Septimal ennealimma
| Interval information |
no-five ennealimma
(Shannon, [math]\sqrt{nd}[/math])
The septimal ennealimma or no-five ennealimma is an unnoticeable 7-limit comma defined as (7/6)9 / (2/1)2 and measuring 1.838 cents.
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.
It can only possibly be tempered out in an EDO if that EDO is a multiple of 9. This temperament is documented below:
Septiennealimmal
The rank 2 temperament septiennealimmal is of interest to anyone who wants a different generator for the "ennealimmal-like structure" by detempering S49 and/or because it represents the part of ennealimmal supported by non-ennealimmal EDOs of interest that do well in the 2.3.7 subgroup, such as 36edo, which adds S7/S8, or 63edo, which in the 7-limit can be used for septimal magic and in higher limits for parapyth (among other things).
Subgroup: 2.3.7
Mapping: [⟨9 0 11], ⟨0 1 1]]
Generators (CTE): ~2592/2401 = (27/25)/S49 = 1\9, ~3 = 1902.004 ¢
Patent val non-ennealimmal EDO tunings < 311 with the 7-limited 9-odd-limit (or here equivalently 21-odd-limit) consistent: 36, 63, 108, 135, 162, 207, 234, 279, 306
Badness: 0.191