Ennealimma
| Ratio | 7629394531250/7625597484987 |
| Factorization | 2 × 3-27 × 518 |
| Monzo | [1 -27 18⟩ |
| Size in cents | 0.8618262¢ |
| Name | ennealimma |
| Color name | sy18-3, satritribiyo negative 3rd |
| FJS name | [math]\text{6d}{-3}^{5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 85.5887 |
| Weil height (log2 max(n, d)) | 85.5894 |
| Wilson height (sopfr(nd)) | 173 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.20517 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
The ennealimma, meaning nine limmas, with monzo [1 -27 18⟩, is a 5-limit unnoticeable comma measuring about 0.86 cents. It is the amount by which a stack of nine large limmas falls short of the octave.
Temperament
Tempering out this comma leads to the 5-limit version of the ennealimmal temperament, which remarkably splits the octave into nine equal parts. Since the 7-limit temperament (definable by tempering out both 2401/2400 and 4375/4374, the two smallest superparticular ratios in the 7-limit) is far more natural to think of than the 5-limit, the 5-limit temperament is only provided below for bookkeeping purposes.
Ennealimmal
For the 7-limit temperament, see Ragismic microtemperaments#Ennealimmal.
Subgroup: 2.3.5
Comma list: 7629394531250/7625597484987
Mapping: [⟨9 1 1], ⟨0 2 3]]
Optimal tuning (CTE): ~27/25 = 1\9, ~5/3 = 884.319
Supporting ETs: 612, 171, 441, 99, 270, 72, 27, 45, 711, 18bc, 9bcc, 243, 369, 126
Etymology
The name consists of Greek ennea- ("nine") + limma, coined by Paul Erlich and Gene Ward Smith in 2001[1].