Hemimage comma: Difference between revisions

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The '''hemimage''', '''10976/10935''', is a [[7-limit]] [[comma]] measuring about 6.5 [[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. It is also the difference between [[245/243]] and [[225/224]], the two simplest commas to define the 7-limit [[magic]] temperament~~. Tempering it out leads to the [[hemimage family]] of temperaments~~.

The '''hemimage''', '''10976/10935''', is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 6.5 [[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. It is also the difference between [[245/243]] and [[225/224]], the two simplest commas to define the 7-limit [[magic]] temperament.

== ~~See also~~ ==

== Temperaments ==

* [[Hemimage family]]

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.

* [[Hemimage temperaments]]

* [[~~Small~~ comma]]

== 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]]''.

== Notes ==

[[Category:Hemimage]]

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

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-The '''hemimage''', '''10976/10935''', is a [[7-limit]] [[comma]] measuring about 6.5 [[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. It is also the difference between [[245/243]] and [[225/224]], the two simplest commas to define the 7-limit [[magic]] temperament. Tempering it out leads to the [[hemimage family]] of temperaments.
+The '''hemimage''', '''10976/10935''', is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 6.5 [[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. It is also the difference between [[245/243]] and [[225/224]], the two simplest commas to define the 7-limit [[magic]] temperament.
-== See also ==
+== Temperaments ==
-* [[Hemimage family]]
+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.
-* [[Hemimage temperaments]]
-* [[Small comma]]
+== 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]]''.
+== Notes ==
 [[Category:Hemimage]]
+[[Category:Commas named by combining multiple temperament names]]