Septendecima: Difference between revisions

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The '''septendecima''' ([[monzo]]: {{monzo| -52 -17 34 }}) is a [[5-limit]] [[~~unnoticeable~~ comma]]. It ~~represents~~ the difference between a stack of seventeen [[25/24]] ~~intervals~~ and one ~~octave, and tempering it out means that~~ [[25/24 equal-step tuning]] is equated with [[17edo]]. Therefore, a temperament must be divisible by 17 in order to temper out this comma, any edo such as [[311edo]], which isn't a multiple of 17 cannot be tempering out the 25/24 kleisma. The temperament which tempers out only this comma is 5-limit [[Ragismic microtemperaments#Chlorine|~~chlorine~~]].

The '''septendecima''' ([[monzo]]: {{monzo| -52 -17 34 }}) is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]]. It is the difference between a stack of seventeen [[25/24]]'s and one [[2/1|octave]].

== ~~See also~~ ==

== Temperaments ==

* [[~~Unnoticeable~~ comma]]

The [[regular temperament|temperament]] which [[tempering out|tempers out]] only this comma is 5-limit [[ragismic microtemperaments #Chlorine|chlorine]]. The octave must be divisible by 17 in order to temper out this comma. Any edo such as [[311edo]], which is not a multiple of 17 cannot be tempering out this comma.

== Etymology ==

This comma was once named by [[Gene Ward Smith]] in 2001 in terms of the corresponding temperament, ''heptadecal'', for the temperament has 17 periods per octave<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2121.html Yahoo! Tuning Group | ''Shismic & co'']</ref>. The logical name for the comma would be ''heptadeca'', following ''[[enneadeca]]''. It was unclear how and why it was changed to ''septendecima'', the Latin equivalent.

== Notes ==

[[Category:Chlorine]]

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

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-The '''septendecima''' ([[monzo]]: {{monzo| -52 -17 34 }}) is a [[5-limit]] [[unnoticeable comma]]. It represents the difference between a stack of seventeen [[25/24]] intervals and one octave, and tempering it out means that [[25/24 equal-step tuning]] is equated with [[17edo]]. Therefore, a temperament must be divisible by 17 in order to temper out this comma, any edo such as [[311edo]], which isn't a multiple of 17 cannot be tempering out the 25/24 kleisma. The temperament which tempers out only this comma is 5-limit [[Ragismic microtemperaments#Chlorine|chlorine]].
+The '''septendecima''' ([[monzo]]: {{monzo| -52 -17 34 }}) is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]]. It is the difference between a stack of seventeen [[25/24]]'s and one [[2/1|octave]].
-== See also ==
+== Temperaments ==
-* [[Unnoticeable comma]]
+The [[regular temperament|temperament]] which [[tempering out|tempers out]] only this comma is 5-limit [[ragismic microtemperaments #Chlorine|chlorine]]. The octave must be divisible by 17 in order to temper out this comma. Any edo such as [[311edo]], which is not a multiple of 17 cannot be tempering out this comma.
+== Etymology ==
+This comma was once named by [[Gene Ward Smith]] in 2001 in terms of the corresponding temperament, ''heptadecal'', for the temperament has 17 periods per octave<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2121.html Yahoo! Tuning Group | ''Shismic & co'']</ref>. The logical name for the comma would be ''heptadeca'', following ''[[enneadeca]]''. It was unclear how and why it was changed to ''septendecima'', the Latin equivalent.
+== Notes ==
 [[Category:Chlorine]]
+[[Category:Commas named for their periods per equave]]