41-comma: Difference between revisions
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{{monzo|65 -41}}, the '''41-comma''', is an interval of 19.845 [[cent]]s. It is the amount by which 41 fifths ([[3/2]]) fall short of 24 [[octave]]s, in other words 2<sup>24</sup>/(3/2)<sup>41</sup>. 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]]. | {{monzo|65 -41}}, the '''41-comma''', is an interval of 19.845 [[cent]]s. It is the amount by which 41 fifths ([[3/2]]) fall short of 24 [[octave]]s, in other words 2<sup>24</sup>/(3/2)<sup>41</sup>. 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]]. | ||
== Temperaments == | |||
Tempering out the 41-comma splits the octave into 41 equal parts and maps the harmonic 3 to 24\41. It leads to a number of regular temperaments in the [[41-commatic family]]. | |||
=== 41-commatic (41&205) === | |||
Subgroup: 2.3.5 | |||
[[Comma list]]: {{monzo|65 -41}} | |||
[[Mapping]]: [{{val| 41 65 0 }}, {{val| 0 0 1 }}] | |||
Mapping generators: ~531441/524288, ~5 | |||
[[POTE generator]]: ~5/4 = 386.668 | |||
{{Val list|legend=1| 41, 164, 205 }} | |||
[[Badness]]: 0.934310 | |||
== See also == | == See also == | ||
Revision as of 21:26, 21 April 2021
| Interval information |
41-3-comma
reduced subharmonic
[65 -41⟩, the 41-comma, is an interval of 19.845 cents. It is the amount by which 41 fifths (3/2) fall short of 24 octaves, in other words 224/(3/2)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.
Temperaments
Tempering out the 41-comma splits the octave into 41 equal parts and maps the harmonic 3 to 24\41. It leads to a number of regular temperaments in the 41-commatic family.
41-commatic (41&205)
Subgroup: 2.3.5
Comma list: [65 -41⟩
Mapping: [⟨41 65 0], ⟨0 0 1]]
Mapping generators: ~531441/524288, ~5
POTE generator: ~5/4 = 386.668
Badness: 0.934310