Septimal ennealimma: Difference between revisions
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The '''septimal ennealimma''', '''septiennealimma''' or '''no-five ennealimma''' is an unnoticeable 7-limit comma defined as 40353607/40310784 and measuring 1.838 cents. It arises as a stack between nine [[7/6]]'s and two octaves. | The '''septimal ennealimma''', '''septiennealimma''' or '''no-five ennealimma''' is an unnoticeable 7-limit comma defined as 40353607/40310784 and measuring 1.838 cents. It arises as a stack between nine [[7/6]]'s and two octaves. | ||
In the 2.3.7 subgroup, tempering it out leads to the 2.3.7 version of the [[ennealimmal temperament]], which is a member of the [[tritrizo clan]]. For edos up to circa 3000, it is tempered if and only if the edo is divisible by 9. | == Temperaments == | ||
In the 2.3.7 subgroup, tempering it out leads to the 2.3.7 version of the [[ennealimmal temperament]], which is a member of the [[tritrizo clan]]. For edos up to circa 3000, it is tempered out if and only if the edo is divisible by 9. | |||
In the full 7-limit, tempering it out leads to the '''septiennealimmal temperament''' (cf. septimal ennealimmal temperament). You may find a list of good equal temperaments that support this temperament below. | |||
=== Septiennealimmal === | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Mapping]]: [{{val| 9 0 0 11 }}, {{val| 0 1 0 1 }}, {{val| 0 0 1 0 }}] | |||
Mapping generators: ~2592/2401, ~3, ~5 | |||
{{Val list|legend=1| 27, 45, 63, 72, 99, 171, 441, 612 }} | |||
[[Badness]]: 0.502 × 10<sup>-3</sup> | |||
== See also == | == See also == | ||
Revision as of 14:39, 11 October 2022
| Interval information |
septiennealimma,
no-five ennealimma
The septimal ennealimma, septiennealimma or no-five ennealimma is an unnoticeable 7-limit comma defined as 40353607/40310784 and measuring 1.838 cents. It arises as a stack between nine 7/6's and two octaves.
Temperaments
In the 2.3.7 subgroup, tempering it out leads to the 2.3.7 version of the ennealimmal temperament, which is a member of the tritrizo clan. For edos up to circa 3000, it is tempered out if and only if the edo is divisible by 9.
In the full 7-limit, tempering it out leads to the septiennealimmal temperament (cf. septimal ennealimmal temperament). You may find a list of good equal temperaments that support this temperament below.
Septiennealimmal
Subgroup: 2.3.5.7
Mapping: [⟨9 0 0 11], ⟨0 1 0 1], ⟨0 0 1 0]]
Mapping generators: ~2592/2401, ~3, ~5
Badness: 0.502 × 10-3