Enneadeca: Difference between revisions

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{{Infobox Interval

| Monzo = -14 -19 19

| Name = enneadeca~~, 19-tone-comma~~

| Name = enneadeca

| Color name = y19-4, Neyo comma

| Comma = yes

}}

{{~~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, 25/(6/5)19.

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, 25/(6/5)19.

== 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 ==

* [[Unnoticeable comma]]

* [[Septimal enneadeca]]

== References ==

[[Category:Enneadecal]]

[[Category:Commas named for their periods per equave]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Monzo = -14 -19 19
-| Name = enneadeca, 19-tone-comma
+| Name = enneadeca
 | Color name = y<sup>19</sup>-4, Neyo comma
 | Comma = yes
 }}
-{{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>.
+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 ==
-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 ==
-* [[Unnoticeable comma]]
 * [[Septimal enneadeca]]
+== References ==
 [[Category:Enneadecal]]
 [[Category:Commas named for their periods per equave]]