17edf: Difference between revisions

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autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
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→Intervals: efficiently format align cells, fixed decimals are better right-aligned, please recap rounding: 0..4↓ and 5..9↑ so it's should feel balanced (50/50) -- what's the problem with that?
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== Intervals ==
== Intervals ==
{| class="wikitable"
 
{| class="wikitable center-all right-2"
|-
|-
! |Degree
! Degree
! |Cents
! Cents
! |Approx. ratiosof the [[15-limit]]
! Approx. ratios of the [[15-odd-limit]]
|-
|-
! colspan="2" style="text-align:center;" |0
| 0
| style="text-align:center;" |1/1
| 0.0000
| 1/1
|-
|-
| style="text-align:center;" |1
| 1
| style="text-align:center;" |41.2915
| 41.2915
| style="text-align:center;" |25/24~33/32~56/55~81/80
| 25/24~33/32~56/55~81/80
|-
|-
| style="text-align:center;" |2
| 2
| style="text-align:center;" |82.5829
| 82.5829
| style="text-align:center;" |21/20
| 21/20
|-
|-
| style="text-align:center;" |3
| 3
| style="text-align:center;" |123.8744
| 123.8744
| style="text-align:center;" |16/15, 15/14, 14/13, 13/12
| 16/15, 15/14, 14/13, 13/12
|-
|-
| style="text-align:center;" |4
| 4
| style="text-align:center;" |165.1659
| 165.1659
| style="text-align:center;" |12/11, 11/10
| 12/11, 11/10
|-
|-
| style="text-align:center;" |5
| 5
| style="text-align:center;" |206.45735
| 206.4574
| style="text-align:center;" |9/8
| 9/8
|-
|-
| style="text-align:center;" |6
| 6
| style="text-align:center;" |248.7488
| 248.7488
| style="text-align:center;" |8/7, 7/6, 15/13
| 8/7, 7/6, 15/13
|-
|-
| style="text-align:center;" |7·
| 7·
| style="text-align:center;" |289.0403
| 289.0403
| style="text-align:center;" |13/11
| 13/11
|-
|-
| style="text-align:center;" |8
| 8
| style="text-align:center;" |330.3318
| 330.3318
| style="text-align:center;" |6/5, 11/9
| 6/5, 11/9
|-
|-
| style="text-align:center;" |9
| 9
| style="text-align:center;" |371.6232
| 371.6232
| style="text-align:center;" |5/4, 16/13
| 5/4, 16/13
|-
|-
| style="text-align:center;" |10
| 10
| style="text-align:center;" |412.9147
| 412.9147
| style="text-align:center;" |14/11
| 14/11
|-
|-
| style="text-align:center;" |11
| 11
| style="text-align:center;" |455.2062
| 455.2062
| style="text-align:center;" |9/7, 13/10
| 9/7, 13/10
|-
|-
| style="text-align:center;" |12·
| 12·
| style="text-align:center;" |495.49765
| 495.4976
| style="text-align:center;" |4/3
| 4/3
|-
|-
| style="text-align:center;" |13
| 13
| style="text-align:center;" |536.7891
| 536.7891
| style="text-align:center;" |11/8, 15/11
| 11/8, 15/11
|-
|-
| style="text-align:center;" |14
| 14
| style="text-align:center;" |578.0806
| 578.0806
| style="text-align:center;" |7/5, 18/13
| 7/5, 18/13
|-
|-
| style="text-align:center;" |15
| 15
| style="text-align:center;" |619.3721
| 619.3721
| style="text-align:center;" |10/7, 13/9
| 10/7, 13/9
|-
|-
| style="text-align:center;" |16
| 16
| style="text-align:center;" |660.6635
| 660.6635
| style="text-align:center;" |16/11, 22/15
| 16/11, 22/15
|-
|-
| style="text-align:center;" |17·
| 17·
| style="text-align:center;" |701.955
| 701.9550
| style="text-align:center;" |3/2
| 3/2
|-
|-
| style="text-align:center;" |18
| 18
| style="text-align:center;" |743.2465
| 743.2465
| style="text-align:center;" |14/9, 20/13
| 14/9, 20/13
|-
|-
| style="text-align:center;" |19
| 19
| style="text-align:center;" |784.5379
| 784.5379
| style="text-align:center;" |11/7
| 11/7
|-
|-
| style="text-align:center;" |20
| 20
| style="text-align:center;" |825.8294
| 825.8294
| style="text-align:center;" |8/5, 13/8
| 8/5, 13/8
|-
|-
| style="text-align:center;" |21
| 21
| style="text-align:center;" |867.1209
| 867.1209
| style="text-align:center;" |5/3, 18/11
| 5/3, 18/11
|-
|-
| style="text-align:center;" |22·
| 22·
| style="text-align:center;" |908.41235
| 908.4124
| style="text-align:center;" |22/13
| 22/13
|-
|-
| style="text-align:center;" |23
| 23
| style="text-align:center;" |949.7038
| 949.7038
| style="text-align:center;" |7/4, 12/7, 26/15
| 7/4, 12/7, 26/15
|-
|-
| style="text-align:center;" |24
| 24
| style="text-align:center;" |990.9952
| 990.9952
| style="text-align:center;" |16/9
| 16/9
|-
|-
| style="text-align:center;" |25
| 25
| style="text-align:center;" |1032.32868
| 1032.3287
| style="text-align:center;" |11/6, 20/11
| 11/6, 20/11
|-
|-
| style="text-align:center;" |26
| 26
| style="text-align:center;" |1073.5782
| 1073.5782
| style="text-align:center;" |15/8, 28/15, 13/7, 24/13
| 15/8, 28/15, 13/7, 24/13
|-
|-
| style="text-align:center;" |27
| 27
| style="text-align:center;" |1114.8697
| 1114.8697
| style="text-align:center;" |40/21
| 40/21
|-
|-
| style="text-align:center;" |28
| 28
| style="text-align:center;" |1156.1612
| 1156.1612
| style="text-align:center;" |48/25~64/33~55/28 ~160/81
| 48/25~64/33~55/28 ~160/81
|-
|-
| style="text-align:center;" |29
| 29
| style="text-align:center;" |1197.45265
| 1197.4526
| style="text-align:center;" |2/1
| 2/1
|-
|-
| style="text-align:center;" |30
| 30
| style="text-align:center;" |1238.7441
| 1238.7441
| style="text-align:center;" |25/12~33/16~112/55~81/40
| 25/12~33/16~112/55~81/40
|-
|-
| style="text-align:center;" |31
| 31
| style="text-align:center;" |1280.0356
| 1280.0356
| style="text-align:center;" |21/10
| 21/10
|-
|-
| style="text-align:center;" |32
| 32
| style="text-align:center;" |1321.3271
| 1321.3271
| style="text-align:center;" |32/15, 15/7, 28/13, 13/6
| 32/15, 15/7, 28/13, 13/6
|-
|-
| style="text-align:center;" |33
| 33
| style="text-align:center;" |1362.6185
| 1362.6185
| style="text-align:center;" |24/11, 11/5
| 24/11, 11/5
|-
|-
| style="text-align:center;" |34
| 34
| style="text-align:center;" |1403.91
| 1403.9100
| style="text-align:center;" |9/4
| 9/4
|}
|}
[[Category:Edf]]
[[Category:Edf]]
[[Category:Edonoi]]
[[Category:Edonoi]]
[[Category:todo:improve synopsis]]
[[Category:todo:improve synopsis]]

Revision as of 20:50, 31 May 2021

Division of the just perfect fifth into 17 equal parts (17EDF) is related to 29 edo, but with the 3/2 rather than the 2/1 being just. The octave is about 2.5474 cents compressed and the step size is about 41.2915 cents. Unlike 29edo, it is only consistent up to the 6-integer-limit, with discrepancy for the 7th harmonic.

Lookalikes: 29edo, 46edt

Intervals

Degree Cents Approx. ratios of the 15-odd-limit
0 0.0000 1/1
1 41.2915 25/24~33/32~56/55~81/80
2 82.5829 21/20
3 123.8744 16/15, 15/14, 14/13, 13/12
4 165.1659 12/11, 11/10
5 206.4574 9/8
6 248.7488 8/7, 7/6, 15/13
7· 289.0403 13/11
8 330.3318 6/5, 11/9
9 371.6232 5/4, 16/13
10 412.9147 14/11
11 455.2062 9/7, 13/10
12· 495.4976 4/3
13 536.7891 11/8, 15/11
14 578.0806 7/5, 18/13
15 619.3721 10/7, 13/9
16 660.6635 16/11, 22/15
17· 701.9550 3/2
18 743.2465 14/9, 20/13
19 784.5379 11/7
20 825.8294 8/5, 13/8
21 867.1209 5/3, 18/11
22· 908.4124 22/13
23 949.7038 7/4, 12/7, 26/15
24 990.9952 16/9
25 1032.3287 11/6, 20/11
26 1073.5782 15/8, 28/15, 13/7, 24/13
27 1114.8697 40/21
28 1156.1612 48/25~64/33~55/28 ~160/81
29 1197.4526 2/1
30 1238.7441 25/12~33/16~112/55~81/40
31 1280.0356 21/10
32 1321.3271 32/15, 15/7, 28/13, 13/6
33 1362.6185 24/11, 11/5
34 1403.9100 9/4
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