45edf: Difference between revisions

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Created page with "'''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 abo..."
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'''[[EDF|Division of the just perfect fifth]] into 45 equal parts''' (45EDF) is related to [[77edo|77 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 1.1230 cents stretched and the step size is about 15.5990 cents. The patent val has a generally sharp tendency for harmonics up to 16, with the exception for 11.
'''[[EDF|Division of the just perfect fifth]] into 45 equal parts''' (45EDF) is related to [[77edo|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]]
Lookalikes: [[77edo]], [[122edt]]


== Intervals ==
{| class="wikitable"
|-
! |Degree
! |Cents
Value
! |Approximate Ratios
in the 13-limit
|-
| style="text-align:right;" |0
| style="text-align:right;" |0.000
| style="text-align:center;" |1/1
|-
| style="text-align:right;" |1
| style="text-align:right;" |15.599
| style="text-align:center;" |81/80, 99/98
|-
| style="text-align:right;" |2
| style="text-align:right;" |31.198
| style="text-align:center;" |64/63, 49/48
|-
| style="text-align:right;" |3
| style="text-align:right;" |46.797
| style="text-align:center;" |33/32, 36/35
|-
| style="text-align:right;" |4
| style="text-align:right;" |62.395
| style="text-align:center;" |28/27, 26/25
|-
| style="text-align:right;" |5
| style="text-align:right;" |77.995
| style="text-align:center;" |21/20, 25/24
|-
| style="text-align:right;" |6
| style="text-align:right;" |93.594
| style="text-align:center;" |135/128
|-
| style="text-align:right;" |7
| style="text-align:right;" |109.193
| style="text-align:center;" |16/15
|-
| style="text-align:right;" |8
| style="text-align:right;" |124.792
| style="text-align:center;" |15/14
|-
| style="text-align:right;" |9
| style="text-align:right;" |140.391
| style="text-align:center;" |13/12
|-
| style="text-align:right;" |10
| style="text-align:right;" |155.99
| style="text-align:center;" |12/11, 11/10
|-
| style="text-align:right;" |11
| style="text-align:right;" |171.589
| style="text-align:center;" |72/65
|-
| style="text-align:right;" |12
| style="text-align:right;" |187.188
| style="text-align:center;" |10/9
|-
| style="text-align:right;" |13
| style="text-align:right;" |202.787
| style="text-align:center;" |9/8
|-
| style="text-align:right;" |14
| style="text-align:right;" |218.386
| style="text-align:center;" |256/225
|-
| style="text-align:right;" |15
| style="text-align:right;" |233.985
| style="text-align:center;" |8/7
|-
| style="text-align:right;" |16
| style="text-align:right;" |249.584
| style="text-align:center;" |15/13
|-
| style="text-align:right;" |17
| style="text-align:right;" |265.183
| style="text-align:center;" |7/6
|-
| style="text-align:right;" |18
| style="text-align:right;" |280.782
| style="text-align:center;" |33/28
|-
| style="text-align:right;" |19
| style="text-align:right;" |296.381
| style="text-align:center;" |32/27, 13/11
|-
| style="text-align:right;" |20
| style="text-align:right;" |311.98
| style="text-align:center;" |6/5
|-
| style="text-align:right;" |21
| style="text-align:right;" |327.579
| style="text-align:center;" |98/81
|-
| style="text-align:right;" |22
| style="text-align:right;" |343.178
| style="text-align:center;" |11/9, 39/32
|-
| style="text-align:right;" |23
| style="text-align:right;" |358.777
| style="text-align:center;" |16/13
|-
| style="text-align:right;" |24
| style="text-align:right;" |374.376
| style="text-align:center;" |56/45, 26/21
|-
| style="text-align:right;" |25
| style="text-align:right;" |389.975
| style="text-align:center;" |5/4
|-
| style="text-align:right;" |26
| style="text-align:right;" |405.574
| style="text-align:center;" |33/26, 81/64
|-
| style="text-align:right;" |27
| style="text-align:right;" |420.173
| style="text-align:center;" |14/11, 32/25
|-
| style="text-align:right;" |28
| style="text-align:right;" |436.772
| style="text-align:center;" |9/7
|-
| style="text-align:right;" |29
| style="text-align:right;" |452.371
| style="text-align:center;" |13/10
|-
| style="text-align:right;" |30
| style="text-align:right;" |467.97
| style="text-align:center;" |21/16
|-
| style="text-align:right;" |31
| style="text-align:right;" |483.569
| style="text-align:center;" |120/91
|-
| style="text-align:right;" |32
| style="text-align:right;" |499.168
| style="text-align:center;" |4/3
|-
| style="text-align:right;" |33
| style="text-align:right;" |514.767
| style="text-align:center;" |27/20
|-
| style="text-align:right;" |34
| style="text-align:right;" |530.366
| style="text-align:center;" |49/36
|-
| style="text-align:right;" |35
| style="text-align:right;" |545.965
| style="text-align:center;" |11/8, 15/11
|-
| style="text-align:right;" |36
| style="text-align:right;" |561.564
| style="text-align:center;" |18/13
|-
| style="text-align:right;" |37
| style="text-align:right;" |577.163
| style="text-align:center;" |7/5
|-
| style="text-align:right;" |38
| style="text-align:right;" |592.762
| style="text-align:center;" |45/32
|-
| style="text-align:right;" |39
| style="text-align:right;" |608.361
| style="text-align:center;" |64/45
|-
| style="text-align:right;" |40
| style="text-align:right;" |623.96
| style="text-align:center;" |10/7
|-
| style="text-align:right;" |41
| style="text-align:right;" |639.559
| style="text-align:center;" |13/9
|-
| style="text-align:right;" |42
| style="text-align:right;" |655.158
| style="text-align:center;" |16/11, 22/15
|-
| style="text-align:right;" |43
| style="text-align:right;" |670.757
| style="text-align:center;" |72/49
|-
| style="text-align:right;" |44
| style="text-align:right;" |686.356
| style="text-align:center;" |40/27
|-
| style="text-align:right;" |45
| style="text-align:right;" |701.955
| style="text-align:center;" |3/2
|-
| style="text-align:right;" |46
| style="text-align:right;" |717.554
| style="text-align:center;" |91/60
|-
| style="text-align:right;" |47
| style="text-align:right;" |733.153
| style="text-align:center;" |32/21
|-
| style="text-align:right;" |48
| style="text-align:right;" |748.752
| style="text-align:center;" |20/13
|-
| style="text-align:right;" |49
| style="text-align:right;" |764.351
| style="text-align:center;" |14/9
|-
| style="text-align:right;" |50
| style="text-align:right;" |779.95
| style="text-align:center;" |11/7, 25/16
|-
| style="text-align:right;" |51
| style="text-align:right;" |795.549
| style="text-align:center;" |52/33, 128/81
|-
| style="text-align:right;" |52
| style="text-align:right;" |818.148
| style="text-align:center;" |8/5
|-
| style="text-align:right;" |53
| style="text-align:right;" |826.747
| style="text-align:center;" |45/28, 21/13
|-
| style="text-align:right;" |54
| style="text-align:right;" |842.346
| style="text-align:center;" |13/8
|-
| style="text-align:right;" |55
| style="text-align:right;" |857.945
| style="text-align:center;" |18/11, 64/39
|-
| style="text-align:right;" |56
| style="text-align:right;" |873.544
| style="text-align:center;" |81/49
|-
| style="text-align:right;" |57
| style="text-align:right;" |889.143
| style="text-align:center;" |5/3
|-
| style="text-align:right;" |58
| style="text-align:right;" |904.742
| style="text-align:center;" |27/16, 22/13
|-
| style="text-align:right;" |59
| style="text-align:right;" |920.341
| style="text-align:center;" |56/33
|-
| style="text-align:right;" |60
| style="text-align:right;" |935.84
| style="text-align:center;" |12/7
|-
| style="text-align:right;" |61
| style="text-align:right;" |951.539
| style="text-align:center;" |26/15
|-
| style="text-align:right;" |62
| style="text-align:right;" |967.138
| style="text-align:center;" |7/4
|-
| style="text-align:right;" |63
| style="text-align:right;" |982.737
| style="text-align:center;" |225/128
|-
| style="text-align:right;" |64
| style="text-align:right;" |998.336
| style="text-align:center;" |16/9
|-
| style="text-align:right;" |65
| style="text-align:right;" |1013.935
| style="text-align:center;" |9/5
|-
| style="text-align:right;" |66
| style="text-align:right;" |1029.534
| style="text-align:center;" |65/36
|-
| style="text-align:right;" |67
| style="text-align:right;" |1045.133
| style="text-align:center;" |11/6, 20/11
|-
| style="text-align:right;" |68
| style="text-align:right;" |1060.732
| style="text-align:center;" |24/13
|-
| style="text-align:right;" |69
| style="text-align:right;" |1076.331
| style="text-align:center;" |28/15
|-
| style="text-align:right;" |70
| style="text-align:right;" |1091.93
| style="text-align:center;" |15/8
|-
| style="text-align:right;" |71
| style="text-align:right;" |1107.529
| style="text-align:center;" |256/135
|-
| style="text-align:right;" |72
| style="text-align:right;" |1123.128
| style="text-align:center;" |40/21, 48/25
|-
| style="text-align:right;" |73
| style="text-align:right;" |1138.727
| style="text-align:center;" |27/14, 25/13
|-
| style="text-align:right;" |74
| style="text-align:right;" |1154.326
| style="text-align:center;" |64/33, 35/18
|-
| style="text-align:right;" |75
| style="text-align:right;" |1169.925
| style="text-align:center;" |63/32, 96/49
|-
| style="text-align:right;" |76
| style="text-align:right;" |1185.524
| style="text-align:center;" |160/81, 196/99
|-
| style="text-align:right;" |77
| style="text-align:right;" |1201.123
| style="text-align:center;" |2/1
|}
[[Category:Edf]]
[[Category:Edf]]
[[Category:Edonoi]]
[[Category:Edonoi]]

Revision as of 01:44, 24 February 2019

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 0.000 1/1
1 15.599 81/80, 99/98
2 31.198 64/63, 49/48
3 46.797 33/32, 36/35
4 62.395 28/27, 26/25
5 77.995 21/20, 25/24
6 93.594 135/128
7 109.193 16/15
8 124.792 15/14
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 2/1
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