Septimal ennealimma

Interval information

Ratio	40353607/40310784
Factorization	2-11 × 3-9 × 79
Monzo	[-11 -9 0 9⟩
Size in cents	1.83815 ¢
Names	septimal ennealimma, septiennealimma, no-five ennealimma
Color name	tritrizo comma
FJS name	[math]\displaystyle{ \text{dddd5}^{7,7,7,7,7,7,7,7,7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	50.5309
Weil norm (log2 max(n, d))	50.5324
Wilson norm (sopfr(nd))	112
Comma size	unnoticeable
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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, or in the no-5 11-limit, the product of the elysia and the argyria.

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

Optimal tunings:

• WE: ~2592/2401 = 133.3357 ¢, ~3/2 = 701.9772 ¢, ~5/4 = 386.2717 ¢

error map: ⟨+0.021 +0.043 -0.000 -0.135]

• CWE: ~2592/2401 = 133.3333 ¢, ~3/2 = 701.9833 ¢, ~5/4 = 386.2877 ¢

error map: ⟨0.000 +0.028 -0.026 -0.176]

Optimal ET sequence: 27, 45, 63, 72, 99, 171, 441, 612

Badness (Sintel): 2.21

See also

• Ennealimma