Septimal ennealimma
Interval information |
septiennealimma,
no-five ennealimma
(Shannon, [math]\sqrt{nd}[/math])
The septimal ennealimma, septiennealimma or no-five ennealimma is an unnoticeable 7-limit comma measuring 1.838 cents. It is the difference between a stack of nine septimal minor thirds (7/6) and two octaves, or (7/6)9 / (2/1)2.
Temperaments
In the 2.3.7 subgroup, tempering it out leads to the 2.3.7-subgroup restriction of the ennealimmal temperament, which is the head of the septiennealimmal clan. It can only possibly be tempered out in an edo if that edo is a multiple of 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
- CTE: ~2592/2401 = 133.3333, ~3/2 = 702.0044, ~5/4 = 386.3137
- error map: ⟨0.0000 +0.0494 0.0000 -0.1549]
- CWE: ~2592/2401 = 133.3333, ~3/2 = 701.9833, ~5/4 = 386.2877
- error map: ⟨0.0000 +0.0283 -0.0260 -0.1759]
Optimal ET sequence: 27, 45, 63, 72, 99, 171, 441, 612
Badness (Smith): 0.502 × 10-3