27/25: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = large limma, acute minor second

~~| Ratio = 27/25~~

| Color name = gg2, gugu 2nd

~~| Monzo = 0 3 -2~~

~~| Cents = 133.23757~~

| Name = large limma

| Color name = gg2, gugu 2nd

| Sound = jid_27_25_pluck_adu_dr220.mp3

| Comma = yes

}}

'''27/25''', called the '''large limma''' or '''acute minor second''', at 133.238 [[cent]]s, has the remarkable property of almost exactly equaling a ~~singe~~ step of [[9edo]], a step of which is 133 1/3 cents. Hence nine large limmas fall just short of an octave by the [[~~ennealimmal~~]] ~~(meaning "nine limmas")~~ which is |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)^2 = 4375/4374. Turning from microtempering to exotempering, 27/25 can be [[~~tempering_out~~|tempered out]], leading to [[~~Bug_family|~~bug ~~temperament~~]]~~, rather than the [[Ragismic_microtemperaments#Ennealimmal|ennealimmal temperament]] which tempering out both the ennealimma and 4375/4374, the [[4375/4374|ragisma]], leads to~~.

'''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.~~

== See also ==

* [[Gallery of just intervals]]

* [[Large comma]]

[[Category:~~5-limit~~]]

[[Category:Second]]

[[Category:Semitone]]

[[Category:Limma]]

[[Category:9edo]]

[[Category:~~Interval~~]]

[[Category:Bug]]

[[Category:~~Limma~~]]

[[Category:Neutral second]]

[[Category:~~Large comma~~]]

[[Category:Supraminor second]]

[[Category:~~Ratio]]~~

[[Category:Commas named after their interval size]]

~~[[Category:Semitone~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = large limma, acute minor second
-| Ratio = 27/25
+| Color name = gg2, gugu 2nd
-| Monzo = 0 3 -2
-| Cents = 133.23757
-| Name = large limma
-| Color name = gg2, gugu 2nd
 | Sound = jid_27_25_pluck_adu_dr220.mp3
+| Comma = yes
 }}
-'''27/25''', called the '''large limma''' or '''acute minor second''', at 133.238 [[cent]]s, has the remarkable property of almost exactly equaling a singe step of [[9edo]], a step of which is 133 1/3 cents. Hence nine large limmas fall just short of an octave by the [[ennealimmal]] (meaning "nine limmas") which is |1 -27 18&gt;, 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)^2 = 4375/4374. Turning from microtempering to exotempering, 27/25 can be [[tempering_out|tempered out]], leading to [[Bug_family|bug temperament]], rather than the [[Ragismic_microtemperaments#Ennealimmal|ennealimmal temperament]] which tempering out both the ennealimma and 4375/4374, the [[4375/4374|ragisma]], leads to.
+'''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.
+== See also ==
+* [[Gallery of just intervals]]
+* [[Large comma]]
-[[Category:5-limit]]
+[[Category:Second]]
+[[Category:Semitone]]
+[[Category:Limma]]
 [[Category:9edo]]
-[[Category:Interval]]
+[[Category:Bug]]
-[[Category:Limma]]
+[[Category:Neutral second]]
-[[Category:Large comma]]
+[[Category:Supraminor second]]
-[[Category:Ratio]]
+[[Category:Commas named after their interval size]]
-[[Category:Semitone]]