34edf: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
No edit summary
No edit summary
Line 16: Line 16:
|56/55, 64/63, 81/80, 128/125
|56/55, 64/63, 81/80, 128/125
|-
|-
| style="text-align:center;" |2
|2
| style="text-align:center;" |41.2915
|41.2915
| style="text-align:center;" |36/35, 49/48, 50/49, 55/54
|6/35, 49/48, 50/49, 55/54
|-
|-
|3
|3
Line 24: Line 24:
|25/24, 26/25, 27/26, 28/27, 33/32
|25/24, 26/25, 27/26, 28/27, 33/32
|-
|-
| style="text-align:center;" |4
|4
| style="text-align:center;" |82.5829
|82.5829
| style="text-align:center;" |21/20, 22/21
|21/20, 22/21
|-
|-
|5
|5
Line 32: Line 32:
|16/15, 17/16, 18/17
|16/15, 17/16, 18/17
|-
|-
| style="text-align:center;" |6
|6
| style="text-align:center;" |123.8744
|123.8744
| style="text-align:center;" |15/14, 14/13
|15/14, 14/13
|-
|-
|7·
|7·
Line 40: Line 40:
|12/11, 13/12
|12/11, 13/12
|-
|-
| style="text-align:center;" |8
|8
| style="text-align:center;" |165.1659
|165.1659
| style="text-align:center;" |11/10
|11/10
|-
|-
|9
|9
Line 48: Line 48:
|10/9
|10/9
|-
|-
| style="text-align:center;" |10
|10
| style="text-align:center;" |206.45735
|206.45735
| style="text-align:center;" |9/8
|9/8
|-
|-
|11
|11
Line 56: Line 56:
|8/7
|8/7
|-
|-
| style="text-align:center;" |12·
|12·
| style="text-align:center;" |248.7488
|248.7488
| style="text-align:center;" |15/13
|15/13
|-
|-
|13
|13
Line 64: Line 64:
|7/6
|7/6
|-
|-
| style="text-align:center;" |14
|14
| style="text-align:center;" |289.0403
|289.0403
| style="text-align:center;" |13/11, 20/17
|13/11, 20/17
|-
|-
|15
|15
Line 72: Line 72:
|6/5
|6/5
|-
|-
| style="text-align:center;" |16
|16
| style="text-align:center;" |330.3318
|330.3318
| style="text-align:center;" |17/14
|17/14
|-
|-
|17·
|17·
Line 80: Line 80:
|11/9, 16/13
|11/9, 16/13
|-
|-
| style="text-align:center;" |18
|18
| style="text-align:center;" |371.6232
|371.6232
| style="text-align:center;" |21/17
|21/17
|-
|-
|19
|19
Line 88: Line 88:
|5/4
|5/4
|-
|-
| style="text-align:center;" |20
|20
| style="text-align:center;" |412.9147
|412.9147
| style="text-align:center;" |14/11
|14/11
|-
|-
|21
|21
Line 96: Line 96:
|9/7
|9/7
|-
|-
| style="text-align:center;" |22·
|22·
| style="text-align:center;" |455.2062
|455.2062
| style="text-align:center;" |13/10, 17/13, 22/17
|13/10, 17/13, 22/17
|-
|-
|23
|23
Line 104: Line 104:
|21/16
|21/16
|-
|-
| style="text-align:center;" |24
|24
| style="text-align:center;" |495.49765
|495.49765
| style="text-align:center;" |4/3
|4/3
|-
|-
|25
|25
Line 112: Line 112:
|27/20
|27/20
|-
|-
| style="text-align:center;" |26
|26
| style="text-align:center;" |536.7891
|536.7891
| style="text-align:center;" |15/11
|15/11
|-
|-
|27
|27
Line 120: Line 120:
|11/8, 18/13
|11/8, 18/13
|-
|-
| style="text-align:center;" |28
|28
| style="text-align:center;" |578.0806
|578.0806
| style="text-align:center;" |7/5  
|7/5  
|-
|-
|29
|29
Line 128: Line 128:
|17/12, 24/17
|17/12, 24/17
|-
|-
| style="text-align:center;" |30
|30
| style="text-align:center;" |619.3721
|619.3721
| style="text-align:center;" |10/7
|10/7
|-
|-
|31
|31
Line 136: Line 136:
|13/9, 16/11
|13/9, 16/11
|-
|-
| style="text-align:center;" |32
|32
| style="text-align:center;" |660.6635
|660.6635
| style="text-align:center;" |22/15
|22/15
|-
|-
|33
|33
Line 144: Line 144:
|40/27
|40/27
|-
|-
| style="text-align:center;" |34
|34
| style="text-align:center;" |701.955
|701.955
| style="text-align:center;" |3/2
|3/2
|-
|-
|35
|35
Line 152: Line 152:
|32/21
|32/21
|-
|-
| style="text-align:center;" |36
|36
| style="text-align:center;" |743.2465
|743.2465
| style="text-align:center;" |20/13, 26/17, 17/11
|20/13, 26/17, 17/11
|-
|-
|37
|37
Line 160: Line 160:
|14/9
|14/9
|-
|-
| style="text-align:center;" |38
|38
| style="text-align:center;" |784.5379
|784.5379
| style="text-align:center;" |11/7
|11/7
|-
|-
|39
|39
Line 168: Line 168:
|8/5
|8/5
|-
|-
| style="text-align:center;" |40
|40
| style="text-align:center;" |825.8294
|825.8294
| style="text-align:center;" |34/21
|34/21
|-
|-
|41
|41
Line 176: Line 176:
|13/8, 18/11
|13/8, 18/11
|-
|-
| style="text-align:center;" |42
|42
| style="text-align:center;" |867.1209
|867.1209
| style="text-align:center;" |28/17
|28/17
|-
|-
|43
|43
Line 184: Line 184:
|5/3,  
|5/3,  
|-
|-
| style="text-align:center;" |44
|44
| style="text-align:center;" |908.41235
|908.41235
| style="text-align:center;" |22/13, 17/10
|22/13, 17/10
|-
|-
|45
|45
Line 192: Line 192:
|12/7
|12/7
|-
|-
| style="text-align:center;" |46
|46
| style="text-align:center;" |949.7038
|949.7038
| style="text-align:center;" |26/15
|26/15
|-
|-
|47
|47
Line 200: Line 200:
|7/4
|7/4
|-
|-
| style="text-align:center;" |48
|48
| style="text-align:center;" |990.9952
|990.9952
| style="text-align:center;" |16/9
|16/9
|-
|-
|49
|49
Line 208: Line 208:
|9/5
|9/5
|-
|-
| style="text-align:center;" |50
|50
| style="text-align:center;" |1032.32868
|1032.32868
| style="text-align:center;" |20/11
|20/11
|-
|-
|51
|51
Line 216: Line 216:
|11/6, 24/13
|11/6, 24/13
|-
|-
| style="text-align:center;" |52
|52
| style="text-align:center;" |1073.5782
|1073.5782
| style="text-align:center;" |28/15, 13/7,
|28/15, 13/7  
|-
|-
|53
|53
Line 224: Line 224:
|15/8, 32/17, 17/9
|15/8, 32/17, 17/9
|-
|-
| style="text-align:center;" |54
|54
| style="text-align:center;" |1114.8697
|1114.8697
| style="text-align:center;" |40/21, 21/11
|40/21, 21/11
|-
|-
|55
|55
Line 232: Line 232:
|48/25, 25/13, 52/27, 27/14, 64/33
|48/25, 25/13, 52/27, 27/14, 64/33
|-
|-
| style="text-align:center;" |56
|56
| style="text-align:center;" |1156.1612
|1156.1612
| style="text-align:center;" |35/18, 96/49, 49/25, 108/55
|35/18, 96/49, 49/25, 108/55
|-
|-
|57
|57
Line 240: Line 240:
|55/28, 63/32, 160/81, 125/64
|55/28, 63/32, 160/81, 125/64
|-
|-
| style="text-align:center;" |58
|58
| style="text-align:center;" |1197.45265
|1197.45265
| style="text-align:center;" |2/1
|2/1
|-
|-
|59
|59

Revision as of 06:20, 19 June 2021

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 1/1
1 20.6457 56/55, 64/63, 81/80, 128/125
2 41.2915 6/35, 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
59 1218.0984 112/55, 128/63, 81/40, 256/125
60 1238.7441 72/35, 49/24, 100/49, 55/27
61 1259.38985 25/12, 52/25, 27/13, 56/27, 33/16
62 1280.0356 21/10, 44/21
63 1300.6813 32/15, 17/8, 36/17
64 1321.3271 15/7, 28/13
65 1341.9728 24/11, 13/5
66 1362.6185 11/10
67 1383.3643 20/9
68 1403.91 9/4
Retrieved from "https://en.xen.wiki/index.php?title=34edf&oldid=72751"