91/90: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = biome comma, superleap comma

~~| Ratio = 91/90~~

| Color name = 3ozg2, thozogu 2nd,<br>Thozogu comma

~~| Monzo = -1 -2 -1 1 0 1~~

| Comma = yes

~~| Cents = 19.12985~~

| Name = biome comma, ~~<br>~~ superleap comma

| Color name =

| ~~FJS name =~~

~~| Sound~~ =

}}

The [[superparticular interval]] '''91/90''', the '''biome comma''' or '''superleap comma''', is a [[small comma]] of about 19 ~~cents~~.

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]]).

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

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

[[~~Category:~~13-~~limit~~]]

== Temperaments ==

[[Category:~~Superparticular~~]]

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.

[[Category:~~Small comma~~]]

== 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]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = biome comma, superleap comma
-| Ratio = 91/90
+| Color name = 3ozg2, thozogu 2nd,<br>Thozogu comma
-| Monzo = -1 -2 -1 1 0 1
+| Comma = yes
-| Cents = 19.12985
-| Name = biome comma, <br> superleap comma
-| Color name =
-| FJS name =
-| Sound =
 }}
-The [[superparticular interval]] '''91/90''', the '''biome comma''' or '''superleap comma''', is a [[small comma]] of about 19 cents.
+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]]).
-For temperaments eliminating this comma, see also [[The Biosphere]].
+Being a [[square superparticular|triangle superparticular]], it factors neatly into ([[169/168]])([[196/195]]).
-[[Category:13-limit]]
+== Temperaments ==
-[[Category:Superparticular]]
+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.
-[[Category:Small comma]]
+== 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]]