46edf: Difference between revisions

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{{Infobox ET}}
'''46EDF''' is the [[EDF|equal division of the just perfect fifth]] into 46 parts of 15.2599 [[cent|cents]] each, corresponding to 78.6375 [[edo]] (similar to every third step of [[236edo]]).
'''46EDF''' is the [[EDF|equal division of the just perfect fifth]] into 46 parts of 15.2599 [[cent|cents]] each, corresponding to 78.6375 [[edo]] (similar to every third step of [[236edo]]).
==Harmonics==
{{Harmonics in equal|46|3|2}}
{{Harmonics in equal|46|3|2|start=12|title=contd.}}


==Intervals==
==Intervals==
Line 9: Line 14:
! | comments
! | comments
|-
|-
| | 0
| colspan="2"| 0
| | 0.0000
| | '''exact [[1/1]]'''
| | '''exact [[1/1]]'''
| |  
| |  
Line 40: Line 44:
|-
|-
| | 6
| | 6
| | 91.5593
| | 91.55935
| | 97/92
| | 97/92
| |  
| |  
Line 55: Line 59:
|-
|-
| | 9
| | 9
| | 137.3390
| | 137.339
| |  
| |  
| |  
| |  
Line 76: Line 80:
| | 13
| | 13
| | 198.3786
| | 198.3786
| | 37/33
| |9/8
| |  
| |  
|-
|-
Line 86: Line 90:
| | 15
| | 15
| | 228.8984
| | 228.8984
| | 105/92
| |8/7
| |  
| |  
|-
|-
Line 95: Line 99:
|-
|-
| | 17
| | 17
| | 259.4182
| | 259.41815
| | 36/31, 79/68
| | 36/31, 79/68
| |  
| |lower pseudo-7/6
|-
|-
| | 18
| | 18
| | 274.6780
| | 274.678
| | [[75/64]]
| | [[75/64]]
| |  
| |upper pseudo-7/6
|-
|-
| | 19
| | 19
Line 116: Line 120:
| | 21
| | 21
| | 320.4577
| | 320.4577
| | 71/59, 65/54
| |6/5
| |  
| |  
|-
|-
Line 136: Line 140:
| | 25
| | 25
| | 381.4973
| | 381.4973
| | 86/69, 91/73
| |5/4
| |  
| |  
|-
|-
Line 150: Line 154:
|-
|-
| | 28
| | 28
| | 427.2770
| | 427.277
| | [[32/25]]
| | [[32/25]]
| |  
| |  
|-
|-
| | 29
| | 29
| | 442.5368
| | 442.53685
| | 31/24
| | 31/24
| |  
| |  
Line 195: Line 199:
|-
|-
| | 37
| | 37
| | 564.6160
| | 564.616
| |  
| |  
| |  
| |  
Line 240: Line 244:
|-
|-
| | 46
| | 46
| | 701.9550
| | 701.955
| | '''exact [[3/2]]'''
| | '''exact [[3/2]]'''
| | just perfect fifth
| | just perfect fifth
|-
|47
|717.2149
|
|
|-
|48
|732.4748
|
|
|-
|49
|737.7347
|
|
|-
|50
|762.9946
|14/9
|
|-
|51
|778.2545
|
|
|-
|52
|793.51435
|
|
|-
|53
|808.7742
|8/5
|
|-
|54
|824.0341
|
|
|-
|55
|839.294
|
|
|-
|56
|854.5539
|
|
|-
|57
|869.8138
|
|
|-
|58
|885.0737
|5/3
|
|-
|59
|900.3336
|
|
|-
|60
|915.5935
|
|
|-
|61
|930.8534
|12/7
|
|-
|62
|946.1133
|
|
|-
|63
|961.37315
|
|lower pseudo-7/6
|-
|64
|976.633
|
|upper pseudo-7/6
|-
|65
|991.8929
|16/9
|
|-
|66
|1007.1528
|
|
|-
|67
|1022.4127
|9/5
|
|-
|68
|1037.6726
|
|
|-
|69
|1052.9235
|
|
|-
|70
|1068.1924
|13/7
|
|-
|71
|1083.4523
|15/8
|
|-
|72
|1098.7122
|
|
|-
|73
|1113.9721
|
|
|-
|74
|1129.232
|
|
|-
|75
|1144.49185
|
|
|-
|76
|1159.7517
|
|
|-
|77
|1175.0116
|
|
|-
|78
|1190.2715
|
|
|-
|79
|1205.5314
|2/1
|
|-
|80
|1220.7913
|81/40
|
|-
|81
|1236.0512
|
|
|-
|82
|1251.3111
|
|
|-
|83
|1266.571
|
|
|-
|84
|1281.8309
|
|
|-
|85
|1297.0908
|
|
|-
|86
|1312.35065
|32/15
|
|-
|87
|1327.61055
|28/13
|
|-
|88
|1342.8704
|
|
|-
|89
|1358.1303
|
|
|-
|90
|1373.3902
|
|
|-
|91
|1388.6501
|20/9
|
|-
|92
|1403.91
|'''exact''' 9/4
|
|}
|}


[[Category:Edf]]
{{todo|expand}}
[[Category:Edonoi]]

Latest revision as of 19:23, 1 August 2025

← 45edf 46edf 47edf →
Prime factorization 2 × 23
Step size 15.2599 ¢ 
Octave 79\46edf (1205.53 ¢)
Twelfth 125\46edf (1907.49 ¢)
Consistency limit 3
Distinct consistency limit 3

46EDF is the equal division of the just perfect fifth into 46 parts of 15.2599 cents each, corresponding to 78.6375 edo (similar to every third step of 236edo).

Harmonics

Approximation of harmonics in 46edf
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +5.53 +5.53 -4.20 +6.25 -4.20 +3.61 +1.33 -4.20 -3.48 -0.63 +1.33
Relative (%) +36.2 +36.2 -27.5 +40.9 -27.5 +23.7 +8.7 -27.5 -22.8 -4.1 +8.7
Steps
(reduced) 		79
(33) 		125
(33) 		157
(19) 		183
(45) 		203
(19) 		221
(37) 		236
(6) 		249
(19) 		261
(31) 		272
(42) 		282
(6)
contd.
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +0.10 -6.12 -3.48 +6.87 -6.53 +1.33 -0.71 +2.05 -6.12 +4.90 +4.25
Relative (%) +0.7 -40.1 -22.8 +45.0 -42.8 +8.7 -4.6 +13.4 -40.1 +32.1 +27.8
Steps
(reduced) 		291
(15) 		299
(23) 		307
(31) 		315
(39) 		321
(45) 		328
(6) 		334
(12) 		340
(18) 		345
(23) 		351
(29) 		356
(34)

Intervals

degree cents value corresponding
JI intervals 		comments
0 exact 1/1
1 15.2599
2 30.5198
3 45.7797
4 61.0396 29/28
5 76.2995 93/89
6 91.55935 97/92
7 106.8192 84/79
8 122.0791 44/41
9 137.339
10 152.5989
11 167.8588
12 183.1187 10/9
13 198.3786 9/8
14 213.6385 43/38
15 228.8984 8/7
16 244.1583 38/33
17 259.41815 36/31, 79/68 lower pseudo-7/6
18 274.678 75/64 upper pseudo-7/6
19 289.9379 13/11
20 305.1978 31/26
21 320.4577 6/5
22 335.7176 17/14
23 350.9775 60/49, 49/40
24 366.2374 21/17
25 381.4973 5/4
26 396.7572 44/35, 83/66
27 412.0171 33/26
28 427.277 32/25
29 442.53685 31/24
30 457.7967 43/33
31 473.0566 46/35
32 488.3165 61/46
33 503.5764
34 518.8363 27/20
35 534.0962 64/47
36 549.3561
37 564.616
38 579.8759
39 595.1358
40 610.3957
41 625.6555
42 640.9154
43 656.1753 19/13
44 671.4352
45 686.6951
46 701.955 exact 3/2 just perfect fifth
47 717.2149
48 732.4748
49 737.7347
50 762.9946 14/9
51 778.2545
52 793.51435
53 808.7742 8/5
54 824.0341
55 839.294
56 854.5539
57 869.8138
58 885.0737 5/3
59 900.3336
60 915.5935
61 930.8534 12/7
62 946.1133
63 961.37315 lower pseudo-7/6
64 976.633 upper pseudo-7/6
65 991.8929 16/9
66 1007.1528
67 1022.4127 9/5
68 1037.6726
69 1052.9235
70 1068.1924 13/7
71 1083.4523 15/8
72 1098.7122
73 1113.9721
74 1129.232
75 1144.49185
76 1159.7517
77 1175.0116
78 1190.2715
79 1205.5314 2/1
80 1220.7913 81/40
81 1236.0512
82 1251.3111
83 1266.571
84 1281.8309
85 1297.0908
86 1312.35065 32/15
87 1327.61055 28/13
88 1342.8704
89 1358.1303
90 1373.3902
91 1388.6501 20/9
92 1403.91 exact 9/4
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