95ed5: Difference between revisions

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Line 20: Line 20:
| | 2
| | 2
| | 58.6592
| | 58.6592
| |  
| | 931/900
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|-
|-
| | 3
| | 3
| | 87.9889
| | 87.9889
| | 81/77
| | 81/77, [[20/19]]
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| |  
|-
|-
| | 4
| | 4
| | 117.3185
| | 117.3185
| |  
| | 1280/1197
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|-
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| | 5
| | 5
| | 146.6481
| | 146.6481
| | [[49/45]]
| | 209/192, [[49/45]]
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|-
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| | 8
| | 8
| | 234.6369
| | 234.6369
| | [[55/48]], [[63/55]]
| | [[63/55]], [[55/48]]
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|-
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| | 12
| | 12
| | 351.9554
| | 351.9554
| | [[60/49]]
| | [[60/49]], 256/209
| |  
| |  
|-
|-
| | 13
| | 13
| | 381.2850
| | 381.2850
| |  
| | 399/320
| | pseudo-[[5/4]]
| | pseudo-[[5/4]]
|-
|-
| | 14
| | 14
| | 410.6147
| | 410.6147
| | 308/243
| | [[19/15]]
| |  
| |  
|-
|-
| | 15
| | 15
| | 439.9443
| | 439.9443
| |  
| | 1200/931
| |  
| |  
|-
|-
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| | 20
| | 20
| | 586.5924
| | 586.5924
| | 108/77, 275/196
| | 108/77, 275/196, 80/57
| |  
| |  
|-
|-
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| | 22
| | 22
| | 645.2516
| | 645.2516
| | 196/135
| | 209/144, 196/135
| |  
| |  
|-
|-
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| | 24
| | 24
| | 703.9108
| | 703.9108
| |  
| | 1539/1024
| | pseudo-[[3/2]]
| | pseudo-[[3/2]]
|-
|-
| | 25
| | 25
| | 733.2405
| | 733.2405
| | 84/55, 55/36
| | 171/112, 84/55, 55/36
| |  
| |  
|-
|-
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| | 29
| | 29
| | 850.5589
| | 850.5589
| |  
| | 1024/627
| |  
| |  
|-
|-
| | 30
| | 30
| | 879.8885
| | 879.8885
| | 539/324
| | 133/80
| | pseudo-[[5/3]]
| | pseudo-[[5/3]]
|-
|-
| | 31
| | 31
| | 909.2182
| | 909.2182
| | 1232/729, 3645/2156
| | 1232/729, 3645/2156, 225/133
| |  
| |  
|-
|-
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| | 37
| | 37
| | 1085.1959
| | 1085.1959
| | 144/77, 275/147
| | 144/77, 275/147, 320/171
| |  
| |  
|-
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| | 39
| | 39
| | 1143.8551
| | 1143.8551
| | 784/405
| | 209/108, 405/209
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|-
|-
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| | 41
| | 41
| | 1202.5143
| | 1202.5143
| | 441/220
| | 513/256, 441/220
| | pseudo-[[octave]]
| | pseudo-[[octave]]
|-
|-
| | 42
| | 42
| | 1231.8440
| | 1231.8440
| | [[56/55|112/55]], [[55/54|55/27]]
| | 57/28, [[56/55|112/55]], [[55/54|55/27]]
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| | 47
| | 1378.4920
| | 1378.4920
| | 539/243
| | 133/60, 539/243
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| |  
|-
|-
| | 48
| | 48
| | 1407.8217
| | 1407.8217
| | 1215/539
| | 1215/539, 300/133
| |  
| |  
|-
|-
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| | 53
| | 53
| | 1554.4698
| | 1554.4698
| | [[27/22|27/11]], 275/112
| | [[27/22|27/11]], 275/112, 140/57
| |  
| |  
|-
|-
| | 54
| | 54
| | 1583.7994
| | 1583.7994
| | 1100/441
| | 1100/441, 1280/513
| | pseudo-[[5/2]]
| | pseudo-[[5/2]]
|-
|-
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| | 56
| | 56
| | 1642.4586
| | 1642.4586
| | 2025/784
| | 209/81, 540/209
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| |  
|-
|-
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| | 58
| | 58
| | 1701.1178
| | 1701.1178
| | 147/55, 385/144
| | 171/64, 147/55, 385/144
| |  
| |  
|-
|-
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| | 64
| | 64
| | 1877.0956
| | 1877.0956
| | 2156/729, 3645/1232
| | 133/45, 2156/729, 3645/1232
| |  
| |  
|-
|-
| | 65
| | 65
| | 1906.4252
| | 1906.4252
| | 1620/539
| | 400/133
| | pseudo-[[3/1]]
| | pseudo-[[3/1]]
|-
|-
| | 66
| | 66
| | 1935.7548
| | 1935.7548
| |  
| | 3135/1024
| |  
| |  
|-
|-
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| | 70
| | 70
| | 2053.0733
| | 2053.0733
| | [[18/11|36/11]], 275/84
| | [[18/11|36/11]], 275/84, 560/171
| |  
| |  
|-
|-
| | 71
| | 71
| | 2082.4029
| | 2082.4029
| |  
| | 5120/1539
| | pseudo-[[10/3]]
| | pseudo-[[10/3]]
|-
|-
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| | 73
| | 2141.0621
| | 2141.0621
| | 675/196
| | 675/196, 720/209
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|-
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| | 75
| | 75
| | 2199.7214
| | 2199.7214
| | 196/55, 385/108
| | 57/16, 196/55, 385/108
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| |  
|-
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| | 80
| | 80
| | 2346.3694
| | 2346.3694
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| | 931/240
| |  
| |  
|-
|-
| | 81
| | 81
| | 2375.6991
| | 2375.6991
| | 1215/308
| | 75/19
| |  
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|-
|-
| | 82
| | 82
| | 2405.0287
| | 2405.0287
| |  
| | 1600/399
| | pseudo-[[4/1]]
| | pseudo-[[4/1]]
|-
|-
| | 83
| | 83
| | 2434.3583
| | 2434.3583
| | [[49/48|49/12]]
| | 1045/256, [[49/48|49/12]]
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| |  
|-
|-
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| | 90
| | 90
| | 2639.6656
| | 2639.6656
| | 225/49
| | 225/49, 960/209
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|-
|-
| | 91
| | 91
| | 2668.9952
| | 2668.9952
| |  
| | 1197/256
| |  
| |  
|-
|-
| | 92
| | 92
| | 2698.3249
| | 2698.3249
| | 385/81
| | 19/4, 385/81
| |  
| |  
|-
|-
| | 93
| | 93
| | 2727.6545
| | 2727.6545
| |  
| | 4500/931
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|-
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95ed5 can also be thought of as a generator of the 11-limit temperament which tempers out 3025/3024, 184877/184320, and 2460375/2458624, which is a [[cluster temperament]] with 41 clusters of notes in an octave. While the small chroma interval between adjacent notes in each cluster represents 385/384, 441/440, and 1479016/1476225 tempered together, the step interval is very versatile, representing 16807/16500 ~ 273375/268912 ~ 295245/290521 ~ 12100/11907 ~ 64/63 all tempered together. This temperament is supported by [[41edo]], [[491edo]] (491e val), and [[532edo]] (532d val) among others.
==95ed5 as a generator==
95ed5 can also be thought of as a generator of the 2.3.5.7.11.19-subgroup temperament which tempers out 1540/1539, 3025/3024, 6875/6859, and 184877/184320, which is a [[cluster temperament]] with 41 clusters of notes in an octave. While the small chroma interval between adjacent notes in each cluster represents 385/384, 441/440, 1479016/1476225, 194579/194400, 204800/204687, and 176000/175959 tempered together, the step interval is very versatile, representing 16807/16500 ~ 19551/19200 ~ 18000/17689 ~ 72900/71687 ~ 273375/268912 ~ 295245/290521 ~ 12100/11907 ~ 64/63 all tempered together. This temperament is supported by [[41edo]], [[491edo]] (491e val), and [[532edo]] (532d val) among others.

Revision as of 22:00, 30 December 2018

Division of the 5th harmonic into 95 equal parts (95ed5) is related to 41 edo, but with the 5/1 rather than the 2/1 being just. The octave is about 2.5143 cents stretched and the step size about 29.3296 cents. This tuning has a generally sharp tendency for harmonics up to 12. Unlike 41edo, it is only consistent up to the 12-integer-limit, with discrepancy for the 13th harmonic.

degree cents value corresponding
JI intervals 		comments
0 0.0000 exact 1/1
1 29.3296
2 58.6592 931/900
3 87.9889 81/77, 20/19
4 117.3185 1280/1197
5 146.6481 209/192, 49/45
6 175.9777 448/405
7 205.3073
8 234.6369 63/55, 55/48
9 263.9666 220/189
10 293.2962
11 322.6258 135/112
12 351.9554 60/49, 256/209
13 381.2850 399/320 pseudo-5/4
14 410.6147 19/15
15 439.9443 1200/931
16 469.2739 21/16
17 498.6035 4/3
18 527.9331
19 557.2627 243/176
20 586.5924 108/77, 275/196, 80/57
21 615.9220
22 645.2516 209/144, 196/135
23 674.5812 2025/1372
24 703.9108 1539/1024 pseudo-3/2
25 733.2405 171/112, 84/55, 55/36
26 762.5701
27 791.8997
28 821.2293 45/28
29 850.5589 1024/627
30 879.8885 133/80 pseudo-5/3
31 909.2182 1232/729, 3645/2156, 225/133
32 938.5478
33 967.8774 7/4
34 997.2070 16/9
35 1026.5366
36 1055.8662 81/44
37 1085.1959 144/77, 275/147, 320/171
38 1114.5255
39 1143.8551 209/108, 405/209
40 1173.1847 675/343
41 1202.5143 513/256, 441/220 pseudo-octave
42 1231.8440 57/28, 112/55, 55/27
43 1261.1736
44 1290.5032
45 1319.8328 15/7
46 1349.1624
47 1378.4920 133/60, 539/243
48 1407.8217 1215/539, 300/133
49 1437.1513
50 1466.4809 7/3
51 1495.8105
52 1525.1401
53 1554.4698 27/11, 275/112, 140/57
54 1583.7994 1100/441, 1280/513 pseudo-5/2
55 1613.1290 343/135
56 1642.4586 209/81, 540/209
57 1671.7882
58 1701.1178 171/64, 147/55, 385/144
59 1730.4475 220/81
60 1759.7771
61 1789.1067 45/16
62 1818.4363 20/7
63 1847.7659
64 1877.0956 133/45, 2156/729, 3645/1232
65 1906.4252 400/133 pseudo-3/1
66 1935.7548 3135/1024
67 1965.0844 28/9
68 1994.4140
69 2023.7436
70 2053.0733 36/11, 275/84, 560/171
71 2082.4029 5120/1539 pseudo-10/3
72 2111.7325 1372/405
73 2141.0621 675/196, 720/209
74 2170.3917
75 2199.7214 57/16, 196/55, 385/108
76 2229.0510 880/243
77 2258.3806
78 2287.7102 15/4
79 2317.0398 80/21
80 2346.3694 931/240
81 2375.6991 75/19
82 2405.0287 1600/399 pseudo-4/1
83 2434.3583 1045/256, 49/12
84 2463.6879 112/27
85 2493.0175
86 2522.3472 189/44
87 2551.6768 48/11, 275/63
88 2581.0064
89 2610.3360 2025/448
90 2639.6656 225/49, 960/209
91 2668.9952 1197/256
92 2698.3249 19/4, 385/81
93 2727.6545 4500/931
94 2756.9841
95 2786.3137 exact 5/1 just major third plus two octaves

95ed5 as a generator

95ed5 can also be thought of as a generator of the 2.3.5.7.11.19-subgroup temperament which tempers out 1540/1539, 3025/3024, 6875/6859, and 184877/184320, which is a cluster temperament with 41 clusters of notes in an octave. While the small chroma interval between adjacent notes in each cluster represents 385/384, 441/440, 1479016/1476225, 194579/194400, 204800/204687, and 176000/175959 tempered together, the step interval is very versatile, representing 16807/16500 ~ 19551/19200 ~ 18000/17689 ~ 72900/71687 ~ 273375/268912 ~ 295245/290521 ~ 12100/11907 ~ 64/63 all tempered together. This temperament is supported by 41edo, 491edo (491e val), and 532edo (532d val) among others.

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