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'''Division of the 5th harmonic into 72 equal parts''' (72ed5) is related to [[31edo]], but with the 5/1 rather than the 2/1 being just. The octave is slightly compressed (about 0.3372 cents) and the step size is about 38.6988 cents. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.
'''Division of the 5th harmonic into 72 equal parts''' (72ed5) is related to [[31edo|31 edo]], but with the 5/1 rather than the 2/1 being just. The octave is slightly compressed (about 0.3372 cents) and the step size is about 38.6988 cents. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.


{| class="wikitable"
{| class="wikitable"
Line 15: Line 15:
| | 1
| | 1
| | 38.6988
| | 38.6988
| |  
| | 46/45, [[45/44]]
| |  
| |  
|-
|-
| | 2
| | 2
| | 77.3976
| | 77.3976
| |  
| | 23/22, 68/65, [[22/21]]
| |  
| |  
|-
|-
| | 3
| | 3
| | 116.0964
| | 116.0964
| | [[16/15]], [[15/14]]
| | [[15/14]]
| |
| | pseudo-[[16/15]]
|-
|-
| | 4
| | 4
| | 154.7952
| | 154.7952
| |  
| | 35/32, 23/21
| |  
| |  
|-
|-
| | 5
| | 5
| | 193.4940
| | 193.4940
| |  
| | [[19/17]], 85/76
| |  
| |  
|-
|-
Line 45: Line 45:
| | 7
| | 7
| | 270.8916
| | 270.8916
| |  
| | 76/65
| |  
| | pseudo-[[7/6]]
|-
|-
| | 8
| | 8
| | 309.5904
| | 309.5904
| |  
| | 55/46
| |  
| | pseudo-[[6/5]]
|-
|-
| | 9
| | 9
Line 65: Line 65:
| | 11
| | 11
| | 425.6868
| | 425.6868
| |  
| | 23/18
| |  
| |  
|-
|-
Line 80: Line 80:
| | 14
| | 14
| | 541.7832
| | 541.7832
| |  
| | 175/128, [[26/19]]
| |  
| |  
|-
|-
Line 90: Line 90:
| | 16
| | 16
| | 619.1808
| | 619.1808
| |  
| | [[10/7]]
| |  
| |  
|-
|-
| | 17
| | 17
| | 657.8796
| | 657.8796
| |  
| | [[19/13]]
| |  
| |  
|-
|-
Line 105: Line 105:
| | 19
| | 19
| | 735.2772
| | 735.2772
| |  
| | [[55/36]], [[26/17]]
| |  
| |  
|-
|-
| | 20
| | 20
| | 773.9760
| | 773.9760
| | [[25/16]]
| | [[25/16]], 36/23
| |  
| |  
|-
|-
Line 120: Line 120:
| | 22
| | 22
| | 851.3736
| | 851.3736
| |  
| | 85/52, [[18/11]]
| |  
| |  
|-
|-
Line 135: Line 135:
| | 25
| | 25
| | 967.4700
| | 967.4700
| |  
| | [[7/4]]
| |  
| |  
|-
|-
| | 26
| | 26
| | 1006.1688
| | 1006.1688
| |  
| | 25/14
| |  
| |  
|-
|-
| | 27
| | 27
| | 1044.8676
| | 1044.8676
| | [[11/6]]
| | 95/52, 64/35
| |  
| |  
|-
|-
Line 155: Line 155:
| | 29
| | 29
| | 1122.2652
| | 1122.2652
| |  
| | [[21/11]], 65/34, 44/23
| |  
| |  
|-
|-
Line 170: Line 170:
| | 32
| | 32
| | 1238.3617
| | 1238.3617
| |  
| | [[45/44|45/22]]
| |  
| |  
|-
|-
Line 185: Line 185:
| | 35
| | 35
| | 1354.4581
| | 1354.4581
| |  
| | 35/16
| |  
| |  
|-
|-
Line 195: Line 195:
| | 37
| | 37
| | 1431.8557
| | 1431.8557
| |  
| | 16/7
| |  
| |  
|-
|-
Line 210: Line 210:
| | 40
| | 40
| | 1547.9521
| | 1547.9521
| |  
| | [[11/9|22/9]]
| |  
| |  
|-
|-
Line 225: Line 225:
| | 43
| | 43
| | 1664.0485
| | 1664.0485
| |  
| | 34/13
| |  
| |  
|-
|-
Line 235: Line 235:
| | 45
| | 45
| | 1741.4461
| | 1741.4461
| | [[15/11|30/11]]
| | 175/64, [[26/19|52/19]]
| |  
| |  
|-
|-
| | 46
| | 46
| | 1780.1449
| | 1780.1449
| |  
| | [[14/5]]
| |  
| |  
|-
|-
| | 47
| | 47
| | 1818.8437
| | 1818.8437
| |  
| | [[10/7|20/7]]
| |  
| |  
|-
|-
Line 260: Line 260:
| | 50
| | 50
| | 1934.9401
| | 1934.9401
| |  
| | [[55/36|55/18]], [[26/17|52/17]]
| |  
| |  
|-
|-
Line 270: Line 270:
| | 52
| | 52
| | 2012.3377
| | 2012.3377
| | [[16/5]]
| | 115/36, [[16/5]]
| |  
| |  
|-
|-
| | 53
| | 53
| | 2051.0365
| | 2051.0365
| |  
| | 85/26, [[18/11|36/11]]
| |  
| |  
|-
|-
Line 285: Line 285:
| | 55
| | 55
| | 2128.4341
| | 2128.4341
| |  
| | 65/19
| |  
| |  
|-
|-
| | 56
| | 56
| | 2167.1329
| | 2167.1329
| |  
| | [[7/2]]
| |  
| |  
|-
|-
Line 300: Line 300:
| | 58
| | 58
| | 2244.5305
| | 2244.5305
| |  
| | 95/26, 128/35
| |  
| |  
|-
|-
Line 316: Line 316:
| | 2360.6269
| | 2360.6269
| |  
| |  
| |  
| | 90/23
|-
|-
| | 62
| | 62
Line 330: Line 330:
| | 64
| | 64
| | 2476.7233
| | 2476.7233
| |  
| | 46/11
| |  
| |  
|-
|-
Line 345: Line 345:
| | 67
| | 67
| | 2592.8197
| | 2592.8197
| |  
| | [[19/17|76/17]], 85/19
| |  
| |  
|-
|-
| | 68
| | 68
| | 2631.5185
| | 2631.5185
| |  
| | 32/7
| |  
| |  
|-
|-
Line 360: Line 360:
| | 70
| | 70
| | 2708.9161
| | 2708.9161
| |  
| | 110/23
| |  
| |  
|-
|-
| | 71
| | 71
| | 2747.6149
| | 2747.6149
| |  
| | [[11/9|44/9]]
| |  
| |  
|-
|-

Revision as of 02:48, 1 January 2019

Division of the 5th harmonic into 72 equal parts (72ed5) is related to 31 edo, but with the 5/1 rather than the 2/1 being just. The octave is slightly compressed (about 0.3372 cents) and the step size is about 38.6988 cents. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.

degree cents value corresponding
JI intervals 		comments
0 0.0000 exact 1/1
1 38.6988 46/45, 45/44
2 77.3976 23/22, 68/65, 22/21
3 116.0964 15/14 pseudo-16/15
4 154.7952 35/32, 23/21
5 193.4940 19/17, 85/76
6 232.1928 8/7
7 270.8916 76/65 pseudo-7/6
8 309.5904 55/46 pseudo-6/5
9 348.2892 11/9
10 386.9880 5/4
11 425.6868 23/18
12 464.3856 17/13
13 503.0844 pseudo-4/3
14 541.7832 175/128, 26/19
15 580.4820 7/5
16 619.1808 10/7
17 657.8796 19/13
18 696.5784 meantone fifth
(pseudo-3/2)
19 735.2772 55/36, 26/17
20 773.9760 25/16, 36/23
21 812.6748 8/5
22 851.3736 85/52, 18/11
23 890.0724 pseudo-5/3
24 928.7712 65/38
25 967.4700 7/4
26 1006.1688 25/14
27 1044.8676 95/52, 64/35
28 1083.5664 pseudo-15/8
29 1122.2652 21/11, 65/34, 44/23
30 1160.9640 45/23
31 1199.6628 2/1
32 1238.3617 45/22
33 1277.0605 23/11
34 1315.7593
35 1354.4581 35/16
36 1393.1569 38/17, 85/38 meantone major second plus an octave
37 1431.8557 16/7
38 1470.5545
39 1509.2533 55/23
40 1547.9521 22/9
41 1586.6509 5/2
42 1625.3497 23/9
43 1664.0485 34/13
44 1702.7473 pseudo-8/3
45 1741.4461 175/64, 52/19
46 1780.1449 14/5
47 1818.8437 20/7
48 1857.5425 38/13
49 1896.2413 pseudo-3/1
50 1934.9401 55/18, 52/17
51 1973.6389 25/8
52 2012.3377 115/36, 16/5
53 2051.0365 85/26, 36/11
54 2089.7353 meantone major sixth plus an octave
(pseudo-10/3)
55 2128.4341 65/19
56 2167.1329 7/2
57 2205.8317 25/7
58 2244.5305 95/26, 128/35
59 2283.2293 pseudo-15/4
60 2321.9281 65/17
61 2360.6269 90/23
62 2399.3257 4/1
63 2438.0245 45/11
64 2476.7233 46/11
65 2515.4221
66 2554.1209 35/8
67 2592.8197 76/17, 85/19
68 2631.5185 32/7
69 2670.2173 14/3
70 2708.9161 110/23
71 2747.6149 44/9
72 2786.3137 exact 5/1 just major third plus two octaves
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