41-comma

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.

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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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.

See also

• Small comma
• Schismic-countercomp equivalence continuum