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 the amount by which twenty-one septimal major seconds exceed five octaves. 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 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