27/25: Difference between revisions

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'''27/25''', called the '''large limma''' or '''acute minor second''', at 133.238 [[cent]]s is a large semitone interval which is a [[81/80|syntonic comma]] above the 5-limit minor second [[16/15]], or 2 syntonic commas above the Pythagorean minor second [[256/243]]. It has the remarkable property of almost exactly equaling a single step of [[9edo]], a step of which is 133 1/3 cents. Hence, nine large limmas fall just short of an octave by the [[ennealimma]] which is {{monzo| 1 -27 18 }}, a comma of less than a cent in size. If all of that were not enough, two large limmas are almost exactly a [[7/6|subminor third]], since (7/6)/(27/25)<sup>2</sup> = [[4375/4374]]. Tempering out both the ennealimma and [[4375/4374]], the ragisma, leads to the [[Ragismic microtemperaments #Ennealimmal|ennealimmal temperament]]. Ennealimmal is an extremely accurate temperament, while still being of a somewhat manageable complexity. Turning from microtempering to exotempering, 27/25 can be [[tempering out|tempered out]], leading to the [[bug family]] of temperaments

'''27/25''', called the '''large limma''' or '''acute minor second''', at 133.238 [[cent]]s is a large semitone interval which is a [[81/80|syntonic comma]] above the 5-limit minor second [[16/15]], or 2 syntonic commas above the Pythagorean minor second [[256/243]]. It has the remarkable property of almost exactly equaling a single step of [[9edo]], a step of which is 133 1/3 cents. Hence, nine large limmas fall just short of an octave by the [[ennealimma]] which is {{monzo| 1 -27 18 }}, a comma of less than a cent in size. If all of that were not enough, two large limmas are almost exactly a [[7/6|subminor third]], since (7/6)/(27/25)<sup>2</sup> = [[4375/4374]]. Tempering out both the ennealimma and [[4375/4374]], the ragisma, leads to the [[Ragismic microtemperaments #Ennealimmal|ennealimmal temperament]]. Ennealimmal is an extremely accurate temperament, while still being of a somewhat manageable complexity. Turning from microtempering to exotempering, 27/25 can be [[tempering out|tempered out]], leading to the [[bug family]] of temperaments.

~~Coincidentally,~~ 27/25 ~~is exactly three octaves below the ratio between 432hz and 50hz, common frequencies in tuning and AC electrical power respectively.~~

== Approximation ==

== See also ==

* [[50/27]] – its [[octave complement]]

* [[Gallery of just intervals]]

* [[Large comma]]

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-'''27/25''', called the '''large limma''' or '''acute minor second''', at 133.238 [[cent]]s is a large semitone interval which is a [[81/80|syntonic comma]] above the 5-limit minor second [[16/15]], or 2 syntonic commas above the Pythagorean minor second [[256/243]]. It has the remarkable property of almost exactly equaling a single step of [[9edo]], a step of which is 133 1/3 cents. Hence, nine large limmas fall just short of an octave by the [[ennealimma]] which is {{monzo| 1 -27 18 }}, a comma of less than a cent in size. If all of that were not enough, two large limmas are almost exactly a [[7/6|subminor third]], since (7/6)/(27/25)<sup>2</sup> = [[4375/4374]]. Tempering out both the ennealimma and [[4375/4374]], the ragisma, leads to the [[Ragismic microtemperaments #Ennealimmal|ennealimmal temperament]]. Ennealimmal is an extremely accurate temperament, while still being of a somewhat manageable complexity.  Turning from microtempering to exotempering, 27/25 can be [[tempering out|tempered out]], leading to the [[bug family]] of temperaments
+'''27/25''', called the '''large limma''' or '''acute minor second''', at 133.238 [[cent]]s is a large semitone interval which is a [[81/80|syntonic comma]] above the 5-limit minor second [[16/15]], or 2 syntonic commas above the Pythagorean minor second [[256/243]]. It has the remarkable property of almost exactly equaling a single step of [[9edo]], a step of which is 133 1/3 cents. Hence, nine large limmas fall just short of an octave by the [[ennealimma]] which is {{monzo| 1 -27 18 }}, a comma of less than a cent in size. If all of that were not enough, two large limmas are almost exactly a [[7/6|subminor third]], since (7/6)/(27/25)<sup>2</sup> = [[4375/4374]]. Tempering out both the ennealimma and [[4375/4374]], the ragisma, leads to the [[Ragismic microtemperaments #Ennealimmal|ennealimmal temperament]]. Ennealimmal is an extremely accurate temperament, while still being of a somewhat manageable complexity.  Turning from microtempering to exotempering, 27/25 can be [[tempering out|tempered out]], leading to the [[bug family]] of temperaments.
-Coincidentally, 27/25 is exactly three octaves below the ratio between 432hz and 50hz, common frequencies in tuning and AC electrical power respectively.
+== Approximation ==
+{{Interval edo approximation|27/25}}
 == See also ==
+* [[50/27]] – its [[octave complement]]
 * [[Gallery of just intervals]]
 * [[Large comma]]