41-comma: Difference between revisions
Name change following pythagorean -> compton |
+terminology section; name of the equivalence continuum |
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== Temperaments == | == 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. | 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 == | == See also == | ||
* [[Small comma]] | * [[Small comma]] | ||
* [[Schismic- | * [[Schismic-countercommatic equivalence continuum]] | ||
[[Category:Countercomp]] | [[Category:Countercomp]] | ||
Revision as of 05:52, 22 December 2022
| Interval information |
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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.
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.