Septendecima: Difference between revisions
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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 [[octave]]. | 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]]. | ||
The [[regular temperament|temperament]] which [[tempering out|tempers out]] only this comma is 5-limit [[ | == 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:Chlorine]] | ||
[[Category:Commas named for their periods per equave]] | [[Category:Commas named for their periods per equave]] | ||
Latest revision as of 05:55, 17 April 2025
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The septendecima (monzo: [-52 -17 34⟩) is an unnoticeable 5-limit comma. It is the difference between a stack of seventeen 25/24's and one octave.
Temperaments
The temperament which tempers out only this comma is 5-limit 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[1]. 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.