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31edo: Difference between revisions

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Line 4,134: Line 4,134:
31 EDO [[tempers out]] the following [[commas]]. (Note: This assumes the [[val]] {{val| 31 49 72 87 107 115 }}, comma values rounded to 5 significant digits.)
31 EDO [[tempers out]] the following [[commas]]. (Note: This assumes the [[val]] {{val| 31 49 72 87 107 115 }}, comma values rounded to 5 significant digits.)


{| class="wikitable center-all left-2 right-3"
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
|-
! [[Ratio]]
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
! [[Monzo]]
! [[Cents]]
! [[Cents]]
! [[Color name]]
! [[Color name]]
! Name 1
! Name(s)
! Name 2
! Name 3
|-
|-
| 34171875/33554432
| 5
| [[34171875/33554432|(16 digits)]]
| {{Monzo| -25 7 6 }}
| {{Monzo| -25 7 6 }}
| 31.567
| 31.567
| Lala-tribiyo
| Lala-tribiyo
| [[ampersand|Ampersand's Comma]]
| [[Ampersand]]
|
|
|-
|-
| 81/80
| 5
| [[81/80]]
| {{Monzo| -4 4 -1 }}
| {{Monzo| -4 4 -1 }}
| 21.506
| 21.506
| Gu
| Gu
| [[Syntonic Comma]]
| [[Syntonic comma]], Didymos comma, meantone comma
| Didymos Comma
| Meantone Comma
|-
|-
| 393216/390625
| 5
| [[393216/390625|(12 digits)]]
| {{Monzo| 17 1 -8 }}
| {{Monzo| 17 1 -8 }}
| 11.445
| 11.445
| Saquadbigu
| Saquadbigu
| [[Würschmidt comma|Würschmidt Comma]]
| [[Würschmidt comma]]
|
|
|-
|-
| 2109375/2097152
| 5
| [[2109375/2097152|(14 digits)]]
| {{Monzo| -21 3 7 }}
| {{Monzo| -21 3 7 }}
| 10.061
| 10.061
| Lasepyo
| Lasepyo
| [[Semicomma]]
| [[Semicomma]], Fokker comma
| Fokker Comma
|
|-
|-
| 6719816/6714445
| 5
| <abbr title="274877906944/274658203125">(24 digits)</abbr>
| {{Monzo| 38 -2 -15 }}
| {{Monzo| 38 -2 -15 }}
| 1.3843
| 1.3843
| Sasa-quintrigu
| Sasa-quintrigu
| Hemithirds Comma
| [[Hemithirds comma]]
|
|
|-
|-
| 9859966/9733137
| 7
| <abbr title="854296875/843308032">(18 digits)</abbr>
| {{Monzo| -10 7 8 -7 }}
| {{Monzo| -10 7 8 -7 }}
| 22.413
| 22.413
| Lasepru-aquadbiyo
| Lasepru-aquadbiyo
| Blackjackisma
| [[Blackjackisma]]
|
|
|-
|-
| 64827/64000
| 7
| [[64827/64000]]
| {{Monzo| -9 3 -3 4 }}
| {{Monzo| -9 3 -3 4 }}
| 22.227
| 22.227
| Laquadzo-atrigu
| Laquadzo-atrigu
| Squalentine
| Squalentine
|
|
|-
|-
| 2430/2401
| 7
| [[2430/2401]]
| {{Monzo| 1 5 1 -4 }}
| {{Monzo| 1 5 1 -4 }}
| 20.785
| 20.785
| Quadru-ayo
| Quadru-ayo
| Nuwell
| Nuwell
|
|
|-
|-
| 50421/50000
| 7
| [[50421/50000]]
| {{Monzo| -4 1 -5 5 }}
| {{Monzo| -4 1 -5 5 }}
| 14.516
| 14.516
| Quinzogu
| Quinzogu
| Trimyna
| Trimyna
|
|
|-
|-
| 126/125
| 7
| [[126/125]]
| {{Monzo| 1 2 -3 1 }}
| {{Monzo| 1 2 -3 1 }}
| 13.795
| 13.795
| Zotrigu
| Zotrigu
| [[126/125|Septimal Semicomma]]
| Septimal semicomma, Starling comma
| Starling Comma
|
|-
|-
| 1728/1715
| 7
| [[1728/1715]]
| {{Monzo| 6 3 -1 -3 }}
| {{Monzo| 6 3 -1 -3 }}
| 13.074
| 13.074
| Trizo-agu
| Trizo-agu
| Orwellisma
| Orwellisma, Orwell comma
| Orwell Comma
|
|-
|-
| 1029/1024
| 7
| [[1029/1024]]
| {{Monzo| -10 1 0 3 }}
| {{Monzo| -10 1 0 3 }}
| 8.4327
| 8.4327
| Latrizo
| Latrizo
| Gamelisma
| Gamelisma
|
|
|-
|-
| 225/224
| 7
| [[225/224]]
| {{Monzo| -5 2 2 -1 }}
| {{Monzo| -5 2 2 -1 }}
| 7.7115
| 7.7115
| Ruyoyo
| Ruyoyo
| [[225/224|Septimal Kleisma]]
| Septimal kleisma, Marvel comma
| Marvel Comma
|
|-
|-
| 16875/16807
| 7
| [[16875/16807]]
| {{Monzo| 0 3 4 -5 }}
| {{Monzo| 0 3 4 -5 }}
| 6.9903
| 6.9903
| Quinru-aquadyo
| Quinru-aquadyo
| Mirkwai
| Mirkwai
|
|
|-
|-
| 3136/3125
| 7
| [[3136/3125]]
| {{Monzo| 6 0 -5 2 }}
| {{Monzo| 6 0 -5 2 }}
| 6.0832
| 6.0832
| Zozoquingu
| Zozoquingu
| Hemimean
| Hemimean
|
|
|-
|-
| 6144/6125
| 7
| [[6144/6125]]
| {{Monzo| 11 1 -3 -2 }}
| {{Monzo| 11 1 -3 -2 }}
| 5.3621
| 5.3621
| Sarurutrigu
| Sarurutrigu
| Porwell
| Porwell
|
|
|-
|-
| 1065875/1063543
| 7
| <abbr title="201768035/201326592">(18 digits)</abbr>
| {{Monzo| -26 -1 1 9 }}
| {{Monzo| -26 -1 1 9 }}
| 3.7919
| 3.7919
| Latritrizo-ayo
| Latritrizo-ayo
| Wadisma
| [[Wadisma]]
|
|
|-
|-
| 65625/65536
| 7
| [[65625/65536]]
| {{Monzo| -16 1 5 1 }}
| {{Monzo| -16 1 5 1 }}
| 2.3495
| 2.3495
| Lazoquinyo
| Lazoquinyo
| Horwell
| Horwell
|
|
|-
|-
| 703125/702464
| 7
| [[703125/702464|(12 digits)]]
| {{Monzo| -11 2 7 -3 }}
| {{Monzo| -11 2 7 -3 }}
| 1.6283
| 1.6283
| Latriru-asepyo
| Latriru-asepyo
| Meter
| [[Meter]]
|
|
|-
|-
| 2401/2400
| 7
| [[2401/2400]]
| {{Monzo| -5 -1 -2 4 }}
| {{Monzo| -5 -1 -2 4 }}
| 0.72120
| 0.72120
| Bizozogu
| Bizozogu
| Breedsma
| Breedsma
|
|
|-
|-
| 99/98
| 11
| [[99/98]]
| {{Monzo| -1 2 0 -2 1 }}
| {{Monzo| -1 2 0 -2 1 }}
| 17.576
| 17.576
| Loruru
| Loruru
| Mothwellsma
| Mothwellsma
|
|
|-
|-
| 121/120
| 11
| [[121/120]]
| {{Monzo| -3 -1 -1 0 2 }}
| {{Monzo| -3 -1 -1 0 2 }}
| 14.367
| 14.367
| Lologu
| Lologu
| Biyatisma
| Biyatisma
|
|
|-
|-
| 176/175
| 11
| [[176/175]]
| {{Monzo| 4 0 -2 -1 1 }}
| {{Monzo| 4 0 -2 -1 1 }}
| 9.8646
| 9.8646
| Lorugugu
| Lorugugu
| Valinorsma
| Valinorsma
|
|
|-
|-
| 243/242
| 11
| [[243/242]]
| {{Monzo| -1 5 0 0 -2 }}
| {{Monzo| -1 5 0 0 -2 }}
| 7.1391
| 7.1391
| Lulu
| Lulu
| Rastma
| Rastma
|
|
|-
|-
| 385/384
| 11
| [[385/384]]
| {{Monzo| -7 -1 1 1 1 }}
| {{Monzo| -7 -1 1 1 1 }}
| 4.5026
| 4.5026
| Lozoyo
| Lozoyo
| [[385/384|Keenanisma]]
| Keenanisma
|
|
|-
|-
| 441/440
| 11
| [[441/440]]
| {{Monzo| -3 2 -1 2 -1 }}
| {{Monzo| -3 2 -1 2 -1 }}
| 3.9302
| 3.9302
| Luzozogu
| Luzozogu
| Werckisma
| Werckisma
|
|
|-
|-
| 540/539
| 11
| [[540/539]]
| {{Monzo| 2 3 1 -2 -1 }}
| {{Monzo| 2 3 1 -2 -1 }}
| 3.2090
| 3.2090
| Lururuyo
| Lururuyo
| Swetisma
| Swetisma
|
|
|-
|-
| 3025/3024
| 11
| [[3025/3024]]
| {{Monzo| -4 -3 2 -1 2 }}
| {{Monzo| -4 -3 2 -1 2 }}
| 0.57240
| 0.57240
| Loloruyoyo
| Loloruyoyo
| Lehmerisma
| Lehmerisma
|
|
|}
|}
<references/>


== Linear temperaments ==
== Linear temperaments ==
Retrieved from "https://en.xen.wiki/w/31edo"