Xenial comma: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Xenllium (talk | contribs)
Created page with "{{Infobox interval | Ratio = 129140163/125000000 | Name = xenial comma | Color name = Lg<sup>9</sup>2, latritrigu 2nd,<br>Latritrigu comma | Comma = yes }} The '''xenial comma''' ({{monzo|legend=1| -6 17 -9 }}, ratio: 129140163/125000000) is a 5-limit comma of about 56.4 cents. It belongs to the syntonic–kleismic equivalence continuum and is equal to the difference between a stack of nine ptolemaic whole tones and the 8/3|perfect eleventh..."
Tags: Mobile edit Mobile web edit
 
+ note
 
Line 8: Line 8:


== Temperaments ==
== Temperaments ==
[[Tempering out]] this comma leads to the [[Xenial|xenial family]] of temperaments. [[Patent val]]s which temper it out include those for {{EDOs| 19, 70, 89, 108, 127, 146 and 235 }}.
[[Tempering out]] this comma leads to the [[5-limit]] version of the [[xenial]] temperament. [[Patent val]]s which temper it out include those for {{EDOs| 19, 70, 89, 108, 127, 146 and 235 }}.


== Etymology ==
== Etymology ==
The comma was named by [[User:Xenllium|Xenllium]] in 2026, in terms of the corresponding temperament, ''xenial'', come from [[wiktionary:ξενία|ξενία]] (Greek for ''hospitable''), after its temperament property.  
The comma was named by [[User:Xenllium|Xenllium]] in 2026, in terms of the corresponding temperament, ''xenial'', come from [[wiktionary:ξενία|ξενία]] (Greek for ''hospitable''), after its temperament property. Despite the similar name, it is unrelated to the earlier named [[xenisma]].  


[[Category:Xenial]]
[[Category:Xenial]]
[[Category:Commas named for their regular temperament properties]]
[[Category:Commas named for their regular temperament properties]]

Latest revision as of 09:50, 2 May 2026

Interval information
Ratio 129140163/125000000
Factorization 2-6 × 317 × 5-9
Monzo [-6 17 -9
Size in cents 56.41159¢
Name xenial comma
Color name Lg92, latritrigu 2nd,
Latritrigu comma
FJS name [math]\displaystyle{ \text{dd2}_{5,5,5,5,5,5,5,5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 53.8417
Weil norm (log2 max(n, d)) 53.8887
Wilson norm (sopfr(nd)) 108
Comma size medium
Open this interval in xen-calc

The xenial comma (monzo[-6 17 -9, ratio: 129140163/125000000) is a 5-limit comma of about 56.4 cents. It belongs to the syntonic–kleismic equivalence continuum and is equal to the difference between a stack of nine ptolemaic whole tones and the perfect eleventh ((8/3)/(10/9)9), or in terms of commas, between a stack of three syntonic commas and a kleisma ((81/80)3/(15625/15552)).

Temperaments

Tempering out this comma leads to the 5-limit version of the xenial temperament. Patent vals which temper it out include those for 19, 70, 89, 108, 127, 146 and 235.

Etymology

The comma was named by Xenllium in 2026, in terms of the corresponding temperament, xenial, come from ξενία (Greek for hospitable), after its temperament property. Despite the similar name, it is unrelated to the earlier named xenisma.