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,
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
open this interval in xen-calc

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

See also