41-comma

Interval information

Ratio	36 893 488 147 419 103 232 / 36 472 996 377 170 786 403
Factorization	265 × 3-41
Monzo	[65 -41⟩
Size in cents	19.84496¢
Names	41-comma, Pythagorean countercomma, countercomp comma
Color name	Tribisawa 5th, Wa-41
FJS name	[math]\displaystyle{ \text{6d5} }[/math]
Special properties	reduced, reduced subharmonic
Tenney norm (log2 nd)	129.983
Weil norm (log2 max(n, d))	130
Wilson norm (sopfr(nd))	253
Comma size	small
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The 41-comma, Pythagorean countercomma, or countercomp comma (monzo: [65 -41⟩), is a 3-limit interval of 19.845 cents. It is the amount by which a stack of 41 perfect fifths (3/2) falls short of 24 octaves, in other words 2²⁴/(3/2)⁴¹.

Temperaments

Tempering out this comma leads to the countercomp temperament, which splits the octave into 41 equal parts and maps the harmonic 3 to 24\41. For equal divisions N up to 1230, the comma is tempered out if and only if 41 divides N. Examples are 41edo, 164edo, 205edo, 246edo, 328edo and 369edo. See countercomp family for a number of rank-2 temperaments where it is tempered out.

Terminology

Pythagorean countercomma is derived by analogy to Pythagorean comma. Countercomp comma is derived from the temperament name, which was changed from counterpyth as in earlier materials, where this comma was also called counterpyth comma. It was renamed after the convention was established that the temperament of the Pythagorean comma should be compton, and never Pythagorean, for fear of confusion with Pythagorean tuning.

See also

• Small comma
• Schismic-countercommatic equivalence continuum