875/864: Difference between revisions
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'''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]]. | '''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 == | == Temperaments == | ||
Tempering out the keema is an important way that septimal harmony is organized in [[ | [[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 [[ | 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 == | == Etymology == | ||
Latest revision as of 10:53, 12 October 2025
| Interval information |
Zotriyo comma
875/864, the keema, is a small 7-limit comma measuring about 21.9 cents. It marks the difference between the septimal minor seventh (7/4) and a stack of three just minor thirds (6/5), or between a septimal major seventh (27/14) and a stack of three 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 edos 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 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[1], 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.