875/864: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = keema | | Name = keema | ||
| Color name = | | Color name = zy<sup>3</sup>1, zotriyo 1sn, <br>Zotriyo comma | ||
| | | Comma = yes | ||
}} | }} | ||
'''875/864''', the '''keema''', is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 21.9 [[cent]]s. It marks the difference between the [[7/4|septimal minor seventh (7/4)]] and a stack of three [[6/5|just minor thirds (6/5)]], or between a [[27/14|septimal major seventh (27/14)]] and a stack of three [[5/4|just major thirds (5/4)]]. It is also the sum of [[245/243]] and [[225/224]], the sum of [[100/99]] and [[385/384]], the sum of [[105/104]] and [[325/324]], and the difference between [[49/48]] and [[126/125]]. | |||
== Temperaments == | |||
[[Tempering out]] the keema is an important way that septimal harmony is organized in [[edo]]s of medium size; keemic sets [[25/24]] and [[36/35]] equal, resulting in the distance between the classical major and minor thirds being narrowed, so that [[7/6]]–6/5–5/4–[[9/7]] are made equidistant (an "opposite" option to [[myna]], which widens that distance instead to insert a neutral third, [[49/40]], into this equidistance). Edos with this structure include {{EDOs| 15, 19, 22, 26, and 41 }} (though 15edo tunes 9/7 very poorly). | |||
== | Tempering it out alone in the 7-limit leads to the [[keemic]] rank-3 temperament, whose extensions form the rank-3 [[keemic family]], enabling [[keemic chords]]. See [[Keemic temperaments]] for a collection of rank-2 temperaments where it is tempered out. | ||
== Etymology == | |||
This comma was first named as ''supermagic'' by [[Gene Ward Smith]] in 2005 as a contraction of ''[[superkleismic]]'' and ''[[magic]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>, hence the name of the corresponding rank-3 temperament. It is not clear how it later became ''keema'', but the root of ''keema'' is obvious, being a contraction of ''[[keemun]]'' and ''magic''. | |||
== Notes == | |||
[[Category:Keemic]] | [[Category:Keemic]] | ||
[[Category:Commas named after music theorists]] | |||