Ennealimma: Difference between revisions
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== 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 == | == Etymology == | ||
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[[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].