Dilemma: Difference between revisions

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~~''See also: [[137438953472/96889010407|antidilemma]].''~~{{Infobox Interval|Ratio=96889010407/68719476736|Comma=Yes|Name=dilemma, 7-13 ~~circular comma~~}}

{{Infobox Interval|Ratio=96889010407/68719476736|Comma=Yes|Name=dilemma, requiem comma, 13-7-comma, 13-fold 7th harmonic }}

'''96889010407/68719476736,''' called the '''dilemma,''' is a "comma" of almost 600 cents. It is the amount by which 13 [[7/4]]<nowiki/>s exceeds 10 [[~~Octave~~|octaves]]. It is called the dilemma after forced moral dilemmas in interactive fiction, and after its location almost perfectly in between two octaves (it is one of the lowest [[Circular temperament|circular]] commas to do this).

'''96889010407/68719476736''', called the '''dilemma''' is a "comma" of almost 600 cents. It forms the amount by which thirteen [[7/4]]<nowiki/>s exceeds ten [[2/1|octaves]], and may be described as ''13-fold 7th harmonic tritone''. It is called the dilemma after forced moral dilemmas in interactive fiction, and after its location almost perfectly halfway between two octaves (it is one of the lowest [[Circular temperament|circular]] commas to do this).

== Temperaments ==

Tempering out the dilemma leads to the [[dilemmic]] (requiem) temperament, which is equivalent to closing the circle of 13 7/4s to create [[13edo]], where 7/4 is represented by ~~10\13~~. (If 7/4 is represented by ~~11\13~~ instead, thus tempering out [[137438953472/96889010407]], it leads to the [[antidilemmic]] or tsuchi temperament).

Tempering out the dilemma leads to the [[dilemmic]] (requiem) temperament, which is equivalent to closing the circle of thirteen 7/4s to create [[13edo]], where 7/4 is represented by 10＼13. (If 7/4 is represented by 11＼13 instead, thus tempering out [[137438953472/96889010407]], it leads to the [[antidilemmic]] or tsuchi temperament).

== Approximation ==

Assigning dilemma (as well as antidilemma) to be equal to exactly 600 cents results in the [[26-7-comma]], and arrives at the strong approximation of harmonic 7 by [[26edo]].

== See also ==

* [[Antidilemma]] (137438953472/96889010407)

[[Category:Commas named for other reasons]]

[[Category:Tritone]]

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-''See also: [[137438953472/96889010407|antidilemma]].''{{Infobox Interval|Ratio=96889010407/68719476736|Comma=Yes|Name=dilemma, 7-13 circular comma}}
+{{Infobox Interval|Ratio=96889010407/68719476736|Comma=Yes|Name=dilemma, requiem comma, 13-7-comma, 13-fold 7th harmonic }}
-'''96889010407/68719476736,''' called the '''dilemma,''' is a "comma" of almost 600 cents. It is the amount by which 13 [[7/4]]<nowiki/>s exceeds 10 [[Octave|octaves]]. It is called the dilemma after forced moral dilemmas in interactive fiction, and after its location almost perfectly in between two octaves (it is one of the lowest [[Circular temperament|circular]] commas to do this).
+'''96889010407/68719476736''', called the '''dilemma''' is a "comma" of almost 600 cents. It forms the amount by which thirteen [[7/4]]<nowiki/>s exceeds ten [[2/1|octaves]], and may be described as ''13-fold 7th harmonic tritone''. It is called the dilemma after forced moral dilemmas in interactive fiction, and after its location almost perfectly halfway between two octaves (it is one of the lowest [[Circular temperament|circular]] commas to do this).
 == Temperaments ==
-Tempering out the dilemma leads to the [[dilemmic]] (requiem) temperament, which is equivalent to closing the circle of 13 7/4s to create [[13edo]], where 7/4 is represented by 10\13. (If 7/4 is represented by 11\13 instead, thus tempering out [[137438953472/96889010407]], it leads to the [[antidilemmic]] or tsuchi temperament).
+Tempering out the dilemma leads to the [[dilemmic]] (requiem) temperament, which is equivalent to closing the circle of thirteen 7/4s to create [[13edo]], where 7/4 is represented by 10＼13. (If 7/4 is represented by 11＼13 instead, thus tempering out [[137438953472/96889010407]], it leads to the [[antidilemmic]] or tsuchi temperament).
 == Approximation ==
 Assigning dilemma (as well as antidilemma) to be equal to exactly 600 cents results in the [[26-7-comma]], and arrives at the strong approximation of harmonic 7 by [[26edo]].
+== See also ==
+* [[Antidilemma]] (137438953472/96889010407)
 [[Category:Commas named for other reasons]]
+[[Category:Tritone]]