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, 19-tone-comma

| Color name = y19-4, Neyo comma

| Comma = yes

}}

{{Monzo| -14 -19 19 }}, the '''enneadeca''' or '''19-tone-comma''', is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]] of 2.816 [[cent]]s which 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]] temperament, supported by equal divisions divisible by 19 such as [[19edo]], [[38edo]], [[57edo]], [[76edo]], [[114edo]], [[152edo]], [[171edo]], [[190edo]] and [[228edo]].

== 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]]

== Notes ==

[[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, 19-tone-comma
+| Color name = y<sup>19</sup>-4, Neyo comma
+| Comma = yes
+}}
+{{Monzo| -14 -19 19 }}, the '''enneadeca''' or '''19-tone-comma''', is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]] of 2.816 [[cent]]s which 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]] temperament, supported by equal divisions divisible by 19 such as [[19edo]], [[38edo]], [[57edo]], [[76edo]], [[114edo]], [[152edo]], [[171edo]], [[190edo]] and [[228edo]].
+== 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]]
+== Notes ==
+[[Category:Enneadecal]]
+[[Category:Commas named for their periods per equave]]