Ennealimma: Difference between revisions
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{{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]]. | 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 == | == 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 == | == See also == | ||
* [[Unnoticeable comma]] | * [[Unnoticeable comma]] | ||
* [[Septimal ennealimma]] | |||
== Notes == | |||
[[Category:Ennealimmal]] | [[Category:Ennealimmal]] | ||
[[Category:Commas named for their periods per equave]] | |||
Latest revision as of 12:59, 29 November 2025
| Interval information |
The ennealimma, meaning nine limmas, with monzo [1 -27 18⟩, is a 5-limit unnoticeable comma measuring about 0.86 cents. It is the amount by which a stack of nine 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. 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: [1 -27 18⟩
Mapping: [⟨9 1 1], ⟨0 2 3]]
- mapping generators: ~27/25, ~5/3
- WE: ~27/25 = 133.3333 ¢, ~5/3 = 884.3190 ¢
- error map: ⟨-0.000 +0.016 -0.023]
- CWE: ~27/25 = 133.3333 ¢, ~5/3 = 884.3191 ¢
- error map: ⟨0.000 +0.017 -0.023]
Optimal ET sequence: 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[1].