Just intonation: Difference between revisions

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; Other approaches

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

~~== 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.

Temperaments also create new structures not found in JI; for example, [[meantone]] temperament (which 12et [[support]]s) tempers out the syntonic comma [[81/80]], making [[5/4]] the same as the major third obtained by stacking four fifths, [[81/64]]; this structural feature is often assumed without thinking in western music. There are many temperaments in various limits, including the 5-limit, the [[7-limit]], and beyond, as well as many subgroups.

[[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 ==

@@ Line 46: / Line 46: @@
 ; Other approaches
 Other approaches include [http://anaphoria.com/wilsonintroMERU.html Meru scales], [[tritriadic scale]]s, and [[combination product set]]s.
-== 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.
-Temperaments also create new structures not found in JI; for example, [[meantone]] temperament (which 12et [[support]]s) tempers out the syntonic comma [[81/80]], making [[5/4]] the same as the major third obtained by stacking four fifths, [[81/64]]; this structural feature is often assumed without thinking in western music. There are many temperaments in various limits, including the 5-limit, the [[7-limit]], and beyond, as well as many subgroups.
-[[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 ==