Septimal ennealimma
| 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 nd) | 50.5309 |
| Weil height (log2 max(n, d)) | 50.5324 |
| Wilson height (sopfr (nd)) | 112 |
| 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 ET sequence: 27, 45, 63, 72, 99, 171, 441, 612
Badness: 0.502 × 10-3