34edf: Difference between revisions

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Created page with "'''Division of the just perfect fifth into 34 equal parts''' (34EDF) is related to 58 edo, but with the 3/2 rather than the 2/1 being just. The octave is abo..."
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Lookalikes: [[58edo]], [[92edt]]
Lookalikes: [[58edo]], [[92edt]]
 
==Intervals==
{| class="wikitable"
|-
! |Degree
! |Cents
! |Approx. ratios
|-
| style="text-align:center;" |0
| style="text-align:center;" |0
| style="text-align:center;" |1/1
|-
|1
|20.6457
|56/55, 64/63, 81/80, 128/125
|-
| style="text-align:center;" |2
| style="text-align:center;" |41.2915
| style="text-align:center;" |36/35, 49/48, 50/49, 55/54
|-
|3
|61.9372
|25/24, 26/25, 27/26, 28/27, 33/32
|-
| style="text-align:center;" |4
| style="text-align:center;" |82.5829
| style="text-align:center;" |21/20, 22/21
|-
|5
|103.2287
|16/15, 17/16, 18/17
|-
| style="text-align:center;" |6
| style="text-align:center;" |123.8744
| style="text-align:center;" |15/14, 14/13
|-
|7·
|144.52015
|12/11, 13/12
|-
| style="text-align:center;" |8
| style="text-align:center;" |165.1659
| style="text-align:center;" |11/10
|-
|9
|185.8116
|10/9
|-
| style="text-align:center;" |10
| style="text-align:center;" |206.45735
| style="text-align:center;" |9/8
|-
|11
|227.1031
|8/7
|-
| style="text-align:center;" |12·
| style="text-align:center;" |248.7488
| style="text-align:center;" |15/13
|-
|13
|268.3946
|7/6
|-
| style="text-align:center;" |14
| style="text-align:center;" |289.0403
| style="text-align:center;" |13/11, 20/17
|-
|15
|309.686
|6/5
|-
| style="text-align:center;" |16
| style="text-align:center;" |330.3318
| style="text-align:center;" |17/14
|-
|17·
|350.9775
|11/9, 16/13
|-
| style="text-align:center;" |18
| style="text-align:center;" |371.6232
| style="text-align:center;" |21/17
|-
|19
|392.269
|5/4
|-
| style="text-align:center;" |20
| style="text-align:center;" |412.9147
| style="text-align:center;" |14/11
|-
|21
|433.5604
|9/7
|-
| style="text-align:center;" |22·
| style="text-align:center;" |455.2062
| style="text-align:center;" |13/10, 17/13, 22/17
|-
|23
|474.8519
|21/16
|-
| style="text-align:center;" |24
| style="text-align:center;" |495.49765
| style="text-align:center;" |4/3
|-
|25
|516.1434
|27/20
|-
| style="text-align:center;" |26
| style="text-align:center;" |536.7891
| style="text-align:center;" |15/11
|-
|27
|557.43485
|11/8, 18/13
|-
| style="text-align:center;" |28
| style="text-align:center;" |578.0806
| style="text-align:center;" |7/5
|-
|29
|598.7263
|17/12, 24/17
|-
| style="text-align:center;" |30
| style="text-align:center;" |619.3721
| style="text-align:center;" |10/7
|-
|31
|640.0178
|13/9, 16/11
|-
| style="text-align:center;" |32
| style="text-align:center;" |660.6635
| style="text-align:center;" |22/15
|-
|33
|681.3093
|40/27
|-
| style="text-align:center;" |34
| style="text-align:center;" |701.955
| style="text-align:center;" |3/2
|-
|35
|722.6007
|32/21
|-
| style="text-align:center;" |36
| style="text-align:center;" |743.2465
| style="text-align:center;" |20/13, 26/17, 17/11
|-
|37
|763.8922
|14/9
|-
| style="text-align:center;" |38
| style="text-align:center;" |784.5379
| style="text-align:center;" |11/7
|-
|39
|805.1837
|8/5
|-
| style="text-align:center;" |40
| style="text-align:center;" |825.8294
| style="text-align:center;" |34/21
|-
|41
|846.47515
|13/8, 18/11
|-
| style="text-align:center;" |42
| style="text-align:center;" |867.1209
| style="text-align:center;" |28/17
|-
|43
|887.7666
|5/3,
|-
| style="text-align:center;" |44
| style="text-align:center;" |908.41235
| style="text-align:center;" |22/13, 17/10
|-
|45
|929.0581
|12/7
|-
| style="text-align:center;" |46
| style="text-align:center;" |949.7038
| style="text-align:center;" |26/15
|-
|47
|970.35
|7/4
|-
| style="text-align:center;" |48
| style="text-align:center;" |990.9952
| style="text-align:center;" |16/9
|-
|49
|1011.641
|9/5
|-
| style="text-align:center;" |50
| style="text-align:center;" |1032.32868
| style="text-align:center;" |20/11
|-
|51
|1052.9235
|11/6, 24/13
|-
| style="text-align:center;" |52
| style="text-align:center;" |1073.5782
| style="text-align:center;" |28/15, 13/7,
|-
|53
|1094.224
|15/8, 32/17, 17/9
|-
| style="text-align:center;" |54
| style="text-align:center;" |1114.8697
| style="text-align:center;" |40/21, 21/11
|-
|55
|1135.5154
|48/25, 25/13, 52/27, 27/14, 64/33
|-
| style="text-align:center;" |56
| style="text-align:center;" |1156.1612
| style="text-align:center;" |35/18, 96/49, 49/25, 108/55
|-
|57
|1176.8069
|55/28, 63/32, 160/81, 125/64
|-
| style="text-align:center;" |58
| style="text-align:center;" |1197.45265
| style="text-align:center;" |2/1
|}
[[Category:Edf]]
[[Category:Edf]]
[[Category:Edonoi]]
[[Category:Edonoi]]

Revision as of 00:38, 21 February 2019

Division of the just perfect fifth into 34 equal parts (34EDF) is related to 58 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 20.6457 cents (corresponding to 58.1234 edo). The patent val has a generally flat tendency for harmonics up to 16, with the exception for 5. Unlike 58edo, it is only consistent up to the 15-integer-limit, with discrepancy for the 16th harmonic (four octaves).

Lookalikes: 58edo, 92edt

Intervals

Degree Cents Approx. ratios
0 0 1/1
1 20.6457 56/55, 64/63, 81/80, 128/125
2 41.2915 36/35, 49/48, 50/49, 55/54
3 61.9372 25/24, 26/25, 27/26, 28/27, 33/32
4 82.5829 21/20, 22/21
5 103.2287 16/15, 17/16, 18/17
6 123.8744 15/14, 14/13
7· 144.52015 12/11, 13/12
8 165.1659 11/10
9 185.8116 10/9
10 206.45735 9/8
11 227.1031 8/7
12· 248.7488 15/13
13 268.3946 7/6
14 289.0403 13/11, 20/17
15 309.686 6/5
16 330.3318 17/14
17· 350.9775 11/9, 16/13
18 371.6232 21/17
19 392.269 5/4
20 412.9147 14/11
21 433.5604 9/7
22· 455.2062 13/10, 17/13, 22/17
23 474.8519 21/16
24 495.49765 4/3
25 516.1434 27/20
26 536.7891 15/11
27 557.43485 11/8, 18/13
28 578.0806 7/5
29 598.7263 17/12, 24/17
30 619.3721 10/7
31 640.0178 13/9, 16/11
32 660.6635 22/15
33 681.3093 40/27
34 701.955 3/2
35 722.6007 32/21
36 743.2465 20/13, 26/17, 17/11
37 763.8922 14/9
38 784.5379 11/7
39 805.1837 8/5
40 825.8294 34/21
41 846.47515 13/8, 18/11
42 867.1209 28/17
43 887.7666 5/3,
44 908.41235 22/13, 17/10
45 929.0581 12/7
46 949.7038 26/15
47 970.35 7/4
48 990.9952 16/9
49 1011.641 9/5
50 1032.32868 20/11
51 1052.9235 11/6, 24/13
52 1073.5782 28/15, 13/7,
53 1094.224 15/8, 32/17, 17/9
54 1114.8697 40/21, 21/11
55 1135.5154 48/25, 25/13, 52/27, 27/14, 64/33
56 1156.1612 35/18, 96/49, 49/25, 108/55
57 1176.8069 55/28, 63/32, 160/81, 125/64
58 1197.45265 2/1
Retrieved from "https://en.xen.wiki/index.php?title=34edf&oldid=40418"