Hemimage comma: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 10976/10935 | | Ratio = 10976/10935 | ||
| Name = hemimage | | Name = hemimage comma | ||
| Color name = sz<sup>3</sup>g3, Satrizo-agu comma | | Color name = sz<sup>3</sup>g3, Satrizo-agu comma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
The '''hemimage comma''' ([[ratio]]: 10976/10935), is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 6.48 [[cent]]s. It marks the difference between a [[16/15|classic diatonic semitone (16/15)]] and a stack of three [[9/7|septimal major thirds (9/7)]] octave reduced, or between a [[10/9|classic whole tone (10/9)]] and a stack of three [[28/27|septimal third tones (28/27)]], therefore interesting to those who work extensively with third tones. | |||
In terms of other commas, it is the difference between [[245/243]] and [[225/224]], the two simplest commas to define the 7-limit [[magic]] temperament. It factors into simpler commas as the [[breedsma]] and the [[aberschisma]], (2401/2400)⋅(5120/5103), or the [[hemimean comma]] and the [[ragisma]], (3136/3125)⋅(4375/4374). | |||
In the [[19-limit]] it factors into ([[343/342]])⋅([[1216/1215]]), and in the [[29-limit]], ([[406/405]])⋅([[784/783]]), which equals (784/783)<sup>2</sup>⋅([[841/840]]) in turn, making it a [[lopsided comma]] with [[S-expression]] S28<sup>2</sup>⋅S29. | |||
== Temperaments == | == Temperaments == | ||
Tempering out this comma alone in the 7-limit leads to the rank-3 [[hemimage]] temperament. See [[Hemimage family]] for the rank-3 family where it is tempered out. See [[Hemimage temperaments]] for a collection of rank-2 temperaments where it is tempered out. | [[Tempering out]] this comma alone in the 7-limit leads to the rank-3 [[hemimage]] temperament. | ||
See [[Hemimage family]] for the rank-3 family where it is tempered out. See [[Hemimage temperaments]] for a collection of rank-2 temperaments where it is tempered out. | |||
== Etymology == | == Etymology == | ||
This comma was first named as ''parahemfi'' by [[Gene Ward Smith]] in 2005 as a contraction of ''[[parakleismic]]'' and ''[[hemififths]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>. It is not clear how it later became ''hemimage'', but the root of ''hemimage'' is obvious, being a contraction of ''hemififths'' and ''[[magic]]''. | This comma was first named as ''parahemfi'' by [[Gene Ward Smith]] in 2005 as a contraction of ''[[parakleismic]]'' and ''[[hemififths]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>. It is not clear how it later became ''hemimage'', but the root of ''hemimage'' is obvious, being a contraction of ''hemififths'' and ''[[magic]]''. | ||
== | == References == | ||
[[Category:Hemimage]] | [[Category:Hemimage]] | ||
[[Category:Commas named by combining multiple temperament names]] | |||