17edf: Difference between revisions
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Lookalikes: [[29edo]], [[46edt]] | Lookalikes: [[29edo]], [[46edt]] | ||
== Intervals == | |||
{| class="wikitable" | |||
|- | |||
! |Degree | |||
! |Cents | |||
! |Approx. ratiosof the [[15-limit]] | |||
|- | |||
| style="text-align:center;" |0 | |||
| style="text-align:center;" |0 | |||
| style="text-align:center;" |1/1 | |||
|- | |||
| style="text-align:center;" |1 | |||
| style="text-align:center;" |41.2915 | |||
| style="text-align:center;" |25/24~33/32~56/55~81/80 | |||
|- | |||
| style="text-align:center;" |2 | |||
| style="text-align:center;" |82.5829 | |||
| style="text-align:center;" |21/20 | |||
|- | |||
| style="text-align:center;" |3 | |||
| style="text-align:center;" |123.8744 | |||
| style="text-align:center;" |16/15, 15/14, 14/13, 13/12 | |||
|- | |||
| style="text-align:center;" |4 | |||
| style="text-align:center;" |165.1659 | |||
| style="text-align:center;" |12/11, 11/10 | |||
|- | |||
| style="text-align:center;" |5 | |||
| style="text-align:center;" |206.45735 | |||
| style="text-align:center;" |9/8 | |||
|- | |||
| style="text-align:center;" |6 | |||
| style="text-align:center;" |248.7488 | |||
| style="text-align:center;" |8/7, 7/6, 15/13 | |||
|- | |||
| style="text-align:center;" |7· | |||
| style="text-align:center;" |289.0403 | |||
| style="text-align:center;" |13/11 | |||
|- | |||
| style="text-align:center;" |8 | |||
| style="text-align:center;" |330.3318 | |||
| style="text-align:center;" |6/5, 11/9 | |||
|- | |||
| style="text-align:center;" |9 | |||
| style="text-align:center;" |371.6232 | |||
| style="text-align:center;" |5/4, 16/13 | |||
|- | |||
| style="text-align:center;" |10 | |||
| style="text-align:center;" |412.9147 | |||
| style="text-align:center;" |14/11 | |||
|- | |||
| style="text-align:center;" |11 | |||
| style="text-align:center;" |455.2062 | |||
| style="text-align:center;" |9/7, 13/10 | |||
|- | |||
| style="text-align:center;" |12· | |||
| style="text-align:center;" |495.49765 | |||
| style="text-align:center;" |4/3 | |||
|- | |||
| style="text-align:center;" |13 | |||
| style="text-align:center;" |536.7891 | |||
| style="text-align:center;" |11/8, 15/11 | |||
|- | |||
| style="text-align:center;" |14 | |||
| style="text-align:center;" |578.0806 | |||
| style="text-align:center;" |7/5, 18/13 | |||
|- | |||
| style="text-align:center;" |15 | |||
| style="text-align:center;" |619.3721 | |||
| style="text-align:center;" |10/7, 13/9 | |||
|- | |||
| style="text-align:center;" |16 | |||
| style="text-align:center;" |660.6635 | |||
| style="text-align:center;" |16/11, 22/15 | |||
|- | |||
| style="text-align:center;" |17· | |||
| style="text-align:center;" |701.955 | |||
| style="text-align:center;" |3/2 | |||
|- | |||
| style="text-align:center;" |18 | |||
| style="text-align:center;" |743.2465 | |||
| style="text-align:center;" |14/9, 20/13 | |||
|- | |||
| style="text-align:center;" |19 | |||
| style="text-align:center;" |784.5379 | |||
| style="text-align:center;" |11/7 | |||
|- | |||
| style="text-align:center;" |20 | |||
| style="text-align:center;" |825.8294 | |||
| style="text-align:center;" |8/5, 13/8 | |||
|- | |||
| style="text-align:center;" |21 | |||
| style="text-align:center;" |867.1209 | |||
| style="text-align:center;" |5/3, 18/11 | |||
|- | |||
| style="text-align:center;" |22· | |||
| style="text-align:center;" |908.41235 | |||
| style="text-align:center;" |22/13 | |||
|- | |||
| style="text-align:center;" |23 | |||
| style="text-align:center;" |949.7038 | |||
| style="text-align:center;" |7/4, 12/7, 26/15 | |||
|- | |||
| style="text-align:center;" |24 | |||
| style="text-align:center;" |990.9952 | |||
| style="text-align:center;" |16/9 | |||
|- | |||
| style="text-align:center;" |25 | |||
| style="text-align:center;" |1032.32868 | |||
| style="text-align:center;" |11/6, 20/11 | |||
|- | |||
| style="text-align:center;" |26 | |||
| style="text-align:center;" |1073.5782 | |||
| style="text-align:center;" |15/8, 28/15, 13/7, 24/13 | |||
|- | |||
| style="text-align:center;" |27 | |||
| style="text-align:center;" |1114.8697 | |||
| style="text-align:center;" |40/21 | |||
|- | |||
| style="text-align:center;" |28 | |||
| style="text-align:center;" |1156.1612 | |||
| style="text-align:center;" |48/25~64/33~55/28 ~160/81 | |||
|- | |||
| style="text-align:center;" |29 | |||
| style="text-align:center;" |1197.45265 | |||
| style="text-align:center;" |2/1 | |||
|} | |||
[[Category:Edf]] | [[Category:Edf]] | ||
[[Category:Edonoi]] | [[Category:Edonoi]] | ||
[[Category:todo:improve synopsis]] | [[Category:todo:improve synopsis]] | ||
Revision as of 22:20, 20 February 2019
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.
Intervals
| Degree | Cents | Approx. ratiosof the 15-limit |
|---|---|---|
| 0 | 0 | 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 | 206.45735 | 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· | 495.49765 | 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· | 701.955 | 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· | 908.41235 | 22/13 |
| 23 | 949.7038 | 7/4, 12/7, 26/15 |
| 24 | 990.9952 | 16/9 |
| 25 | 1032.32868 | 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 | 1197.45265 | 2/1 |