41-comma: Difference between revisions
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m Normalising usage of Infobox Interval |
Name change following pythagorean -> compton |
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| Ratio = 36 893 488 147 419 103 232 / <br>36 472 996 377 170 786 403 | | Ratio = 36 893 488 147 419 103 232 / <br>36 472 996 377 170 786 403 | ||
| Monzo = 65 -41 | | Monzo = 65 -41 | ||
| Name = 41-comma, | | Name = 41-comma, Pythagorean countercomma, countercomp comma | ||
| Color name = Tribisawa 5th, Wa-41 | | Color name = Tribisawa 5th, Wa-41 | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
The '''41-comma''', '''Pythagorean countercomma''', or '''countercomp comma''' ([[monzo]]: {{monzo| 65 -41 }}), is a [[3-limit]] interval of 19.845 [[cent]]s. It is the amount by which a stack of 41 perfect fifths ([[3/2]]) falls short of 24 [[octave]]s, in other words 2<sup>24</sup>/(3/2)<sup>41</sup>. | |||
== Temperaments == | == Temperaments == | ||
Tempering out this comma splits the octave into 41 equal parts and maps the harmonic 3 to 24\41 | 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 == | == See also == | ||
* [[Small comma]] | * [[Small comma]] | ||
* [[Schismic- | * [[Schismic-countercomp equivalence continuum]] | ||
[[Category: | [[Category:Countercomp]] | ||
Revision as of 04:51, 22 December 2022
| Interval information |
36 472 996 377 170 786 403
Pythagorean countercomma,
countercomp comma
reduced subharmonic
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.