45edf: Difference between revisions

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| style="text-align:center;" |1/1
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| style="text-align:right;" |1
|1
| style="text-align:right;" |15.599
|15.599
| style="text-align:center;" |81/80, 99/98
|81/80, 99/98
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|-
| style="text-align:right;" |2
|2
| style="text-align:right;" |31.198
|31.198
| style="text-align:center;" |64/63, 49/48
|64/63, 49/48
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| style="text-align:right;" |3
|3
| style="text-align:right;" |46.797
|46.797
| style="text-align:center;" |33/32, 36/35
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| style="text-align:right;" |4
|4
| style="text-align:right;" |62.396
|62.396
| style="text-align:center;" |28/27, 27/26, 26/25
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| style="text-align:right;" |5
|5
| style="text-align:right;" |77.995
|77.995
| style="text-align:center;" |21/20, 22/21, 25/24
|21/20, 22/21, 25/24
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| style="text-align:right;" |6
|6
| style="text-align:right;" |93.594
|93.594
| style="text-align:center;" |135/128
|135/128
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| style="text-align:right;" |7
|7
| style="text-align:right;" |109.193
|109.193
| style="text-align:center;" |16/15
|16/15
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| style="text-align:right;" |8
|8
| style="text-align:right;" |124.792
|124.792
| style="text-align:center;" |15/14, 14/13
|15/14, 14/13
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| style="text-align:right;" |9
|9
| style="text-align:right;" |140.391
|140.391
| style="text-align:center;" |13/12
|13/12
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| style="text-align:right;" |10
|10
| style="text-align:right;" |155.99
|155.99
| style="text-align:center;" |12/11, 11/10
|12/11, 11/10
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| style="text-align:right;" |11
|11
| style="text-align:right;" |171.589
|171.589
| style="text-align:center;" |72/65
|72/65
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| style="text-align:right;" |12
|12
| style="text-align:right;" |187.188
|187.188
| style="text-align:center;" |10/9
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| style="text-align:right;" |13
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| style="text-align:right;" |202.787
|202.787
| style="text-align:center;" |9/8
|9/8
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| style="text-align:right;" |14
|14
| style="text-align:right;" |218.386
|218.386
| style="text-align:center;" |256/225
|256/225
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| style="text-align:right;" |15
|15
| style="text-align:right;" |233.985
|233.985
| style="text-align:center;" |8/7
|8/7
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| style="text-align:right;" |16
|16
| style="text-align:right;" |249.584
|249.584
| style="text-align:center;" |15/13
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| style="text-align:right;" |265.183
|265.183
| style="text-align:center;" |7/6
|7/6
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| style="text-align:right;" |280.782
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| style="text-align:center;" |33/28
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| style="text-align:right;" |19
|19
| style="text-align:right;" |296.381
|296.381
| style="text-align:center;" |32/27, 13/11
|32/27, 13/11
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| style="text-align:right;" |20
|20
| style="text-align:right;" |311.98
|311.98
| style="text-align:center;" |6/5
|6/5
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| style="text-align:right;" |21
|21
| style="text-align:right;" |327.579
|327.579
| style="text-align:center;" |98/81
|98/81
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| style="text-align:right;" |22
|22
| style="text-align:right;" |343.178
|343.178
| style="text-align:center;" |11/9, 39/32
|11/9, 39/32
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| style="text-align:right;" |23
|23
| style="text-align:right;" |358.777
|358.777
| style="text-align:center;" |16/13
|16/13
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| style="text-align:right;" |24
|24
| style="text-align:right;" |374.376
|374.376
| style="text-align:center;" |56/45, 26/21
|56/45, 26/21
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| style="text-align:right;" |25
|25
| style="text-align:right;" |389.975
|389.975
| style="text-align:center;" |5/4
|5/4
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| style="text-align:right;" |26
|26
| style="text-align:right;" |405.574
|405.574
| style="text-align:center;" |33/26, 81/64
|33/26, 81/64
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| style="text-align:right;" |27
|27
| style="text-align:right;" |420.173
|420.173
| style="text-align:center;" |14/11, 32/25
|14/11, 32/25
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| style="text-align:right;" |28
|28
| style="text-align:right;" |436.772
|436.772
| style="text-align:center;" |9/7
|9/7
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| style="text-align:right;" |29
|29
| style="text-align:right;" |452.371
|452.371
| style="text-align:center;" |13/10
|13/10
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| style="text-align:right;" |30
|30
| style="text-align:right;" |467.97
|467.97
| style="text-align:center;" |21/16
|21/16
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| style="text-align:right;" |31
|31
| style="text-align:right;" |483.569
|483.569
| style="text-align:center;" |120/91
|120/91
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| style="text-align:right;" |32
|32
| style="text-align:right;" |499.168
|499.168
| style="text-align:center;" |4/3
|4/3
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| style="text-align:right;" |33
|33
| style="text-align:right;" |514.767
|514.767
| style="text-align:center;" |27/20
|27/20
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| style="text-align:right;" |34
|34
| style="text-align:right;" |530.366
|530.366
| style="text-align:center;" |49/36
|49/36
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| style="text-align:right;" |35
|35
| style="text-align:right;" |545.965
|545.965
| style="text-align:center;" |11/8, 15/11
|11/8, 15/11
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| style="text-align:right;" |36
|36
| style="text-align:right;" |561.564
|561.564
| style="text-align:center;" |18/13
|18/13
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| style="text-align:right;" |37
|37
| style="text-align:right;" |577.163
|577.163
| style="text-align:center;" |7/5
|7/5
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| style="text-align:right;" |38
|38
| style="text-align:right;" |592.762
|592.762
| style="text-align:center;" |45/32
|45/32
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| style="text-align:right;" |39
|39
| style="text-align:right;" |608.361
|608.361
| style="text-align:center;" |64/45
|64/45
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| style="text-align:right;" |40
|40
| style="text-align:right;" |623.96
|623.96
| style="text-align:center;" |10/7
|10/7
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| style="text-align:right;" |41
|41
| style="text-align:right;" |639.559
|639.559
| style="text-align:center;" |13/9
|13/9
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|-
| style="text-align:right;" |42
|42
| style="text-align:right;" |655.158
|655.158
| style="text-align:center;" |16/11, 22/15
|16/11, 22/15
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|-
| style="text-align:right;" |43
|43
| style="text-align:right;" |670.757
|670.757
| style="text-align:center;" |72/49
|72/49
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| style="text-align:right;" |44
|44
| style="text-align:right;" |686.356
|686.356
| style="text-align:center;" |40/27
|40/27
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|-
| style="text-align:right;" |45
|45
| style="text-align:right;" |701.955
|701.955
| style="text-align:center;" |3/2
|3/2
|-
|-
| style="text-align:right;" |46
|46
| style="text-align:right;" |717.554
|717.554
| style="text-align:center;" |91/60
|91/60
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|-
| style="text-align:right;" |47
|47
| style="text-align:right;" |733.153
|733.153
| style="text-align:center;" |32/21
|32/21
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|-
| style="text-align:right;" |48
|48
| style="text-align:right;" |748.752
|748.752
| style="text-align:center;" |20/13
|20/13
|-
|-
| style="text-align:right;" |49
|49
| style="text-align:right;" |764.351
|764.351
| style="text-align:center;" |14/9
|14/9
|-
|-
| style="text-align:right;" |50
|50
| style="text-align:right;" |779.95
|779.95
| style="text-align:center;" |11/7, 25/16
|11/7, 25/16
|-
|-
| style="text-align:right;" |51
|51
| style="text-align:right;" |795.549
|795.549
| style="text-align:center;" |52/33, 128/81
|52/33, 128/81
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|-
| style="text-align:right;" |52
|52
| style="text-align:right;" |818.148
|818.148
| style="text-align:center;" |8/5
|8/5
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|-
| style="text-align:right;" |53
|53
| style="text-align:right;" |826.747
|826.747
| style="text-align:center;" |45/28, 21/13
|45/28, 21/13
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|-
| style="text-align:right;" |54
|54
| style="text-align:right;" |842.346
|842.346
| style="text-align:center;" |13/8
|13/8
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|-
| style="text-align:right;" |55
|55
| style="text-align:right;" |857.945
|857.945
| style="text-align:center;" |18/11, 64/39
|18/11, 64/39
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|-
| style="text-align:right;" |56
|56
| style="text-align:right;" |873.544
|873.544
| style="text-align:center;" |81/49
|81/49
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|-
| style="text-align:right;" |57
|57
| style="text-align:right;" |889.143
|889.143
| style="text-align:center;" |5/3
|5/3
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|-
| style="text-align:right;" |58
|58
| style="text-align:right;" |904.742
|904.742
| style="text-align:center;" |27/16, 22/13
|27/16, 22/13
|-
|-
| style="text-align:right;" |59
|59
| style="text-align:right;" |920.341
|920.341
| style="text-align:center;" |56/33
|56/33
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|-
| style="text-align:right;" |60
|60
| style="text-align:right;" |935.84
|935.84
| style="text-align:center;" |12/7
|12/7
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|-
| style="text-align:right;" |61
|61
| style="text-align:right;" |951.539
|951.539
| style="text-align:center;" |26/15
|26/15
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|-
| style="text-align:right;" |62
|62
| style="text-align:right;" |967.138
|967.138
| style="text-align:center;" |7/4
|7/4
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|-
| style="text-align:right;" |63
|63
| style="text-align:right;" |982.737
|982.737
| style="text-align:center;" |225/128
|225/128
|-
|-
| style="text-align:right;" |64
|64
| style="text-align:right;" |998.336
|998.336
| style="text-align:center;" |16/9
|16/9
|-
|-
| style="text-align:right;" |65
|65
| style="text-align:right;" |1013.935
|1013.935
| style="text-align:center;" |9/5
|9/5
|-
|-
| style="text-align:right;" |66
|66
| style="text-align:right;" |1029.534
|1029.534
| style="text-align:center;" |65/36
|65/36
|-
|-
| style="text-align:right;" |67
|67
| style="text-align:right;" |1045.133
|1045.133
| style="text-align:center;" |11/6, 20/11
|11/6, 20/11
|-
|-
| style="text-align:right;" |68
|68
| style="text-align:right;" |1060.732
|1060.732
| style="text-align:center;" |24/13
|24/13
|-
|-
| style="text-align:right;" |69
|69
| style="text-align:right;" |1076.331
|1076.331
| style="text-align:center;" |28/15
|28/15
|-
|-
| style="text-align:right;" |70
|70
| style="text-align:right;" |1091.93
|1091.93
| style="text-align:center;" |15/8
|15/8
|-
|-
| style="text-align:right;" |71
|71
| style="text-align:right;" |1107.529
|1107.529
| style="text-align:center;" |256/135
|256/135
|-
|-
| style="text-align:right;" |72
|72
| style="text-align:right;" |1123.128
|1123.128
| style="text-align:center;" |40/21, 48/25
|40/21, 48/25
|-
|-
| style="text-align:right;" |73
|73
| style="text-align:right;" |1138.727
|1138.727
| style="text-align:center;" |27/14, 25/13
|27/14, 25/13
|-
|-
| style="text-align:right;" |74
|74
| style="text-align:right;" |1154.326
|1154.326
| style="text-align:center;" |64/33, 35/18
|64/33, 35/18
|-
|-
| style="text-align:right;" |75
|75
| style="text-align:right;" |1169.925
|1169.925
| style="text-align:center;" |63/32, 96/49
|63/32, 96/49
|-
|-
| style="text-align:right;" |76
|76
| style="text-align:right;" |1185.524
|1185.524
| style="text-align:center;" |160/81, 196/99
|160/81, 196/99
|-
|-
| style="text-align:right;" |77
|77
| style="text-align:right;" |1201.123
|1201.123
| style="text-align:center;" |2/1
|/1
|-
|-
|78
|78

Revision as of 06:45, 19 June 2021

Division of the just perfect fifth into 45 equal parts (45EDF) is related to 77 edo, but with the 3/2 rather than the 2/1 being just. The octave is about 1.123 cents stretched and the step size is about 15.599 cents. The patent val has a generally sharp tendency for harmonics up to 16, with the exception for 11.

Lookalikes: 77edo, 122edt

Intervals

Degree Cents

Value

Approximate Ratios

in the 13-limit

0 1/1
1 15.599 81/80, 99/98
2 31.198 64/63, 49/48
3 46.797 33/32, 36/35
4 62.396 28/27, 27/26, 26/25
5 77.995 21/20, 22/21, 25/24
6 93.594 135/128
7 109.193 16/15
8 124.792 15/14, 14/13
9 140.391 13/12
10 155.99 12/11, 11/10
11 171.589 72/65
12 187.188 10/9
13 202.787 9/8
14 218.386 256/225
15 233.985 8/7
16 249.584 15/13
17 265.183 7/6
18 280.782 33/28
19 296.381 32/27, 13/11
20 311.98 6/5
21 327.579 98/81
22 343.178 11/9, 39/32
23 358.777 16/13
24 374.376 56/45, 26/21
25 389.975 5/4
26 405.574 33/26, 81/64
27 420.173 14/11, 32/25
28 436.772 9/7
29 452.371 13/10
30 467.97 21/16
31 483.569 120/91
32 499.168 4/3
33 514.767 27/20
34 530.366 49/36
35 545.965 11/8, 15/11
36 561.564 18/13
37 577.163 7/5
38 592.762 45/32
39 608.361 64/45
40 623.96 10/7
41 639.559 13/9
42 655.158 16/11, 22/15
43 670.757 72/49
44 686.356 40/27
45 701.955 3/2
46 717.554 91/60
47 733.153 32/21
48 748.752 20/13
49 764.351 14/9
50 779.95 11/7, 25/16
51 795.549 52/33, 128/81
52 818.148 8/5
53 826.747 45/28, 21/13
54 842.346 13/8
55 857.945 18/11, 64/39
56 873.544 81/49
57 889.143 5/3
58 904.742 27/16, 22/13
59 920.341 56/33
60 935.84 12/7
61 951.539 26/15
62 967.138 7/4
63 982.737 225/128
64 998.336 16/9
65 1013.935 9/5
66 1029.534 65/36
67 1045.133 11/6, 20/11
68 1060.732 24/13
69 1076.331 28/15
70 1091.93 15/8
71 1107.529 256/135
72 1123.128 40/21, 48/25
73 1138.727 27/14, 25/13
74 1154.326 64/33, 35/18
75 1169.925 63/32, 96/49
76 1185.524 160/81, 196/99
77 1201.123 /1
78 1216.722 81/40, 99/49
79 1232.321 128/63, 49/24
80 1247.92 33/16, 72/35
81 1263.519 56/27, 27/13, 52/25
82 1279.118 21/10, 44/21,25/12
83 1294.717 135/64
84 1310.316 32/15
85 1325.915 15/7, 28/13
86 1341.514 13/6
87 1357.113 24/11, 11/5
88 1372.712 144/65
89 1388.311 20/9
90 1403.91 9/4
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