Dilemma
See also: antidilemma.
| Ratio | 96889010407/68719476736 |
| Factorization | 2-36 × 713 |
| Monzo | [-36 0 0 13⟩ |
| Size in cents | 594.73678¢ |
| Names | dilemma, 7-13 circular comma |
| FJS name | [math]\text{ddd9}^{7,7,7,7,7,7,7,7,7,7,7,7,7}[/math] |
| Special properties | reduced, reduced harmonic |
| Tenney height (log2 nd) | 72.4956 |
| Weil height (log2 max(n, d)) | 72.9912 |
| Wilson height (sopfr(nd)) | 163 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.19649 bits |
| Comma size | large |
| open this interval in xen-calc | |
96889010407/68719476736, called the dilemma, is a "comma" of almost 600 cents. It is the amount by which 13 7/4s exceeds 10 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 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).
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.