Septendecima: Difference between revisions

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{{Infobox Interval

|Ratio=582~~.07 sextillion~~/581~~.59 sextillion~~

| Ratio = 582 076 609 134 674 072 265 625 / <br>581 595 589 965 365 114 830 848

~~|Cents=1.4314~~

| Monzo = -52 -17 34

|Monzo=-52 -17 34

| Name = septendecima

|Name=25/~~24 equal step tuning kleisma~~

| Color name = LLy<sup>34</sup>-8, lala-sebiyo negative octave

| Comma = yes

}}

'''~~25/24 equal step tuning kleisma~~'''~~, or 582076609134674072265625/581595589965365114830848 when fully written out,~~ is a 5-limit ~~unnoticeable~~ comma. It ~~represents~~ the difference between a stack of 17 [[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 '''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]].

== Temperaments ==

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]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-|Ratio=582.07 sextillion/581.59 sextillion
+| Ratio = 582 076 609 134 674 072 265 625 / <br>581 595 589 965 365 114 830 848
-|Cents=1.4314
+| Monzo = -52 -17 34
-|Monzo=-52 -17 34
+| Name = septendecima
-|Name=25/24 equal step tuning kleisma
+| Color name = LLy<sup>34</sup>-8, lala-sebiyo negative octave
+| Comma = yes
 }}
-'''25/24 equal step tuning kleisma''', or 582076609134674072265625/581595589965365114830848 when fully written out, is a 5-limit unnoticeable comma. It represents the difference between a stack of 17 [[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 '''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]].
+== Temperaments ==
+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]]