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56edo: Difference between revisions

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No need to remind readers of what a regular temperament is everywhere
Tag: Undo
→Intervals: reduce cent values to one decimal place, per discussion on Discord
Line 18: Line 18:
{| class="wikitable center-all right-2 left-3"
{| class="wikitable center-all right-2 left-3"
|-
|-
! #
! #
! Cents
! Cents
! Approximate ratios*
! Approximate ratios*
Line 24: Line 24:
|-
|-
| 0
| 0
| 0.000
| 0.0
| [[1/1]]
| [[1/1]]
| {{UDnote|step=0}}
| {{UDnote|step=0}}
|-
|-
| 1
| 1
| 21.429
| 21.4
| ''[[49/48]]'', [[64/63]]
| ''[[49/48]]'', [[64/63]]
| {{UDnote|step=1}}
| {{UDnote|step=1}}
|-
|-
| 2
| 2
| 42.857
| 42.9
| ''[[28/27]]'', [[50/49]], ''[[81/80]]''
| ''[[28/27]]'', [[50/49]], ''[[81/80]]''
| {{UDnote|step=2}}
| {{UDnote|step=2}}
|-
|-
| 3
| 3
| 64.286
| 64.3
| [[25/24]], ''[[36/35]]'', ''[[33/32]]''
| [[25/24]], ''[[36/35]]'', ''[[33/32]]''
| {{UDnote|step=3}}
| {{UDnote|step=3}}
|-
|-
| 4
| 4
| 85.714
| 85.7
| [[21/20]], [[22/21]]
| [[21/20]], [[22/21]]
| {{UDnote|step=4}}
| {{UDnote|step=4}}
|-
|-
| 5
| 5
| 107.143
| 107.1
| [[16/15]]
| [[16/15]]
| {{UDnote|step=5}}
| {{UDnote|step=5}}
|-
|-
| 6
| 6
| 128.571
| 128.6
| [[15/14]], [[13/12]], [[14/13]]
| [[15/14]], [[13/12]], [[14/13]]
| {{UDnote|step=6}}
| {{UDnote|step=6}}
|-
|-
| 7
| 7
| 150.000
| 150.0
| [[12/11]]
| [[12/11]]
| {{UDnote|step=7}}
| {{UDnote|step=7}}
|-
|-
| 8
| 8
| 171.429
| 171.4
| ''[[10/9]]'', [[11/10]]
| ''[[10/9]]'', [[11/10]]
| {{UDnote|step=8}}
| {{UDnote|step=8}}
|-
|-
| 9
| 9
| 192.857
| 192.9
| [[28/25]]
| [[28/25]]
| {{UDnote|step=9}}
| {{UDnote|step=9}}
|-
|-
| 10
| 10
| 214.286
| 214.3
| [[9/8]]
| [[9/8]]
| {{UDnote|step=10}}
| {{UDnote|step=10}}
|-
|-
| 11
| 11
| 235.714
| 235.7
| [[8/7]]
| [[8/7]]
| {{UDnote|step=11}}
| {{UDnote|step=11}}
|-
|-
| 12
| 12
| 257.143
| 257.1
| [[7/6]], [[15/13]]
| [[7/6]], [[15/13]]
| {{UDnote|step=12}}
| {{UDnote|step=12}}
|-
|-
| 13
| 13
| 278.571
| 278.6
| [[75/64]], [[13/11]]
| [[75/64]], [[13/11]]
| {{UDnote|step=13}}
| {{UDnote|step=13}}
|-
|-
| 14
| 14
| 300.000
| 300.0
| [[25/21]]
| [[25/21]]
| {{UDnote|step=14}}
| {{UDnote|step=14}}
|-
|-
| 15
| 15
| 321.429
| 321.4
| [[6/5]]
| [[6/5]]
| {{UDnote|step=15}}
| {{UDnote|step=15}}
|-
|-
| 16
| 16
| 342.857
| 342.9
| [[11/9]], [[39/32]]
| [[11/9]], [[39/32]]
| {{UDnote|step=16}}
| {{UDnote|step=16}}
|-
|-
| 17
| 17
| 364.286
| 364.3
| [[27/22]], [[16/13]], [[26/21]]
| [[27/22]], [[16/13]], [[26/21]]
| {{UDnote|step=17}}
| {{UDnote|step=17}}
|-
|-
| 18
| 18
| 385.714
| 385.7
| [[5/4]]
| [[5/4]]
| {{UDnote|step=18}}
| {{UDnote|step=18}}
|-
|-
| 19
| 19
| 407.143
| 407.1
| [[14/11]]
| [[14/11]]
| {{UDnote|step=19}}
| {{UDnote|step=19}}
|-
|-
| 20
| 20
| 428.571
| 428.6
| [[32/25]], [[33/26]]
| [[32/25]], [[33/26]]
| {{UDnote|step=20}}
| {{UDnote|step=20}}
|-
|-
| 21
| 21
| 450.000
| 450.0
| ''[[9/7]]'', [[13/10]]
| ''[[9/7]]'', [[13/10]]
| {{UDnote|step=21}}
| {{UDnote|step=21}}
|-
|-
| 22
| 22
| 471.429
| 471.4
| [[21/16]]
| [[21/16]]
| {{UDnote|step=22}}
| {{UDnote|step=22}}
|-
|-
| 23
| 23
| 492.857
| 492.9
| [[4/3]]
| [[4/3]]
| {{UDnote|step=23}}
| {{UDnote|step=23}}
|-
|-
| 24
| 24
| 514.286
| 514.3
| [[35/26]]
| [[35/26]]
| {{UDnote|step=24}}
| {{UDnote|step=24}}
|-
|-
| 25
| 25
| 535.714
| 535.7
| ''[[27/20]]'', [[15/11]]
| ''[[27/20]]'', [[15/11]]
| {{UDnote|step=25}}
| {{UDnote|step=25}}
|-
|-
| 26
| 26
| 557.143
| 557.1
| [[11/8]]
| [[11/8]]
| {{UDnote|step=26}}
| {{UDnote|step=26}}
|-
|-
| 27
| 27
| 578.571
| 578.6
| [[7/5]]
| [[7/5]]
| {{UDnote|step=27}}
| {{UDnote|step=27}}
|-
|-
| 28
| 28
| 600.000
| 600.0
| [[45/32]], [[64/45]]
| [[45/32]], [[64/45]]
| {{UDnote|step=28}}
| {{UDnote|step=28}}
Line 173: Line 173:
| …
| …
|}
|}
<nowiki />* The following table assumes the [[patent val]] {{val| 56 89 130 157 194 207 }}; other approaches are possible. Inconsistent intervals are marked in ''italics''.
<nowiki/>* The following table assumes the 19-limit [[patent val]]; other approaches are possible. Inconsistent intervals are marked in ''italics''.


== Notation ==
== Notation ==
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