Ennealimma: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 7629394531250/7625597484987 | |||
| Monzo = 1 -27 18 | | Monzo = 1 -27 18 | ||
| Name = ennealimma | | Name = ennealimma | ||
| Color name = sy<sup>18</sup>-3, satritribiyo negative 3rd | |||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
| Line 7: | Line 9: | ||
== 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]]: 7629394531250/7625597484987 | |||
{{Mapping|legend=1|9 1 1|0 2 3}} | |||
[[Optimal tuning]] ([[CTE]]): ~27/25 = 1\9, ~5/3 = 884.319 | |||
[[Support]]ing [[ET]]s: {{EDOs|612, 171, 441, 99, 270, 72, 27, 45, 711, 18bc, 9bcc, 243, 369, 126 }} | |||
== 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 14:29, 18 March 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: 7629394531250/7625597484987
Mapping: [⟨9 1 1], ⟨0 2 3]]
Optimal tuning (CTE): ~27/25 = 1\9, ~5/3 = 884.319
Supporting ETs: 612, 171, 441, 99, 270, 72, 27, 45, 711, 18bc, 9bcc, 243, 369, 126
Etymology
The name consists of Greek ennea- ("nine") + limma, coined by Paul Erlich and Gene Ward Smith in 2001[1].