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}}

Latest revision as of 08:44, 20 December 2024

← 16edf 17edf 18edf →
Prime factorization 17 (prime)
Step size 41.2915 ¢ 
Octave 29\17edf (1197.45 ¢)
(semiconvergent)
Twelfth 46\17edf (1899.41 ¢)
(semiconvergent)
Consistency limit 6
Distinct consistency limit 6

17EDF is the 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 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, 46edt

Harmonics

Approximation of prime harmonics in 17edf
Harmonic 2 3 5 7 11 13 17 19
Error Absolute (¢) -2.5 -2.5 -19.8 +17.1 +19.1 +19.0 +8.7 -18.7
Relative (%) -6.2 -6.2 -47.9 +41.4 +46.3 +45.9 +21.1 -45.2
Steps
(reduced) 		29
(12) 		46
(12) 		67
(16) 		82
(14) 		101
(16) 		108
(6) 		119
(0) 		123
(4)
Approximation of prime harmonics in 17edf
Harmonic 23 29 31 37 41 43 47 53
Error Absolute (¢) -19.1 -7.5 +0.9 -16.3 +12.4 +12.5 -17.6 -19.1
Relative (%) -46.2 -18.1 +2.3 -39.6 +30.0 +30.4 -42.6 -46.3
Steps
(reduced) 		131
(12) 		141
(5) 		144
(8) 		151
(15) 		156
(3) 		158
(5) 		161
(8) 		166
(13)

Intervals

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
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