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}} | ||
*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 [[ | 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}} | ||
*[[List of approaches to musical tuning]] | |||
*[[Gallery of just intervals]] | * [[List of approaches to musical tuning]] | ||
*[[Families of scales | * [[Gallery of just intervals]] | ||
* [[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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