27/25: Difference between revisions
CompactStar (talk | contribs) Cleanup |
CompactStar (talk | contribs) No edit summary |
||
| Line 6: | Line 6: | ||
}} | }} | ||
'''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]]. | '''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. | Coincidentally, 27/25 is exactly three octaves below the ratio between 432hz and 50hz, common frequencies in tuning and AC electrical power respectively. | ||
Revision as of 09:21, 7 February 2024
| 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 Coincidentally, 27/25 is exactly three octaves below the ratio between 432hz and 50hz, common frequencies in tuning and AC electrical power respectively.