Antidilemma

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 height (log2 nd)	73.4956
Weil height (log2 max(n, d))	74
Wilson height (sopfr(nd))	165
Harmonic entropy (Shannon, [math]\displaystyle{ \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 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

• Dilemma (96889010407/68719476736)