Antidilemma
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See also: dilemma.
| Ratio | 137438953472/96889010407 |
| Factorization | 237 × 7-13 |
| Monzo | [37 0 0 -13⟩ |
| Size in cents | 605.26322¢ |
| 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 |
| open this interval in xen-calc | |
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).