Ennealimma: Difference between revisions

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{{Infobox Interval

| Ratio = ~~7629394531250~~/~~7625597484987~~

| Ratio = 7 629 394 531 250 / 7 625 597 484 987

~~| Monzo = 1 -27 18~~

| Name = ennealimma

| Color name = sy<sup>18</sup>-3, satritribiyo negative 3rd

| Comma = yes

}}

The '''ennealimma''', meaning ''nine limmas'', with [[monzo]] {{monzo| 1 -27 18 }}, is a [[5-limit]] [[~~unnoticeable~~ comma]] measuring about 0.86 [[cent]]s. It is the amount by which a stack of nine [[27/25|large limmas]] falls short of the [[octave]].

The '''ennealimma''', meaning ''nine limmas'', with [[monzo]] {{monzo| 1 -27 18 }}, is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]] measuring about 0.862 [[cent]]s. It is the amount by which a stack of nine [[27/25|large limmas]] falls short of the [[octave]]. In terms of commas, it is also the difference between the [[enneadeca]] and the [[schisma]].

== Temperament ==

Tempering out this comma leads to the 5-limit version of the [[ennealimmal]] temperament, which remarkably splits the octave into nine equal parts. Since the [[7-limit]] temperament (definable by tempering out both [[2401/2400]] and [[4375/4374]], the two smallest superparticular ratios in the 7-limit) is far more natural to think of than the 5-limit, the 5-limit temperament is only provided below for bookkeeping purposes.

[[Tempering out]] this comma leads to the 5-limit version of the [[ennealimmal]] temperament, which remarkably splits the octave into nine equal parts.

~~=== Ennealimmal ===~~

~~: ''For the 7-limit temperament, see [[Septiennealimmal clan #Ennealimmal]].''~~

~~[[Subgroup]]: 2.3.5~~

~~[[Comma list]]: {{monzo| 1 -27 18 }}~~

~~{{Mapping|legend=1| 9 1 1 | 0 2 3 }}~~

~~: mapping generators: ~27/25, ~5/3~~

~~[[Optimal tuning]]s:~~

* [[WE]]: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3190{{c}}

~~: [[error map]]: {{val| -0.000 +0.016 -0.023 }}~~

* [[CWE]]: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3191{{c}}

~~: error map: {{val| 0.000 +0.017 -0.023 }}~~

~~{{Optimal ET sequence|legend=1| 27, 45, 72, 99, 171, 441, 612, 1665, 2277, 2889, 3501, 6390, 16281, 22671, 29061c }}~~

~~[[Badness]] (Sintel): 0.403~~

== Etymology ==

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== See also ==

* [[Unnoticeable comma]]

* [[Septimal ennealimma]]

== ~~Notes~~ ==

== References ==

[[Category:Ennealimmal]]

[[Category:Commas named for their periods per equave]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 7629394531250/7625597484987
+| Ratio = 7 629 394 531 250 / 7 625 597 484 987
-| Monzo = 1 -27 18
 | Name = ennealimma
 | Color name = sy<sup>18</sup>-3, satritribiyo negative 3rd
 | Comma = yes
 }}
-The '''ennealimma''', meaning ''nine limmas'', with [[monzo]] {{monzo| 1 -27 18 }}, is a [[5-limit]] [[unnoticeable comma]] measuring about 0.86 [[cent]]s. It is the amount by which a stack of nine [[27/25|large limmas]] falls short of the [[octave]].
+The '''ennealimma''', meaning ''nine limmas'', with [[monzo]] {{monzo| 1 -27 18 }}, is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]] measuring about 0.862 [[cent]]s. It is the amount by which a stack of nine [[27/25|large limmas]] falls short of the [[octave]]. In terms of commas, it is also the difference between the [[enneadeca]] and the [[schisma]].
 == Temperament ==
-Tempering out this comma leads to the 5-limit version of the [[ennealimmal]] temperament, which remarkably splits the octave into nine equal parts. Since the [[7-limit]] temperament (definable by tempering out both [[2401/2400]] and [[4375/4374]], the two smallest superparticular ratios in the 7-limit) is far more natural to think of than the 5-limit, the 5-limit temperament is only provided below for bookkeeping purposes.
+[[Tempering out]] this comma leads to the 5-limit version of the [[ennealimmal]] temperament, which remarkably splits the octave into nine equal parts.
-=== Ennealimmal ===
-: ''For the 7-limit temperament, see [[Septiennealimmal clan #Ennealimmal]].''
-[[Subgroup]]: 2.3.5
-[[Comma list]]: {{monzo| 1 -27 18 }}
-{{Mapping|legend=1| 9 1 1 | 0 2 3 }}
-: mapping generators: ~27/25, ~5/3
-[[Optimal tuning]]s:
-* [[WE]]: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3190{{c}}
-: [[error map]]: {{val| -0.000 +0.016 -0.023 }}
-* [[CWE]]: ~27/25 = 133.3333{{c}}, ~5/3 = 884.3191{{c}}
-: error map: {{val| 0.000 +0.017 -0.023 }}
-{{Optimal ET sequence|legend=1| 27, 45, 72, 99, 171, 441, 612, 1665, 2277, 2889, 3501, 6390, 16281, 22671, 29061c }}
-[[Badness]] (Sintel): 0.403
 == Etymology ==
@@ Line 35: / Line 14: @@
 == See also ==
-* [[Unnoticeable comma]]
 * [[Septimal ennealimma]]
-== Notes ==
+== References ==
 [[Category:Ennealimmal]]
 [[Category:Commas named for their periods per equave]]