Ennealimma: Difference between revisions

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The '''ennealimma''', meaning ''nine limmas'', with [[monzo]] {{monzo| 1 -27 18 }}, is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]] measuring about 0.862 [[cent]]s. It is the amount by which a stack of nine [[27/25|large limmas]] falls short of the [[octave]]. In terms of commas, it is also the difference between the [[enneadeca]] and the [[schisma]].  
The '''ennealimma''', meaning ''nine limmas'', with [[monzo]] {{monzo| 1 -27 18 }}, is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]] measuring about 0.862 [[cent]]s. It is the amount by which a stack of nine [[27/25|large limmas]] falls short of the [[octave]]. In terms of commas, it is also the difference between the [[enneadeca]] and the [[schisma]], and in the [[7-limit]] between a stack of 4 [[ragisma]]<nowiki/>s and the [[breedsma]].  


== Temperament ==
== Temperament ==

Latest revision as of 09:46, 25 August 2026

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
Open this interval in xen-calc

The ennealimma, meaning nine limmas, with monzo [1 -27 18, is an unnoticeable 5-limit comma measuring about 0.862 cents. It is the amount by which a stack of nine large limmas falls short of the octave. In terms of commas, it is also the difference between the enneadeca and the schisma, and in the 7-limit between a stack of 4 ragismas and the breedsma.

Temperament

Tempering out this comma leads to the 5-limit version of the ennealimmal temperament, which remarkably splits the octave into nine equal parts.

Etymology

The name consists of Greek ennea- ("nine") + limma, coined by Paul Erlich and Gene Ward Smith in 2001[1].

See also

References