1029/1000: Difference between revisions

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{{Infobox Interval

| Name = Keega

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'''1029/1000''', the '''keega''', is a [[medium comma|medium]] [[7-limit]] [[comma]] measuring about 49.5 [[cent]]s. It is the difference between a stack of three [[10/7]]'s and a perfect twelfth ([[3/1]]), or between a stack of three [[7/5]]'s and a perfect eleventh ([[8/3]]), and arises from [[10/7]] being a convergent in the continued fraction of <math>\sqrt[3]{3}</math>.

~~'''1029/1000''', the '''keega''', is a~~ [[~~medium comma|medium]] [[7-limit]] [[comma]] measuring about~~ 49~~.5 [[cent~~]]~~s. It is the difference between a stack of three~~ [[7/5]]'s and ~~a perfect eleventh~~ ([[8/3]])~~, and arises from~~ [[10/7]] ~~being a convergent in the continued fraction of <math>\sqrt[3]{3}</math>~~.

It factors into simpler commas as ([[49/48]])⋅([[126/125]]) and ([[81/80]])⋅([[686/675]]).

== Temperaments ==

Tempering out this comma in the 7-limit leads to the rank-3 [[keegic]] temperament. See [[~~keegic~~ temperaments]] for a collection of rank-2 temperaments where it is tempered out.

[[Tempering out]] this comma in the 7-limit leads to the rank-3 [[keegic]] temperament. See [[Keegic temperaments]] for a collection of rank-2 temperaments where it is tempered out.

== Etymology ==

The name ''keega'' was given by [[Gene Ward Smith]] in 2005. It is a contraction of ''[[keemun]]'' and ''gawel'', although ''gawel'' was later renamed to ''[[liese]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>.

== ~~Notes~~ ==

== References ==

[[Category:Keegic]]

[[Category:Commas named ~~for their regular~~ temperament ~~properties~~]]

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

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+{{Interwiki
+| en = 1029/1000
+| de = 1029/1000
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 {{Infobox Interval
 | Name = Keega
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 | Comma = yes
 }}
+'''1029/1000''', the '''keega''', is a [[medium comma|medium]] [[7-limit]] [[comma]] measuring about 49.5 [[cent]]s. It is the difference between a stack of three [[10/7]]'s and a perfect twelfth ([[3/1]]), or between a stack of three [[7/5]]'s and a perfect eleventh ([[8/3]]), and arises from [[10/7]] being a convergent in the continued fraction of <math>\sqrt[3]{3}</math>.
-'''1029/1000''', the '''keega''', is a [[medium comma|medium]] [[7-limit]] [[comma]] measuring about 49.5 [[cent]]s. It is the difference between a stack of three [[7/5]]'s and a perfect eleventh ([[8/3]]), and arises from [[10/7]] being a convergent in the continued fraction of <math>\sqrt[3]{3}</math>.
+It factors into simpler commas as ([[49/48]])⋅([[126/125]]) and ([[81/80]])⋅([[686/675]]).
 == Temperaments ==
-Tempering out this comma in the 7-limit leads to the rank-3 [[keegic]] temperament. See [[keegic temperaments]] for a collection of rank-2 temperaments where it is tempered out.
+[[Tempering out]] this comma in the 7-limit leads to the rank-3 [[keegic]] temperament. See [[Keegic temperaments]] for a collection of rank-2 temperaments where it is tempered out.
 == Etymology ==
 The name ''keega'' was given by [[Gene Ward Smith]] in 2005. It is a contraction of ''[[keemun]]'' and ''gawel'', although ''gawel'' was later renamed to ''[[liese]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>.
-== Notes ==
+== References ==
 [[Category:Keegic]]
-[[Category:Commas named for their regular temperament properties]]
+[[Category:Commas named by combining multiple temperament names]]