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31edo: Difference between revisions

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m →Theory: shorten the prime harmonics table (per discussion on Discord)
m →Intervals: cleanup. Reduced to one decimal place for cent values, per discussion on Discord
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! Degree
! Degree
! Cents
! Cents
! Approximate Ratios<ref group="note">{{sg|limit=23-limit}}</ref>
! Approximate ratios<ref group="note">{{sg|limit=23-limit}}</ref>
! colspan="3" | [[Ups and Downs Notation|Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and vd2)
! colspan="3" | [[Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and vd2)
! colspan="3" | Extended pythagorean notation
! colspan="3" | Extended pythagorean notation
! colspan="3" | [[SKULO interval names|SKULO]] notation (S or {{nowrap|U {{=}} 1}})
! colspan="3" | [[SKULO interval names|SKULO notation]] (S or {{nowrap|U {{=}} 1}})
|-
|-
| 0
| 0
| 0.00
| 0.0
| 1/1
| 1/1
| P1
| P1
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|-
|-
| 1
| 1
| 38.71
| 38.7
| 45/44, 49/48, 46/45, 128/125, 36/35
| 45/44, 49/48, 46/45, 128/125, 36/35
| ^1, d2
| ^1, d2
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|-
|-
| 2
| 2
| 77.42
| 77.4
| 25/24, 21/20, 22/21, 23/22
| 25/24, 21/20, 22/21, 23/22
| A1, vm2
| A1, vm2
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|-
|-
| 3
| 3
| 116.13
| 116.1
| 15/14, 16/15
| 15/14, 16/15
| m2
| m2
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|-
|-
| 4
| 4
| 154.84
| 154.8
| 12/11, 11/10, 35/32
| 12/11, 11/10, 35/32
| ~2
| ~2
Line 105: Line 105:
|-
|-
| 5
| 5
| 193.55
| 193.5
| 9/8, 10/9, 19/17, 28/25
| 9/8, 10/9, 19/17, 28/25
| M2
| M2
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|-
|-
| 6
| 6
| 232.26
| 232.3
| 8/7, 144/125
| 8/7, 144/125
| ^M2
| ^M2
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|-
|-
| 7
| 7
| 270.97
| 271.0
| 7/6, 75/64
| 7/6, 75/64
| vm3
| vm3
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|-
|-
| 8
| 8
| 309.68
| 309.7
| 6/5, 25/21
| 6/5, 25/21
| m3
| m3
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|-
|-
| 9
| 9
| 348.39
| 348.4
| 11/9, 27/22, 16/13, 60/49, 49/40
| 11/9, 27/22, 16/13, 60/49, 49/40
| ~3
| ~3
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|-
|-
| 10
| 10
| 387.10
| 387.1
| 5/4
| 5/4
| M3
| M3
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|-
|-
| 11
| 11
| 425.81
| 425.8
| 9/7, 14/11, 23/18, 32/25
| 9/7, 14/11, 23/18, 32/25
| ^M3
| ^M3
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|-
|-
| 12
| 12
| 464.52
| 464.5
| 21/16, 64/49, 13/10, 17/13, 125/96
| 21/16, 64/49, 13/10, 17/13, 125/96
| v4
| v4
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|-
|-
| 13
| 13
| 503.23
| 503.2
| 4/3
| 4/3
| P4
| P4
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|-
|-
| 14
| 14
| 541.94
| 541.9
| 175/128, 11/8, 15/11, 26/19
| 175/128, 11/8, 15/11, 26/19
| ^4, ~4
| ^4, ~4
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|-
|-
| 15
| 15
| 580.65
| 580.6
| 7/5, 45/32, 25/18
| 7/5, 45/32, 25/18
| A4, vd5
| A4, vd5
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|-
|-
| 16
| 16
| 619.35
| 619.4
| 10/7, 64/45, 36/25
| 10/7, 64/45, 36/25
| ^A4, d5
| ^A4, d5
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|-
|-
| 17
| 17
| 658.06
| 658.1
| 256/175, 16/11, 22/15, 19/13
| 256/175, 16/11, 22/15, 19/13
| v5, ~5
| v5, ~5
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|-
|-
| 18
| 18
| 696.77
| 696.8
| 3/2
| 3/2
| P5
| P5
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|-
|-
| 19
| 19
| 735.48
| 735.5
| 32/21, 49/32, 20/13, 26/17, 192/125
| 32/21, 49/32, 20/13, 26/17, 192/125
| ^5
| ^5
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|-
|-
| 20
| 20
| 774.19
| 774.2
| 14/9, 11/7, 25/16
| 14/9, 11/7, 25/16
| vm6
| vm6
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|-
|-
| 21
| 21
| 812.90
| 812.9
| 8/5
| 8/5
| m6
| m6
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|-
|-
| 22
| 22
| 851.61
| 851.6
| 18/11, 44/27, 13/8, 49/30, 80/49
| 18/11, 44/27, 13/8, 49/30, 80/49
| ~6
| ~6
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|-
|-
| 23
| 23
| 890.32
| 890.3
| 5/3, 42/25
| 5/3, 42/25
| M6
| M6
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|-
|-
| 24
| 24
| 929.03
| 929.0
| 12/7, 128/75
| 12/7, 128/75
| ^M6
| ^M6
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|-
|-
| 25
| 25
| 967.74
| 967.7
| 7/4, 125/72
| 7/4, 125/72
| vm7
| vm7
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|-
|-
| 26
| 26
| 1006.45
| 1006.5
| 16/9, 9/5, 34/19, 25/14
| 16/9, 9/5, 34/19, 25/14
| m7
| m7
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|-
|-
| 27
| 27
| 1045.16
| 1045.2
| 11/6, 20/11, 64/35
| 11/6, 20/11, 64/35
| ~7
| ~7
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|-
|-
| 28
| 28
| 1083.87
| 1083.9
| 28/15, 15/8
| 28/15, 15/8
| M7
| M7
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|-
|-
| 29
| 29
| 1122.58
| 1122.6
| 48/25, 40/21, 21/11, 44/23
| 48/25, 40/21, 21/11, 44/23
| ^M7
| ^M7
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|-
|-
| 30
| 30
| 1161.29
| 1161.3
| 88/45, 96/49, 45/23, 125/64, 35/18
| 88/45, 96/49, 45/23, 125/64, 35/18
| v8
| v8
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|-
|-
| 31
| 31
| 1200.00
| 1200.0
| 2/1
| 2/1
| P8
| P8
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! Quality
! Quality
! [[Color name]]
! [[Color name]]
! Monzo Format
! Monzo format
! Examples
! Examples
|-
|-
| downminor
| downminor
| zo
| zo
| {{monzo|a b 0 1}}
| {{monzo| a b 0 1 }}
| 7/6, 7/4
| 7/6, 7/4
|-
|-
| rowspan="2" | minor
| rowspan="2" | minor
| fourthward wa
| fourthward wa
| {{monzo|a b}} where {{nowrap|b &lt; −1}}
| {{monzo| a b }} where {{nowrap| b > −1 }}
| 32/27, 16/9
| 32/27, 16/9
|-
|-
| gu
| gu
| {{monzo|a b -1}}
| {{monzo| a b -1 }}
| 6/5, 9/5
| 6/5, 9/5
|-
|-
| rowspan="2" | mid
| rowspan="2" | mid
| ilo
| ilo
| {{monzo|a b 0 0 1}}
| {{monzo| a b 0 0 1 }}
| 11/9, 11/6
| 11/9, 11/6
|-
|-
| lu
| lu
| {{monzo|a b 0 0 -1}}
| {{monzo| a b 0 0 -1 }}
| 12/11, 18/11
| 12/11, 18/11
|-
|-
| rowspan="2" | major
| rowspan="2" | major
| yo
| yo
| {{monzo|a b 1}}
| {{monzo| a b 1 }}
| 5/4, 5/3
| 5/4, 5/3
|-
|-
| fifthward wa
| fifthward wa
| {{monzo|a b}} where {{nowrap|b &gt; 1}}
| {{monzo| a b }} where {{nowrap| b > 1 }}
| 9/8, 27/16
| 9/8, 27/16
|-
|-
| upmajor
| upmajor
| ru
| ru
| {{monzo|a b 0 -1}}
| {{monzo| a b 0 -1 }}
| 9/7, 12/7
| 9/7, 12/7
|}
|}
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|-
|-
! [[Color notation|Color of the 3rd]]
! [[Color notation|Color of the 3rd]]
! JI Chord
! JI chord
! Edosteps
! Edosteps
! Notes of C Chord
! Notes of C chord
! Written name
! Written name
! Spoken name
! Spoken name
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|}
|}


For a more complete list of chords, see [[31edo Chord Names]] and [[Ups and Downs Notation #Chords and Chord Progressions]].
For a more complete list of chords, see [[31edo Chord Names]] and [[Ups and downs notation #Chords and chord progressions]].


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