16edo: Difference between revisions

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Intervals: add simpler ratios
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== Intervals ==
== Intervals ==
Inconsistent intervals are in ''italics''.


{| class="wikitable center-all"
{| class="wikitable center-all right-2"
|+ style="font-size: 105%" | Intervals of 16edo
|-
|-
! Degree
! rowspan="2" | Degree
! [[Cent]]s
! rowspan="2" | [[Cent]]s
! Approximate ratios*
! colspan="3" | Approximate ratios
|-
! [[2.3.5.11 subgroup|2.3.5.11]] mavila
! 13-limit armodue
! JI approximation*
|-
|-
| 0
| 0
| 0
| 0
| [[1/1]]
| 1/1
| 1/1
| 1/1
|-
|-
| 1
| 1
| 75
| 75
| 28/27, 27/26
| [[25/24]]
| ''[[15/14]]'', [[21/20]], [[22/21]], [[26/25]]
| [[28/27]], [[27/26]]
|-
|-
| 2
| 2
| 150
| 150
| 12/11, 35/32
| ''[[9/8]]'', [[11/10]], [[12/11]], ''[[16/15]]''
| [[13/12]], [[14/13]]
| 12/11, [[35/32]]
|-
|-
| 3
| 3
| 225
| 225
| ''[[10/9]]'', [[25/22]]
| [[8/7]], [[15/13]], [[28/25]]
| 8/7
| 8/7
|-
|-
| 4
| 4
| 300
| 300
| 19/16, 32/27
| [[6/5]]
| [[7/6]], [[13/11]], [[25/21]]
| [[19/16]], [[32/27]]
|-
|-
| 5
| 5
| 375
| 375
| [[5/4]], [[11/9]]
| ''[[9/7]]'', [[16/13]], [[26/21]]
| 5/4, 16/13, 26/21
| 5/4, 16/13, 26/21
|-
|-
| 6
| 6
| 450
| 450
| 13/10, 35/27
| [[32/25]]
| [[14/11]], [[13/10]], [[21/16]]
| 13/10, [[35/27]]
|-
|-
| 7
| 7
| 525
| 525
| 19/14, 27/20, 35/26
| [[4/3]], [[11/8]], [[15/11]]
| ''[[18/13]]''
| [[19/14]], [[27/20]], [[35/26]]
|-
|-
| 8
| 8
| 600
| 600
| [[25/18]], [[36/25]]
| [[7/5]], [[10/7]]
| 7/5, 10/7
| 7/5, 10/7
|-
|-
| 9
| 9
| 675
| 675
| 28/19, 40/27, 52/35
| [[3/2]], [[16/11]], [[22/15]]
| ''[[13/9]]''
| [[28/19]], [[40/27]], [[52/35]]
|-
|-
| 10
| 10
| 750
| 750
| 20/13, 54/35
| [[25/16]]
| [[11/7]], [[20/13]], [[32/21]]
| 20/13, [[54/35]]
|-
|-
| 11
| 11
| 825
| 825
| [[8/5]], [[18/11]]
| ''[[14/9]]'', [[13/8]], [[21/13]]
| 8/5, 13/8, 21/13
| 8/5, 13/8, 21/13
|-
|-
| 12
| 12
| 900
| 900
| 27/16, 32/19
| [[5/3]]
| [[12/7]], [[22/13]], [[42/25]]
| [[27/16]], [[32/19]]
|-
|-
| 13
| 13
| 975
| 975
| ''[[9/5]]'', [[44/25]]
| [[7/4]], [[26/15]], [[25/14]]
| 7/4
| 7/4
|-
|-
| 14
| 14
| 1050
| 1050
| 11/6, 64/35
| ''[[16/9]]'', [[20/11]], [[11/6]], ''[[15/8]]''
| [[24/13]], [[13/7]]
| [[11/6]], 64/35
|-
|-
| 15
| 15
| 1125
| 1125
| 27/14, 52/27
| [[48/25]]
| ''[[28/15]]'', [[40/21]], [[21/11]], [[25/13]]
| [[27/14]], [[52/27]]
|-
|-
| 16
| 16
| 1200
| 1200
| 2/1
| [[2/1]]
| [[2/1]]
| [[2/1]]
|}
|}


<nowiki />* Based on treating 16edo as a 2.27.5.7.13.19 subgroup temperament; other approaches are possible.
<nowiki />* Based on treating 16edo as a 2.27.5.7.13.19 subgroup temperament; other approaches are possible. Odd 27 is approximated via [[direct approximation]].


== Notation ==
== Notation ==