2080/2079: Difference between revisions

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| Comma = yes

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'''2080/2079''', the '''ibnsinma''', otherwise known as the '''sinaisma''', is a [[13-limit]] [[~~unnoticeable~~ comma]] measuring about 0.83 [[cent]]s. It is the amount by which a stack consisting of [[11/10]] and [[14/13]] falls short of Pythagorean minor third, [[32/27]].

'''2080/2079''', the '''ibnsinma''', otherwise known as the '''sinaisma''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] [[comma]] measuring about 0.83 [[cent]]s. It is the amount by which a stack consisting of [[11/10]] and [[14/13]] falls short of Pythagorean minor third, [[32/27]].

== Commatic relations ==

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== Temperaments ==

~~By tempering it~~ out ~~is defined~~ the '''ibnsinmic''' or '''sinaismic ~~temperament~~''', which enables the [[ibnsinmic chords|ibnsinmic a.k.a. sinaismic chords]], the [[essentially tempered chord]]s in the [[21-odd-limit]]. Another consequence is that it makes ~~[[fifth complement]]s of~~ [[13/11]] and [[80/63]], ~~and of~~ [[40/33]] and [[26/21]]. You may find a list of good equal ~~temperaments~~ that support this temperament below.

[[Tempering out]] this comma in the 13-limit defines the rank-5 '''ibnsinmic''' or '''sinaismic''' temperament, which enables the [[ibnsinmic chords|ibnsinmic a.k.a. sinaismic chords]], the [[essentially tempered chord]]s in the [[21-odd-limit]]. Another consequence is that it makes [[13/11]] and [[80/63]] [[fifth complement]]s of each other, as well as [[40/33]] and [[26/21]]. You may find a list of good [[equal temperament]]s that [[support]] this temperament below.

[[Subgroup]]: 2.3.5.7.11.13

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| ⟨ || 0 || 0 || 0 || 0 || 1 || 1 || ]]

|}

: mapping generators: ~2, ~3, ~5, ~7, ~11

: ~~mapping generators~~: ~2, ~3, ~5, ~7, ~11

[[Optimal tuning]]s:

: [[WE]]: ~2 = 1199.9519{{c}}, ~3/2 = 702.0756{{c}}, ~5/4 = 386.3580{{c}}, ~7/4 = 968.9979{{c}}, ~11/8 = 551.5774{{c}}

: [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0843{{c}}, ~5/4 = 386.3184{{c}}, ~7/4 = 968.9934{{c}}, ~11/8 = 551.5497{{c}}

{{Optimal ET sequence|legend=1| 12f, 14cf, 15, 17c, 19, 22f, 26, 29, 31f, 39df, 41, 46, 53, 58, 72, 87, 111, 130, 183, 198, 224, 270, 494, 764, 935, 1075, 1205, 1699, 2280, 2774e, 3326de, 3596de, 3907bdee, 4401bdee, 4671bde }} *

<nowiki>*</nowiki> [[optimal patent val]]: [[3044edo|3044]]

[[Badness]] (Sintel): 0.149

== Etymology ==

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== See also ==

* [[Unnoticeable comma]]

* [[List of superparticular intervals]]

== ~~Notes~~ ==

== References ==

[[Category:Ibnsinmic]]

[[Category:Commas named after polymaths]]

@@ Line 4: / Line 4: @@
 | Comma = yes
 }}
-'''2080/2079''', the '''ibnsinma''', otherwise known as the '''sinaisma''', is a [[13-limit]] [[unnoticeable comma]] measuring about 0.83 [[cent]]s. It is the amount by which a stack consisting of [[11/10]] and [[14/13]] falls short of Pythagorean minor third, [[32/27]].
+'''2080/2079''', the '''ibnsinma''', otherwise known as the '''sinaisma''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] [[comma]] measuring about 0.83 [[cent]]s. It is the amount by which a stack consisting of [[11/10]] and [[14/13]] falls short of Pythagorean minor third, [[32/27]].
 == Commatic relations ==
@@ Line 32: / Line 32: @@
 == Temperaments ==
-By tempering it out is defined the '''ibnsinmic''' or '''sinaismic temperament''', which enables the [[ibnsinmic chords|ibnsinmic a.k.a. sinaismic chords]], the [[essentially tempered chord]]s in the [[21-odd-limit]]. Another consequence is that it makes [[fifth complement]]s of [[13/11]] and [[80/63]], and of [[40/33]] and [[26/21]]. You may find a list of good equal temperaments that support this temperament below.
+[[Tempering out]] this comma in the 13-limit defines the rank-5 '''ibnsinmic''' or '''sinaismic''' temperament, which enables the [[ibnsinmic chords|ibnsinmic a.k.a. sinaismic chords]], the [[essentially tempered chord]]s in the [[21-odd-limit]]. Another consequence is that it makes [[13/11]] and [[80/63]] [[fifth complement]]s of each other, as well as [[40/33]] and [[26/21]]. You may find a list of good [[equal temperament]]s that [[support]] this temperament below.
 [[Subgroup]]: 2.3.5.7.11.13
@@ Line 49: / Line 49: @@
 | ⟨ || 0 || 0 || 0 || 0 || 1 || 1 || ]]
 |}
+: mapping generators: ~2, ~3, ~5, ~7, ~11
-: mapping generators: ~2, ~3, ~5, ~7, ~11
+[[Optimal tuning]]s:
+: [[WE]]: ~2 = 1199.9519{{c}}, ~3/2 = 702.0756{{c}}, ~5/4 = 386.3580{{c}}, ~7/4 = 968.9979{{c}}, ~11/8 = 551.5774{{c}}
+: [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0843{{c}}, ~5/4 = 386.3184{{c}}, ~7/4 = 968.9934{{c}}, ~11/8 = 551.5497{{c}}
 {{Optimal ET sequence|legend=1| 12f, 14cf, 15, 17c, 19, 22f, 26, 29, 31f, 39df, 41, 46, 53, 58, 72, 87, 111, 130, 183, 198, 224, 270, 494, 764, 935, 1075, 1205, 1699, 2280, 2774e, 3326de, 3596de, 3907bdee, 4401bdee, 4671bde }} *
 <nowiki>*</nowiki> [[optimal patent val]]: [[3044edo|3044]]
+[[Badness]] (Sintel): 0.149
 == Etymology ==
@@ Line 60: / Line 65: @@
 == See also ==
-* [[Unnoticeable comma]]
 * [[List of superparticular intervals]]
-== Notes ==
+== References ==
 [[Category:Ibnsinmic]]
+[[Category:Commas named after polymaths]]