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]\displaystyle{ \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 norm (log2 nd)	85.5887
Weil norm (log2 max(n, d))	85.5894
Wilson norm (sopfr(nd))	173
Comma size	unnoticeable
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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 Septiennealimmal clan #Ennealimmal.

Subgroup: 2.3.5

Comma list: [1 -27 18⟩

Mapping: [⟨9 1 1], ⟨0 2 3]]

mapping generators: ~27/25, ~5/3

Optimal tunings:

• WE: ~27/25 = 133.3333 ¢, ~5/3 = 884.3190 ¢

error map: ⟨-0.000 +0.016 -0.023]

• CWE: ~27/25 = 133.3333 ¢, ~5/3 = 884.3191 ¢

error map: ⟨0.000 +0.017 -0.023]

Optimal ET sequence: 27, 45, 72, 99, 171, 441, 612, 1665, 2277, 2889, 3501, 6390, 16281, 22671, 29061c

Badness (Sintel): 0.403

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