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87edo: Difference between revisions

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→Intervals: reduce cent values to one decimal place, per discussion on Discord. "31-limit extension" would be good enough; no need to explicitly exclude prime 7
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{| class="wikitable center-all right-2 left-3 left-4"
{| class="wikitable center-all right-2 left-3 left-4"
|-
|-
! rowspan="2" | #
! rowspan="2" | #
! rowspan="2" | Cents
! rowspan="2" | Cents
! colspan="2" | Approximated Ratios
! colspan="2" | Approximated ratios
! colspan="2" rowspan="2" | [[Ups and Downs Notation]]
! colspan="2" rowspan="2" | [[Ups and downs notation]]
|-
|-
! 13-Limit
! 13-limit
! 31-Limit No-7s Extension
! 31-limit extension
|-
|-
| 0
| 0
| 0.000
| 0.0
| [[1/1]]
| [[1/1]]
|
|
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|-
|-
| 1
| 1
| 13.793
| 13.8
| [[91/90]], [[100/99]], [[126/125]]
| [[91/90]], [[100/99]], [[126/125]]
|
|
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|-
|-
| 2
| 2
| 27.586
| 27.6
| ''[[49/48]]'', [[55/54]], [[64/63]], [[65/64]], [[81/80]]
| ''[[49/48]]'', [[55/54]], [[64/63]], [[65/64]], [[81/80]]
|
|
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|-
|-
| 3
| 3
| 41.379
| 41.4
| [[40/39]], [[45/44]], [[50/49]]
| [[40/39]], [[45/44]], [[50/49]]
| [[39/38]]
| [[39/38]]
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|-
|-
| 4
| 4
| 55.172
| 55.2
| ''[[28/27]]'', [[33/32]], [[36/35]]
| ''[[28/27]]'', [[33/32]], [[36/35]]
| [[30/29]], [[31/30]], [[32/31]], [[34/33]]
| [[30/29]], [[31/30]], [[32/31]], [[34/33]]
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|-
|-
| 5
| 5
| 68.966
| 69.0
| [[25/24]], [[26/25]], [[27/26]]
| [[25/24]], [[26/25]], [[27/26]]
| [[24/23]]
| [[24/23]]
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|-
|-
| 6
| 6
| 82.759
| 82.8
| [[21/20]], [[22/21]]
| [[21/20]], [[22/21]]
| [[20/19]], [[23/22]]
| [[20/19]], [[23/22]]
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|-
|-
| 7
| 7
| 96.552
| 96.6
| [[35/33]]
| [[35/33]]
| [[18/17]], [[19/18]]
| [[18/17]], [[19/18]]
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|-
|-
| 8
| 8
| 110.345
| 110.3
| [[16/15]]
| [[16/15]]
| [[17/16]], [[31/29]], [[33/31]]
| [[17/16]], [[31/29]], [[33/31]]
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|-
|-
| 9
| 9
| 124.138
| 124.1
| [[14/13]], [[15/14]]
| [[14/13]], [[15/14]]
| [[29/27]]
| [[29/27]]
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|-
|-
| 10
| 10
| 137.931
| 137.9
| [[13/12]], [[27/25]]
| [[13/12]], [[27/25]]
| [[25/23]]
| [[25/23]]
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|-
|-
| 11
| 11
| 151.724
| 151.7
| [[12/11]], [[35/32]]
| [[12/11]], [[35/32]]
|
|
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|-
|-
| 12
| 12
| 165.517
| 165.5
| [[11/10]]
| [[11/10]]
| [[32/29]], [[34/31]]
| [[32/29]], [[34/31]]
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|-
|-
| 13
| 13
| 179.310
| 179.3
| [[10/9]]
| [[10/9]]
|
|
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|-
|-
| 14
| 14
| 193.103
| 193.1
| [[28/25]]
| [[28/25]]
| [[19/17]], [[29/26]]
| [[19/17]], [[29/26]]
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|-
|-
| 15
| 15
| 206.897
| 206.9
| [[9/8]]
| [[9/8]]
| [[26/23]]
| [[26/23]]
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|-
|-
| 16
| 16
| 220.690
| 220.7
| [[25/22]]
| [[25/22]]
| [[17/15]], [[33/29]]
| [[17/15]], [[33/29]]
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|-
|-
| 17
| 17
| 234.483
| 234.5
| [[8/7]]
| [[8/7]]
| [[31/27]]
| [[31/27]]
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|-
|-
| 18
| 18
| 248.276
| 248.3
| [[15/13]]
| [[15/13]]
| [[22/19]], [[23/20]], [[38/33]]
| [[22/19]], [[23/20]], [[38/33]]
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|-
|-
| 19
| 19
| 262.089
| 262.1
| [[7/6]]
| [[7/6]]
| [[29/25]], [[36/31]]
| [[29/25]], [[36/31]]
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|-
|-
| 20
| 20
| 275.862
| 275.9
| [[75/64]]
| [[75/64]]
| [[20/17]], [[27/23]], [[34/29]]
| [[20/17]], [[27/23]], [[34/29]]
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|-
|-
| 21
| 21
| 289.655
| 289.7
| [[13/11]], [[32/27]], [[33/28]]
| [[13/11]], [[32/27]], [[33/28]]
|
|
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|-
|-
| 22
| 22
| 303.448
| 303.4
| [[25/21]]
| [[25/21]]
| [[19/16]], [[31/26]]
| [[19/16]], [[31/26]]
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|-
|-
| 23
| 23
| 317.241
| 317.2
| [[6/5]]
| [[6/5]]
|
|
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|-
|-
| 24
| 24
| 331.034
| 331.0
| [[40/33]]
| [[40/33]]
| [[23/19]], [[29/24]]
| [[23/19]], [[29/24]]
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|-
|-
| 25
| 25
| 344.828
| 344.8
| [[11/9]], [[39/32]]
| [[11/9]], [[39/32]]
|
|
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|-
|-
| 26
| 26
| 358.621
| 358.6
| [[16/13]], [[27/22]]
| [[16/13]], [[27/22]]
| [[38/31]]
| [[38/31]]
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|-
|-
| 27
| 27
| 372.414
| 372.4
| [[26/21]]
| [[26/21]]
| [[31/25]], [[36/29]]
| [[31/25]], [[36/29]]
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|-
|-
| 28
| 28
| 386.207
| 386.2
| [[5/4]]
| [[5/4]]
|
|
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|-
|-
| 29
| 29
| 400.000
| 400.0
| [[44/35]]
| [[44/35]]
| [[24/19]], [[29/23]], [[34/27]]
| [[24/19]], [[29/23]], [[34/27]]
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|-
|-
| 30
| 30
| 413.793
| 413.8
| [[14/11]], [[33/26]], [[81/64]]
| [[14/11]], [[33/26]], [[81/64]]
| [[19/15]]
| [[19/15]]
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|-
|-
| 31
| 31
| 427.586
| 427.6
| [[32/25]]
| [[32/25]]
| [[23/18]]
| [[23/18]]
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|-
|-
| 32
| 32
| 441.379
| 441.4
| [[9/7]], [[35/27]]
| [[9/7]], [[35/27]]
| [[22/17]], [[31/24]], [[40/31]]
| [[22/17]], [[31/24]], [[40/31]]
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|-
|-
| 33
| 33
| 455.172
| 455.2
| [[13/10]]
| [[13/10]]
| [[30/23]]
| [[30/23]]
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|-
|-
| 34
| 34
| 468.966
| 469.0
| [[21/16]]
| [[21/16]]
| [[17/13]], [[25/19]], [[38/29]]
| [[17/13]], [[25/19]], [[38/29]]
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|-
|-
| 35
| 35
| 482.759
| 482.8
| [[33/25]]
| [[33/25]]
|
|
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|-
|-
| 36
| 36
| 496.552
| 496.6
| [[4/3]]
| [[4/3]]
|
|
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|-
|-
| 37
| 37
| 510.345
| 510.3
| [[35/26]]
| [[35/26]]
| [[31/23]]
| [[31/23]]
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|-
|-
| 38
| 38
| 524.138
| 524.1
| [[27/20]]
| [[27/20]]
| [[23/17]]
| [[23/17]]
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|-
|-
| 39
| 39
| 537.931
| 537.9
| [[15/11]]
| [[15/11]]
| [[26/19]], [[34/25]]
| [[26/19]], [[34/25]]
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|-
|-
| 40
| 40
| 551.724
| 551.7
| [[11/8]], [[48/35]]
| [[11/8]], [[48/35]]
|
|
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|-
|-
| 41
| 41
| 565.517
| 565.5
| [[18/13]]
| [[18/13]]
| [[32/23]]
| [[32/23]]
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|-
|-
| 42
| 42
| 579.310
| 579.3
| [[7/5]]
| [[7/5]]
| [[46/33]]
| [[46/33]]
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|-
|-
| 43
| 43
| 593.103
| 593.1
| [[45/32]]
| [[45/32]]
| [[24/17]], [[31/22]], [[38/27]]
| [[24/17]], [[31/22]], [[38/27]]
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