Ennealimma

Interval information

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.

See also

• Unnoticeable comma
• Septimal ennealimma