Hemimage comma: Difference between revisions

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{{Infobox Interval

| Ratio = 10976/10935

| Name = hemimage

| Name = hemimage comma

| Color ~~Name~~ = sz3g3, Satrizo-agu comma

| Color name = sz3g3, Satrizo-agu comma

| 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.

~~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~~.

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).

== ~~See also~~ ==

In the [[19-limit]] it factors into ([[343/342]])⋅([[1216/1215]]), and in the [[29-limit]], ([[406/405]])⋅([[784/783]]), which equals (784/783)2⋅([[841/840]]) in turn, making it a [[lopsided comma]] with [[S-expression]] S282⋅S29.

* [[Hemimage family]]

* [[Hemimage temperaments]]

== Temperaments ==

* [[~~Small~~ comma]]

[[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 ==

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:Commas named by combining multiple temperament names]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | 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
 }}
+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.
-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.
+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).
-== See also ==
+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.
-* [[Hemimage family]]
-* [[Hemimage temperaments]]
+== Temperaments ==
-* [[Small comma]]
+[[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 ==
+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:Commas named by combining multiple temperament names]]