Ennealimma: Difference between revisions

(15 intermediate revisions by 8 users not shown)

Line 1:

{{Infobox Interval

| Ratio = 7629394531250/7625597484987

| 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]].

== Temperament ==

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

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.

=== Ennealimmal ===

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

[[Subgroup]]: 2.3.5

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

: 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 ==

The name consists of Greek ''ennea-'' ("nine") + ''limma'', coined by [[Paul Erlich]] and [[Gene Ward Smith]] in 2001<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_29667.html Yahoo! Tuning Group | ''Name that comma!'']</ref>.

== See also ==

* [[Unnoticeable comma]]

* [[Septimal ennealimma]]

== Notes ==

~~[[Category:5-limit]]~~

~~[[Category:Unnoticeable comma]]~~

[[Category:Ennealimmal]]

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

@@ Line 1: / Line 1: @@
+{{Infobox Interval
+| Ratio = 7629394531250/7625597484987
+| 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]].
 == Temperament ==
-Tempering out this comma leads to the 5-limit version of the [[ennealimmal]] temperament, which remarkably splits the octave into nine equal parts.
+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.
+=== 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 ==
+The name consists of Greek ''ennea-'' ("nine") + ''limma'', coined by [[Paul Erlich]] and [[Gene Ward Smith]] in 2001<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_29667.html Yahoo! Tuning Group | ''Name that comma!'']</ref>.
 == See also ==
 * [[Unnoticeable comma]]
+* [[Septimal ennealimma]]
+== Notes ==
-[[Category:5-limit]]
-[[Category:Unnoticeable comma]]
 [[Category:Ennealimmal]]
+[[Category:Commas named for their periods per equave]]