17edf: Difference between revisions
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{{Infobox ET}} | |||
'''17EDF''' is the [[EDF|Division of the just perfect fifth]] into 17 equal parts. It is related to [[29edo]], but with the [[3/2]] rather than the [[2/1]] being [[just]]. The [[octave]] is [[Octave shrinking|compressed]] by about 2.5474 [[cents]] 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| | Lookalikes: [[29edo]], [[46edt]] | ||
== Harmonics == | |||
{{Harmonics in equal|17|3|2|intervals=prime|columns=8}} | |||
{{Harmonics in equal|17|3|2|start=9|intervals=prime|columns=8}} | |||
== Intervals == | |||
{| class="wikitable center-all right-2 mw-collapsible" | |||
|+ Intervals of 17edf | |||
|- | |||
! 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 | |||
|} | |||
{{todo|expand}} | |||