Ennealimma: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Ratio = 7629394531250/7625597484987
| Ratio = 7 629 394 531 250 / 7 625 597 484 987
| Monzo = 1 -27 18
| Name = ennealimma
| Name = ennealimma
| Color name = sy<sup>18</sup>-3, satritribiyo negative 3rd
| Color name = sy<sup>18</sup>-3, satritribiyo negative 3rd
| Comma = yes
| Comma = yes
}}
}}
The '''ennealimma''', meaning ''nine limmas'', with [[monzo]] {{monzo| 1 -27 18 }}, is a [[5-limit]] [[unnoticeable comma]] measuring about 0.86 [[cent]]s. It is the amount by which a stack of nine [[27/25|large limmas]] falls short of the [[octave]].  
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]].  


== Temperament ==
== 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.
[[Tempering out]] this comma leads to the 5-limit version of the [[ennealimmal]] temperament, which remarkably splits the octave into nine equal parts.  
 
=== Ennealimmal ===
''For the 7-limit temperament, see [[Ragismic microtemperaments#Ennealimmal]].''
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: 7629394531250/7625597484987
 
{{Mapping|legend=1|9 1 1|0 2 3}}
 
[[Optimal tuning]] ([[CTE]]): ~27/25 = 1\9, ~5/3 = 884.319
 
[[Support]]ing [[ET]]s: {{EDOs|612, 171, 441, 99, 270, 72, 27, 45, 711, 18bc, 9bcc, 243, 369, 126 }}


== Etymology ==
== Etymology ==
Line 28: Line 14:


== See also ==
== See also ==
* [[Unnoticeable comma]]
* [[Septimal ennealimma]]
* [[Septimal ennealimma]]


== Notes ==
== References ==


[[Category:Ennealimmal]]
[[Category:Ennealimmal]]
[[Category:Commas named for their regular temperament properties]]
[[Category:Commas named for their periods per equave]]

Latest revision as of 19:19, 19 July 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.

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