91/90: Difference between revisions

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The [[superparticular interval]] '''91/90''', the '''biome comma''' or '''superleap comma''', is a [[small comma|small]] [[13-limit]] [[comma]] of about 19 [[cent]]s. It arises in several places in 13-limit just intonation, most notably as the difference between [[13/12]] and [[15/14]], between [[13/9]] and [[7/5]], between [[7/6]] and [[15/13]], and between [[9/7]] and [[13/10]] (and their [[octave complement]]s, i.e. between [[24/13]] and [[28/15]], between [[18/13]] and [[10/7]], between [[12/7]] and [[26/15]], and between [[14/9]] and [[20/13]]).

The [[superparticular interval]] '''91/90''', the '''biome comma''' or '''superleap comma''', is a [[small comma|small]] [[13-limit]] [[comma]] of about 19 [[cent]]s. It arises in several places in 13-limit just intonation, most notably as the difference between [[13/12]] and [[15/14]], between [[13/9]] and [[10/7]], between [[7/6]] and [[15/13]], and between [[9/7]] and [[13/10]] (and their [[octave complement]]s, i.e. between [[24/13]] and [[28/15]], between [[18/13]] and [[10/7]], between [[12/7]] and [[26/15]], and between [[14/9]] and [[20/13]]).

Being a [[square superparticular|triangle superparticular]], it factors neatly into ([[169/168]])([[196/195]]).

== Temperaments ==

~~For temperaments eliminating~~ this comma~~, see~~ [[The Biosphere]].

Tempering out this comma in the full 13-limit results in the rank-5 '''biosphere temperament'''. See [[The Biosphere]]. An obvious further temperament is to temper out 169/168 and/or 196/195, equating [[14/13]] with 13/12~15/14. This in the 2.3.5.7.13 [[subgroup]] results in the [[sengic]] temperament.

== Etymology ==

''Superleap'' is a contraction of ''superpyth'' and ''leapday'', referring to the two rank-2 temperaments that temper out this comma.

== See also ==

* [[List of superparticular intervals]]

{{todo|research|add etymology|inline=1|comment=Add etymology for “biome”.}}

[[Category:Commas with unknown etymology]]

[[Category:Commas named by combining multiple temperament names]]

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-The [[superparticular interval]] '''91/90''', the '''biome comma''' or '''superleap comma''', is a [[small comma|small]] [[13-limit]] [[comma]] of about 19 [[cent]]s. It arises in several places in 13-limit just intonation, most notably as the difference between [[13/12]] and [[15/14]], between [[13/9]] and [[7/5]], between [[7/6]] and [[15/13]], and between [[9/7]] and [[13/10]] (and their [[octave complement]]s, i.e. between [[24/13]] and [[28/15]], between [[18/13]] and [[10/7]], between [[12/7]] and [[26/15]], and between [[14/9]] and [[20/13]]).
+The [[superparticular interval]] '''91/90''', the '''biome comma''' or '''superleap comma''', is a [[small comma|small]] [[13-limit]] [[comma]] of about 19 [[cent]]s. It arises in several places in 13-limit just intonation, most notably as the difference between [[13/12]] and [[15/14]], between [[13/9]] and [[10/7]], between [[7/6]] and [[15/13]], and between [[9/7]] and [[13/10]] (and their [[octave complement]]s, i.e. between [[24/13]] and [[28/15]], between [[18/13]] and [[10/7]], between [[12/7]] and [[26/15]], and between [[14/9]] and [[20/13]]).
+Being a [[square superparticular|triangle superparticular]], it factors neatly into ([[169/168]])([[196/195]]).
 == Temperaments ==
-For temperaments eliminating this comma, see [[The Biosphere]].
+Tempering out this comma in the full 13-limit results in the rank-5 '''biosphere temperament'''. See [[The Biosphere]]. An obvious further temperament is to temper out 169/168 and/or 196/195, equating [[14/13]] with 13/12~15/14. This in the 2.3.5.7.13 [[subgroup]] results in the [[sengic]] temperament.
+== Etymology ==
+''Superleap'' is a contraction of ''superpyth'' and ''leapday'', referring to the two rank-2 temperaments that temper out this comma.
 == See also ==
 * [[List of superparticular intervals]]
+{{todo|research|add etymology|inline=1|comment=Add etymology for “biome”.}}
+[[Category:Commas with unknown etymology]]
+[[Category:Commas named by combining multiple temperament names]]