Antidilemma: Difference between revisions

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


{{Infobox Interval|Comma=Yes|Ratio=137438953472/96889010407|Name=antidilemma, tsuchi comma}}
'''137438953472/96889010407''', called the '''antidilemma,''' is a "comma" of over 600 cents. It forms the amount by which eleven [[2/1|octaves]] exceeds thirteen [[7/4]]<nowiki/>s, and may be described as ''13-fold 7th subharmonic tritone''. It is called the antidilemma as a counterpart to the dilemma, after forced moral dilemmas in interactive fiction, and after its location almost perfectly in between two octaves (the dilemma is one of the lowest [[Circular temperament|circular]] commas to do this).


'''137438953472/96889010407''', called the '''antidilemma,''' is a "comma" of over 600 cents. It is the amount by which 11 [[Octave|octaves]] exceeds 13 [[7/4]]<nowiki/>s. It is called the antidilemma as a counterpart to the dilemma, after forced moral dilemmas in interactive fiction, and after its location almost perfectly in between two octaves (the dilemma is one of the lowest [[Circular temperament|circular]] commas to do this).
== Temperaments ==
Tempering out the antidilemma leads to the [[Dilemmic and antidilemmic|antidilemmic]] (tsuchi) temperament, which is equivalent to closing the circle of thirteen 7/4s to create [[13edo]], where 7/4 is represented by 11＼13. (If 7/4 is represented by 10＼13 instead, thus tempering out [[96889010407/68719476736]], it leads to the [[dilemmic]] or requiem temperament).


== Temperaments ==
== See also ==
Tempering out the antidilemma leads to the [[Dilemmic and antidilemmic|antidilemmic]] (tsuchi) temperament, which is equivalent to closing the circle of 13 7/4s to create [[13edo]], where 7/4 is represented by 11\13. (If 7/4 is represented by 10\13 instead, thus tempering out [[96889010407/68719476736]], it leads to the [[dilemmic]] or requiem temperament).
* [[Dilemma]] (96889010407/68719476736)


[[Category:Commas named for other reasons]]
[[Category:Commas named for other reasons]]
[[Category:Tritone]]

Revision as of 00:25, 20 April 2025

Interval information
Ratio 137438953472/96889010407
Factorization 237 × 7-13
Monzo [37 0 0 -13⟩
Size in cents 605.2632¢
Names antidilemma,
tsuchi comma,
13-fold 7th subharmonic
FJS name [math]\displaystyle{ \text{ddd}{-2}_{7,7,7,7,7,7,7,7,7,7,7,7,7} }[/math]
Special properties reduced,
reduced subharmonic
Tenney norm (log2 nd) 73.4956
Weil norm (log2 max(n, d)) 74
Wilson norm (sopfr(nd)) 165
Comma size large
Open this interval in xen-calc

137438953472/96889010407, called the antidilemma, is a "comma" of over 600 cents. It forms the amount by which eleven octaves exceeds thirteen 7/4s, and may be described as 13-fold 7th subharmonic tritone. It is called the antidilemma as a counterpart to the dilemma, after forced moral dilemmas in interactive fiction, and after its location almost perfectly in between two octaves (the dilemma is one of the lowest circular commas to do this).

Temperaments

Tempering out the antidilemma leads to the antidilemmic (tsuchi) temperament, which is equivalent to closing the circle of thirteen 7/4s to create 13edo, where 7/4 is represented by 11＼13. (If 7/4 is represented by 10＼13 instead, thus tempering out 96889010407/68719476736, it leads to the dilemmic or requiem temperament).

See also

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