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]\text{dddd5}^{7,7,7,7,7,7,7,7,7}[/math]
Special properties	reduced
Tenney height (log2 nd)	50.5309
Weil height (log2 max(n, d))	50.5324
Wilson height (sopfr(nd))	112
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.23064 bits
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.

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:

• 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

See also

• Ennealimma