Dilemma

See also: antidilemma.

Interval information

Ratio	96889010407/68719476736
Factorization	2-36 × 713
Monzo	[-36 0 0 13⟩
Size in cents	594.7368¢
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
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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.