Fynn's comma

Interval information

Factorization	273 × 7-26
Monzo	[73 0 0 -26⟩
Size in cents	10.52643¢
Names	Fynn's comma, 26-7-comma
FJS name	[math]\displaystyle{ \text{7d}{-10}_{7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7} }[/math]
Special properties	reduced, reduced subharmonic
Tenney norm (log2 nd)	145.991
Weil norm (log2 max(n, d))	146
Wilson norm (sopfr(nd))	328
Comma size	small
Open this interval in xen-calc

Fynn's comma (monzo: [73 0 0 -26⟩, ratio: 9 444 732 965 739 290 427 392 / 9 387 480 337 647 754 305 649), or systematically, the 26-7-comma, is a small 7-limit comma measuring about 10.5 cents. It is the amount by which twenty-one octaves exceed twenty-six harmonic sevenths, or 2²¹/(7/4)²⁶. It explains the high accuracy of 26edo's approximate harmonic 7.

Temperaments

Tempering out this comma splits the octave into 26 equal parts and maps 7/4 to 21\26, For edos N up to 1456, it is tempered out if and only if 26 divides N.

Trivia

This interval is the difference between the dilemma, the difference between a 13 7/4s and 10 octaves, and the antidilemma, difference between 13 7/4s and 11 octaves. Since 26edo has an accurate 7/4 not shared with any lower edo, 13edo has almost 50% relative error on it.

See also

• 26th-octave temperaments