27/25: Difference between revisions

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'''27/25'''
{{Infobox Interval
|0 3 -2>
| Icon =
| Ratio = 27/25
| Monzo = 0 3 -2
| Cents = 133.23757
| Name = large limma
| Color name = gg2, gugu 2nd
| Sound = jid_27_25_pluck_adu_dr220.mp3
}}


133.2376 cents
'''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 [[ennealimma]] (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 [[ragisma]], leads to.


[[File:jid_27_25_pluck_adu_dr220.mp3]] [[:File:jid_27_25_pluck_adu_dr220.mp3|sound sample]]
Coincidentally 27/25 is exactly three octaves below the ratio between 432hz and 50hz, common frequencies in tuning and AC electrical power respectively.


'''27/25''', called the '''large limma''' or '''acute minor second''', at 133.238 [[cent|cent]]s, has the remarkable property of almost exactly equaling a singe step of [[9edo|9edo]], a step of which is 133 1/3 cents. Hence nine large limmas fall just short of an octave by the [[ennealimma|ennealimma]] (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|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 [[ragisma|ragisma]], leads to.
Coincidentally 27/25 is exactly three octaves below the ratio between 432hz and 50hz, common frequencies in tuning and AC electrical power respectively.
[[Category:9edo]]
[[Category:9edo]]
[[Category:interval]]
[[Category:Interval]]
[[Category:limma]]
[[Category:Limma]]
[[Category:ratio]]
[[Category:Ratio]]
[[Category:Semitone]]

Revision as of 23:03, 24 October 2018

Interval information
Ratio 27/25
Factorization 33 × 5-2
Monzo [0 3 -2⟩
Size in cents 133.2376¢
Name large limma
Color name gg2, gugu 2nd
FJS name [math]\displaystyle{ \text{m2}_{5,5} }[/math]
Special properties reduced
Tenney height (log2 nd) 9.39874
Weil height (log2 max(n, d)) 9.50978
Wilson height (sopfr(nd)) 19

[sound info]
Open this interval in xen-calc

27/25, called the large limma or acute minor second, at 133.238 cents, 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 ennealimma (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 subminor third, since (7/6)/(27/25)^2 = 4375/4374. Turning from microtempering to exotempering, 27/25 can be tempered out, leading to bug temperament, rather than the ennealimmal temperament which tempering out both the ennealimma and 4375/4374, the ragisma, leads to.

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

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