by Mark Nowitzky
* [http://nowitzky.hostwebs.com/justint/ Just Intonation] by Mark Nowitzky
*[http://www.kylegann.com/tuning.html Just Intonation Explained] by Kyle Gann
* [http://www.kylegann.com/tuning.html Just Intonation Explained] by Kyle Gann
*[http://www.kylegann.com/Octave.html Anatomy of an Octave] by Kyle Gann
* [http://www.kylegann.com/Octave.html Anatomy of an Octave] by Kyle Gann
*[http://www.dbdoty.com/Words/What-is-Just-Intonation.html What is Just Intonation?] by David B. Doty
* [http://www.dbdoty.com/Words/What-is-Just-Intonation.html What is Just Intonation?] by David B. Doty
*[http://lumma.org/tuning/faq/#whatisJI What is "just intonation"?] by Carl Lumma
* [http://lumma.org/tuning/faq/#whatisJI What is "just intonation"?] by Carl Lumma
*[http://www.dbdoty.com/Words/werntz.html A Response to Julia Werntz] by David B. Doty
* [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
* [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
 
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