53ed7: Difference between revisions

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Line 15: Line 15:
| | 1
| | 1
| | 63.5628
| | 63.5628
| |  
| | [[28/27]], [[27/26]]
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|-
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| | 2
| | 2
| | 127.1255
| | 127.1255
| |  
| | [[14/13]]
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| |  
|-
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| | 3
| | 3
| | 190.6883
| | 190.6883
| |  
| | [[19/17]]
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| |  
|-
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| | 4
| | 4
| | 254.2510
| | 254.2510
| |  
| | [[22/19]]
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| | 5
| | 5
| | 317.8138
| | 317.8138
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| | [[6/5]], 77/64
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| | 6
| | 6
| | 381.3765
| | 381.3765
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| | 96/77
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| | 7
| | 7
| | 444.9393
| | 444.9393
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| | [[22/17]]
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| | 9
| | 9
| | 572.0648
| | 572.0648
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| | [[32/23]]
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|-
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| | 10
| | 10
| | 635.6275
| | 635.6275
| |  
| | [[13/9]]
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|-
|-
| | 11
| | 11
| | 699.1903
| | 699.1903
| |  
| | [[3/2]]
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| |  
|-
|-
| | 12
| | 12
| | 762.7530
| | 762.7530
| |  
| | [[14/9]]
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|-
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| | 14
| | 14
| | 889.8785
| | 889.8785
| |  
| | 77/46
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| |  
|-
|-
| | 15
| | 15
| | 953.4413
| | 953.4413
| |  
| | [[26/15]]
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| |  
|-
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| | 16
| | 16
| | 1017.0040
| | 1017.0040
| |  
| | [[9/5]]
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| |  
|-
|-
| | 17
| | 17
| | 1080.5668
| | 1080.5668
| |  
| | [[28/15]]
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|-
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| | 18
| | 18
| | 1144.1296
| | 1144.1296
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| | 64/33
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|-
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| | 19
| | 19
| | 1207.6923
| | 1207.6923
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| | 161/80
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|-
|-
| | 20
| | 20
| | 1271.2551
| | 1271.2551
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| | [[25/24|25/12]]
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| | 21
| | 21
| | 1334.8178
| | 1334.8178
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| | [[27/25|54/25]]
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| | 22
| | 22
| | 1398.3806
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| | 56/25, 110/49
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| | 1589.0688
| | 1589.0688
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| | [[5/2]]
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| | 26
| | 1652.6316
| | 1652.6316
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| | [[13/5]]
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| | 27
| | 27
| | 1716.1943
| | 1716.1943
| |  
| | 35/13
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|-
| | 28
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| | 1779.7571
| | 1779.7571
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| | [[14/5]]
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| | 31
| | 1970.4453
| | 1970.4453
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| | [[25/16|25/8]]
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|-
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| | 32
| | 32
| | 2034.0081
| | 2034.0081
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| | 68/21
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| | 33
| | 33
| | 2097.5708
| | 2097.5708
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| | [[42/25|84/25]]
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| | 34
| | 34
| | 2161.1336
| | 2161.1336
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| | 80/23
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| | 35
| | 2224.6964
| | 2224.6964
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| | 76/21
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| | 36
| | 2288.2591
| | 2288.2591
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| | [[15/4]]
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|-
|-
| | 37
| | 37
| | 2351.8219
| | 2351.8219
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| | 35/9
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|-
|-
| | 38
| | 38
| | 2415.3846
| | 2415.3846
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| | 105/26
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| | 39
| | 39
| | 2478.9474
| | 2478.9474
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| | 46/11, [[22/21|88/21]]
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| | 2542.5101
| | 2542.5101
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| | 100/23
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| | 2606.0729
| | 2606.0729
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| | [[9/2]]
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| | 2669.6356
| | 2669.6356
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| | [[14/3]]
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| | 2733.1984
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| | 63/13
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| | 2796.7611
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| | 161/32
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| | 45
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| | 2860.3239
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| | 46
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| | 2923.8866
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| | 119/22
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| | 47
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| | 2987.4494
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| | 48
| | 48
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| | 3051.0121
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| | 64/11, 35/6
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| | 3114.5749
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| | 133/22
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| | 3178.1376
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| | 119/19
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| | 51
| | 51
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| | 3241.7004
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| | [[13/2]]
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|-
|-
| | 52
| | 52
| |  
| | 3305.2632
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| | [[27/16|27/4]]
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| |  
|-
|-

Revision as of 10:44, 10 January 2019

Division of the 7th harmonic into 53 equal parts (53ed7) is related to 19edo and 30edt, but with the 7/1 rather than the 2/1 being just. The octave is about 7.6923 cents stretched and the step size is about 63.5628 cents. The patent val has a generally sharp tendency for harmonics up to 16, with exception for 11th harmonic.

degree cents value corresponding
JI intervals 		comments
0 0.0000 exact 1/1
1 63.5628 28/27, 27/26
2 127.1255 14/13
3 190.6883 19/17
4 254.2510 22/19
5 317.8138 6/5, 77/64
6 381.3765 96/77
7 444.9393 22/17
8 508.5020
9 572.0648 32/23
10 635.6275 13/9
11 699.1903 3/2
12 762.7530 14/9
13 826.3158
14 889.8785 77/46
15 953.4413 26/15
16 1017.0040 9/5
17 1080.5668 28/15
18 1144.1296 64/33
19 1207.6923 161/80
20 1271.2551 25/12
21 1334.8178 54/25
22 1398.3806 56/25, 110/49
23 1461.9433
24 1525.5061
25 1589.0688 5/2
26 1652.6316 13/5
27 1716.1943 35/13
28 1779.7571 14/5
29 1843.3198
30 1906.8826
31 1970.4453 25/8
32 2034.0081 68/21
33 2097.5708 84/25
34 2161.1336 80/23
35 2224.6964 76/21
36 2288.2591 15/4
37 2351.8219 35/9
38 2415.3846 105/26
39 2478.9474 46/11, 88/21
40 2542.5101 100/23
41 2606.0729 9/2
42 2669.6356 14/3
43 2733.1984 63/13
44 2796.7611 161/32
45 2860.3239
46 2923.8866 119/22
47 2987.4494
48 3051.0121 64/11, 35/6
49 3114.5749 133/22
50 3178.1376 119/19
51 3241.7004 13/2
52 3305.2632 27/4
53 3368.8259 exact 7/1 harmonic seventh plus two octaves
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