Enneadeca: Difference between revisions

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|-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, 2^5/(6/5)^19. ~~Equal divisions divisible by 19 less than or equal to 228 temper~~ out the enneadeca~~; these include~~ [[~~19edo|19edo~~]], [[~~38edo|38edo~~]], [[~~57edo|57edo~~]], [[~~76edo|76edo~~]], [[~~114edo|114edo~~]], [[~~152edo~~|~~152edo]~~], [[~~171edo|171edo~~]], [[~~190edo|190edo~~]] ~~and~~ [[~~228edo|228edo~~]].

{{Infobox Interval

| Monzo = -14 -19 19

| Name = enneadeca

| Color name = y19-4, 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, 25/(6/5)19.

== Temperament ==

[[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 ==

* [[Septimal enneadeca]]

== References ==

[[Category:Enneadecal]]

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

@@ Line 1: / Line 1: @@
-|-14 -19 19&gt;, 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, 2^5/(6/5)^19. Equal divisions divisible by 19 less than or equal to 228 temper out the enneadeca; these include [[19edo|19edo]], [[38edo|38edo]], [[57edo|57edo]], [[76edo|76edo]], [[114edo|114edo]], [[152edo|152edo]], [[171edo|171edo]], [[190edo|190edo]] and [[228edo|228edo]].
+{{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 ==
+[[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 ==
+* [[Septimal enneadeca]]
+== References ==
+[[Category:Enneadecal]]
+[[Category:Commas named for their periods per equave]]