Antidilemma

See also: dilemma.

Interval information

Ratio	137438953472/96889010407
Factorization	237 × 7-13
Monzo	[37 0 0 -13⟩
Size in cents	605.2632¢
Names	antidilemma, tsuchi comma
FJS name	[math]\text{ddd}{-2}_{7,7,7,7,7,7,7,7,7,7,7,7,7}[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	73.4956
Weil height (log2 max(n, d))	74
Wilson height (sopfr(nd))	165
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.2322 bits
Comma size	large
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137438953472/96889010407, called the antidilemma, is a "comma" of over 600 cents. It is the amount by which 11 octaves exceeds 13 7/4s. 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 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).