Septimal ennealimma
Ratio | 40353607/40310784 |
Factorization | 2^{-11} × 3^{-9} × 7^{9} |
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 (log_{2} nd) | 50.5309 |
Weil height (log_{2} 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