27/25: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = large limma, acute minor second | |||
| Name = large limma | |||
| Color name = gg2, gugu 2nd | | Color name = gg2, gugu 2nd | ||
| Sound = jid_27_25_pluck_adu_dr220.mp3 | | 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 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. 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. | ||
== See also == | == See also == | ||
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* [[Large comma]] | * [[Large comma]] | ||
[[Category:Second]] | [[Category:Second]] | ||
[[Category:Semitone]] | [[Category:Semitone]] | ||
[[Category:Limma]] | [[Category:Limma]] | ||
[[Category:9edo]] | [[Category:9edo]] | ||
[[Category:Bug]] | [[Category:Bug]] | ||
[[Category: | [[Category:Neutral second]] | ||
[[Category:Supraminor second]] | |||
[[Category:Commas named after their interval size]] | |||
Latest revision as of 23:48, 2 April 2025
| Interval information |
acute minor second
S3 / S5
[sound info]
27/25, called the large limma or acute minor second, at 133.238 cents is a large semitone interval which is a 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 [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 subminor third, since (7/6)/(27/25)2 = 4375/4374. Tempering out both the ennealimma and 4375/4374, the ragisma, leads to the 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 tempered out, leading to the bug family of temperaments.