Septimal ennealimma

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Interval information
Ratio 40353607/40310784
Factorization 2-11 × 3-9 × 79
Monzo [-11 -9 0 9
Size in cents 1.8381504¢
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 n⋅d) 50.5309
Weil height (max(n, d)) 40353607
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.41315 bits
Comma size unnoticeable
open this interval in xen-calc

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

Optimal GPV sequence27, 45, 63, 72, 99, 171, 441, 612

Badness: 0.502 × 10-3

See also