# Septimal ennealimma

 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 $\text{dddd5}^{7,7,7,7,7,7,7,7,7}$ 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, $\sqrt{nd}$) ~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