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53edo: Difference between revisions

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m →Intervals: 36/25 and 25/18 were missing, but also, 53edo is a model of 2.3.5.7.13 JI so it helps to have more accurate descriptors, but also, the cent values feel wrong and this is amplified by stacking them
 
(One intermediate revision by one other user not shown)
Line 49: Line 49:
|-
|-
| 1
| 1
| 22.6
| 22.64
| ''[[50/49]]'', [[64/63]], [[81/80]]
| ''[[50/49]]'', [[64/63]], [[81/80]]
| ^1
| ^1
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|-
| 2
| 2
| 45.3
| 45.28
| [[33/32]], [[36/35]], [[49/48]], [[128/125]]
| [[33/32]], [[36/35]], [[49/48]], [[128/125]]
| ^^1, vvm2
| ^^1, vvm2
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|-
| 3
| 3
| 67.9
| 67.92
| ''[[22/21]]'', [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| ''[[22/21]]'', [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| vvA1, vm2
| vvA1, vm2
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|-
| 4
| 4
| 90.6
| 90.57
| [[19/18]], [[20/19]], [[21/20]], [[256/243]]
| [[19/18]], [[20/19]], [[21/20]], [[256/243]]
| vA1, m2
| vA1, m2
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|-
| 5
| 5
| 113.2
| 113.21
| [[15/14]], [[16/15]]
| [[15/14]], [[16/15]]
| A1, ^m2
| A1, ^m2
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|-
|-
| 6
| 6
| 135.8
| 135.85
| [[13/12]], [[14/13]], [[27/25]]
| [[13/12]], [[14/13]], [[27/25]]
| ^^m2
| ^^m2
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|-
| 7
| 7
| 158.5
| 158.49
| [[11/10]], [[12/11]], [[35/32]], [[57/52]], [[800/729]]
| [[11/10]], [[12/11]], [[35/32]], [[57/52]], [[800/729]]
| vvM2
| vvM2
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| 8
| 8
| 181.1
| 181.13
| [[10/9]]
| [[10/9]]
| vM2
| vM2
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|-
|-
| 9
| 9
| 203.8
| 203.77
| [[9/8]]
| [[9/8]]
| M2
| M2
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|-
|-
| 10
| 10
| 226.4
| 226.42
| [[8/7]], [[256/225]]
| [[8/7]], [[256/225]]
| ^M2
| ^M2
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|-
|-
| 11
| 11
| 249.1
| 249.06
| [[15/13]], [[22/19]], [[125/108]], [[144/125]]
| [[15/13]], [[22/19]], [[125/108]], [[144/125]]
| ^^M2, vvm3
| ^^M2, vvm3
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|-
| 12
| 12
| 271.7
| 271.70
| [[7/6]], [[75/64]]
| [[7/6]], [[75/64]]
| vm3
| vm3
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|-
| 13
| 13
| 294.3
| 294.34
| [[13/11]], [[19/16]], [[32/27]]
| [[13/11]], [[19/16]], [[32/27]]
| m3
| m3
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| 14
| 14
| 317.0
| 316.98
| [[6/5]]
| [[6/5]]
| ^m3
| ^m3
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|-
|-
| 15
| 15
| 339.6
| 339.62
| [[11/9]], [[243/200]]
| [[11/9]], [[243/200]]
| ^^m3
| ^^m3
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|-
| 16
| 16
| 362.3
| 362.26
| [[16/13]], [[100/81]]
| [[16/13]], [[100/81]]
| vvM3
| vvM3
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|-
| 17
| 17
| 384.9
| 384.91
| [[5/4]]
| [[5/4]]
| vM3
| vM3
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|-
| 18
| 18
| 407.5
| 407.55
| [[19/15]], [[24/19]], [[81/64]]
| [[19/15]], [[24/19]], [[81/64]]
| M3
| M3
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|-
|-
| 19
| 19
| 430.2
| 430.19
| [[9/7]], ''[[14/11]]''
| [[9/7]], ''[[14/11]]''
| ^M3
| ^M3
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|-
|-
| 20
| 20
| 452.8
| 452.83
| [[13/10]], [[125/96]], [[162/125]]
| [[13/10]], [[125/96]], [[162/125]]
| ^^M3, vv4
| ^^M3, vv4
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| 21
| 21
| 475.5
| 475.47
| [[21/16]], [[25/19]], [[320/243]], [[675/512]]
| [[21/16]], [[25/19]], [[320/243]], [[675/512]]
| v4
| v4
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| 22
| 22
| 498.1
| 498.11
| [[4/3]]
| [[4/3]]
| P4
| P4
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|-
| 23
| 23
| 520.8
| 520.75
| [[19/14]], [[27/20]]
| [[19/14]], [[27/20]]
| ^4
| ^4
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|-
| 24
| 24
| 543.4
| 543.40
| [[11/8]], [[15/11]], [[26/19]]
| [[11/8]], [[15/11]], [[26/19]]
| ^^4
| ^^4
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|-
|-
| 25
| 25
| 566.0
| 566.04
| [[18/13]]
| [[18/13]], [[25/18]]
| vvA4, vd5
| vvA4, vd5
| dudaug 4th, downdim 5th
| dudaug 4th, downdim 5th
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|-
| 26
| 26
| 588.7
| 588.68
| [[7/5]], [[45/32]]
| [[7/5]], [[45/32]]
| vA4, d5
| vA4, d5
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| 27
| 27
| 611.3
| 611.32
| [[10/7]], [[64/45]]
| [[10/7]], [[64/45]]
| A4, ^d5
| A4, ^d5
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|-
| 28
| 28
| 634.0
| 633.96
| [[13/9]]
| [[13/9]], [[36/25]]
| ^A4, ^^d5
| ^A4, ^^d5
| upaug 4th, dupdim 5th
| upaug 4th, dupdim 5th
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|-
| 29
| 29
| 656.6
| 656.60
| [[16/11]], [[19/13]], [[22/15]]
| [[16/11]], [[19/13]], [[22/15]]
| vv5
| vv5
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|-
| 30
| 30
| 679.2
| 679.25
| [[28/19]], [[40/27]]
| [[28/19]], [[40/27]]
| v5
| v5
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| 31
| 31
| 701.9
| 701.89
| [[3/2]]
| [[3/2]]
| P5
| P5
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|-
| 32
| 32
| 724.5
| 724.53
| [[32/21]], [[38/25]], [[243/160]], [[1024/675]]
| [[32/21]], [[38/25]], [[243/160]], [[1024/675]]
| ^5
| ^5
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|-
| 33
| 33
| 747.2
| 747.17
| [[20/13]], [[125/81]], [[192/125]]
| [[20/13]], [[125/81]], [[192/125]]
| ^^5, vvm6
| ^^5, vvm6
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|-
| 34
| 34
| 769.8
| 769.81
| ''[[11/7]]'', [[14/9]], [[25/16]]
| ''[[11/7]]'', [[14/9]], [[25/16]]
| vm6
| vm6
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|-
| 35
| 35
| 792.5
| 792.45
| [[19/12]], [[30/19]], [[128/81]]
| [[19/12]], [[30/19]], [[128/81]]
| m6
| m6
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|-
| 36
| 36
| 815.1
| 815.09
| [[8/5]]
| [[8/5]]
| ^m6
| ^m6
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|-
|-
| 37
| 37
| 837.7
| 837.74
| [[13/8]], [[81/50]]
| [[13/8]], [[81/50]]
| ^^m6
| ^^m6
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|-
| 38
| 38
| 860.4
| 860.38
| [[18/11]], [[400/243]]
| [[18/11]], [[400/243]]
| vvM6
| vvM6
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|-
| 39
| 39
| 883.0
| 883.02
| [[5/3]]
| [[5/3]]
| vM6
| vM6
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|-
| 40
| 40
| 905.7
| 905.66
| [[22/13]], [[27/16]], [[32/19]]
| [[22/13]], [[27/16]], [[32/19]]
| M6
| M6
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|-
|-
| 41
| 41
| 928.3
| 928.30
| [[12/7]]
| [[12/7]]
| ^M6
| ^M6
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|-
| 42
| 42
| 950.9
| 950.94
| [[19/11]], [[26/15]], [[125/72]], [[216/125]]
| [[19/11]], [[26/15]], [[125/72]], [[216/125]]
| ^^M6, vvm7
| ^^M6, vvm7
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|-
| 43
| 43
| 973.6
| 973.58
| [[7/4]]
| [[7/4]]
| vm7
| vm7
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|-
|-
| 44
| 44
| 996.2
| 996.23
| [[16/9]]
| [[16/9]]
| m7
| m7
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|-
|-
| 45
| 45
| 1018.9
| 1018.87
| [[9/5]]
| [[9/5]]
| ^m7
| ^m7
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|-
|-
| 46
| 46
| 1041.5
| 1041.51
| [[11/6]], [[20/11]], [[64/35]], [[729/400]]
| [[11/6]], [[20/11]], [[64/35]], [[729/400]]
| ^^m7
| ^^m7
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|-
| 47
| 47
| 1064.2
| 1064.15
| [[13/7]], [[24/13]], [[50/27]]
| [[13/7]], [[24/13]], [[50/27]]
| vvM7
| vvM7
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|-
|-
| 48
| 48
| 1086.8
| 1086.79
| [[15/8]]
| [[15/8]]
| vM7
| vM7
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|-
|-
| 49
| 49
| 1109.4
| 1109.43
| [[19/10]], [[36/19]], [[40/21]], [[243/128]]
| [[19/10]], [[36/19]], [[40/21]], [[243/128]]
| M7
| M7
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|-
|-
| 50
| 50
| 1132.1
| 1132.08
| ''[[21/11]]'', [[25/13]], [[27/14]], [[52/27]], [[48/25]]
| ''[[21/11]]'', [[25/13]], [[27/14]], [[52/27]], [[48/25]]
| ^M7
| ^M7
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|-
|-
| 51
| 51
| 1154.7
| 1154.72
| [[35/18]], [[64/33]], [[96/49]], [[125/64]]
| [[35/18]], [[64/33]], [[96/49]], [[125/64]]
| ^^M7, vv8
| ^^M7, vv8
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|-
|-
| 52
| 52
| 1177.4
| 1177.36
| ''[[49/25]]'', [[63/32]], [[160/81]]
| ''[[49/25]]'', [[63/32]], [[160/81]]
| v8
| v8
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=== Sagittal notation ===
=== Sagittal notation ===
53edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal notation#Spartan extension single-shaft|Spartan extension]], with the apotome equal to 5 edosteps and the limma to 4 edosteps. Here is a simplified table:
53edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal notation#Spartan|Spartan set]], with the apotome equal to 5 edosteps and the limma to 4 edosteps. Here is a simplified table:


{| class="wikitable" style="text-align: center;"
{| class="wikitable" style="text-align: center;"
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| rowspan="2" | <big>{{sagittal|/|}}</big>
| rowspan="2" | <big>{{sagittal|/|}}</big>
| rowspan="2" | <big>{{sagittal|//|}}</big>
| rowspan="2" | <big>{{sagittal|//|}}</big>
| <small>{{sagittal|#}}{{sagittal|\\!}}</small>
| {{sagittal|\\!}}{{sagittal|#}}
| <small>{{sagittal|#}}{{sagittal|\!}}</small>
| {{sagittal|\!}}{{sagittal|#}}
| <big>{{sagittal|#}}</big>
| <big>{{sagittal|#}}</big>
|-
|-
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