Enneadeca: Difference between revisions

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{{Monzo| -14 -19 19 }}, the '''enneadeca''' or '''19-tone-comma''', is an interval of 2.816 cents which is the amount by which nineteen minor thirds fall short of five octaves, that is, 2<sup>5</sup>/(6/5)<sup>19</sup>.  
{{Infobox Interval
| Monzo = -14 -19 19
| Name = enneadeca
| Color name = y<sup>19</sup>-4, Neyo comma
| Comma = yes
}}
The '''enneadeca''' ({{monzo|legend=1| -14 -19 19 }}) is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]] of 2.816 [[cent]]s. It is the amount by which nineteen [[6/5|classical minor thirds]] fall short of five [[2/1|octaves]], that is, 2<sup>5</sup>/(6/5)<sup>19</sup>.  


== Temperament ==
== Temperament ==
Tempering out the enneadeca leads to the [[enneadecal|enneadecal temperament]], supported by equal divisions divisible by 19 such as [[19edo]], [[38edo]], [[57edo]], [[76edo]], [[114edo]], [[152edo]], [[171edo]], [[190edo]] and [[228edo]].  
[[Tempering out]] the enneadeca leads to the 5-limit [[enneadecal]] temperament, [[support]]ed by equal divisions divisible by 19 such as [[152edo]], [[171edo]], and [[190edo]].
 
== Etymology ==
This comma was named by [[Gene Ward Smith]] in 2001 in terms of the corresponding temperament, ''enneadecal''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2121.html Yahoo! Tuning Group | ''Shismic & co'']</ref>, for the temperament has 19 periods per octave. The comma was at one point dubbed ''enneadecima''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']</ref>, though it was ''enneadeca'' that stuck.  


== See also ==
== See also ==
* [[Unnoticeable comma]]
* [[Septimal enneadeca]]
 
== References ==


[[Category:5-limit]]
[[Category:Unnoticeable commas]]
[[Category:Enneadecal]]
[[Category:Enneadecal]]
[[Category:Commas named for their periods per equave]]

Latest revision as of 08:13, 18 June 2026

Interval information
Factorization 2-14 × 3-19 × 519
Monzo [-14 -19 19
Size in cents 2.815547¢
Name enneadeca
Color name y19-4, Neyo comma
FJS name [math]\displaystyle{ \text{8d}{-4}^{5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 88.2309
Weil norm (log2 max(n, d)) 88.2333
Wilson norm (sopfr(nd)) 180
Comma size unnoticeable
Open this interval in xen-calc

The enneadeca (monzo[-14 -19 19) is an unnoticeable 5-limit comma of 2.816 cents. It is the amount by which nineteen classical minor thirds fall short of five octaves, that is, 25/(6/5)19.

Temperament

Tempering out the enneadeca leads to the 5-limit enneadecal temperament, supported by equal divisions divisible by 19 such as 152edo, 171edo, and 190edo.

Etymology

This comma was named by Gene Ward Smith in 2001 in terms of the corresponding temperament, enneadecal[1], for the temperament has 19 periods per octave. The comma was at one point dubbed enneadecima[2], though it was enneadeca that stuck.

See also

References