17edf: Difference between revisions

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-'''17edf''' stands for the 17-part equal division of the fifth ([[3/2]]).
+{{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|29edo]] (very close)
+Lookalikes: [[29edo]], [[46edt]]
-[[Category:Edf]]
+== Harmonics ==
+{{Harmonics in equal|17|3|2|intervals=prime|columns=8}}
+{{Harmonics in equal|17|3|2|start=9|intervals=prime|columns=8}}
-[[Category:todo:expand]]
+== Intervals ==
-[[Category:todo:improve synopsis]]
+{| 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}}