95ed5: Difference between revisions

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Created page with "'''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 cent..."
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Xenllium (talk | contribs)
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Line 25: Line 25:
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| | [[4/3]]
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| | 108/77, 275/196
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| | 674.5812
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| | 2025/1372
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| | 84/55, [[55/36]]
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| | [[45/28]]
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| | 30
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| | 879.8885
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| | 539/324
| | pseudo-[[5/3]]
| | pseudo-[[5/3]]
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| | 31
| | 31
| | 909.2182
| | 909.2182
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| | 1232/729, 3645/2156
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| | 967.8774
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| | 997.2070
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| | [[16/9]]
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| | 1085.1959
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| | 144/77, 275/147
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| | 1173.1847
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| | 675/343
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| | 41
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| | 1202.5143
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| | 441/220
| | pseudo-[[octave]]
| | pseudo-[[octave]]
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|-
| | 42
| | 42
| | 1231.8440
| | 1231.8440
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| | [[56/55|112/55]], [[55/54|55/27]]
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| | [[15/14|15/7]]
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| | [[7/3]]
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| | [[27/22|27/11]], 275/112
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| | 1583.7994
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| | pseudo-[[5/2]]
| | pseudo-[[5/2]]
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| | 1818.4363
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| | [[10/7|20/7]]
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| | 2156/729, 3645/1232
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| | 65
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| | 1906.4252
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| | 1620/539
| | pseudo-[[3/1]]
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| | [[14/9|28/9]]
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| | [[15/4]]
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| | [[40/21|80/21]]
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| | 2434.3583
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| | [[49/48|49/12]]
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| | 2463.6879
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| | [[28/27|112/27]]
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| | [[12/11|48/11]], 275/63
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| | 2639.6656
| | 2639.6656
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| | 225/49
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|-
Line 488: Line 488:
| | just major third plus two octaves
| | just major third plus two octaves
|}
|}
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. The small chroma interval between adjacent notes in each cluster is very versatile, representing 64/63 ~ 12100/11907 ~ 295245/290521 ~ 273375/268912 ~ 16807/16500 all tempered together. This temperament is supported by [[41edo]], [[491edo]] (491e val), and [[532edo]] (532d val) among others.

Revision as of 11:03, 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
3 87.9889 81/77
4 117.3185
5 146.6481 49/45
6 175.9777 448/405
7 205.3073
8 234.6369 55/48, 63/55
9 263.9666 220/189
10 293.2962
11 322.6258 135/112
12 351.9554 60/49
13 381.2850 pseudo-5/4
14 410.6147 308/243
15 439.9443
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
21 615.9220
22 645.2516 196/135
23 674.5812 2025/1372
24 703.9108 pseudo-3/2
25 733.2405 84/55, 55/36
26 762.5701
27 791.8997
28 821.2293 45/28
29 850.5589
30 879.8885 539/324 pseudo-5/3
31 909.2182 1232/729, 3645/2156
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
38 1114.5255
39 1143.8551 784/405
40 1173.1847 675/343
41 1202.5143 441/220 pseudo-octave
42 1231.8440 112/55, 55/27
43 1261.1736
44 1290.5032
45 1319.8328 15/7
46 1349.1624
47 1378.4920 539/243
48 1407.8217 1215/539
49 1437.1513
50 1466.4809 7/3
51 1495.8105
52 1525.1401
53 1554.4698 27/11, 275/112
54 1583.7994 1100/441 pseudo-5/2
55 1613.1290 343/135
56 1642.4586 2025/784
57 1671.7882
58 1701.1178 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 2156/729, 3645/1232
65 1906.4252 1620/539 pseudo-3/1
66 1935.7548
67 1965.0844 28/9
68 1994.4140
69 2023.7436
70 2053.0733 36/11, 275/84
71 2082.4029 pseudo-10/3
72 2111.7325 1372/405
73 2141.0621 675/196
74 2170.3917
75 2199.7214 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
81 2375.6991 1215/308
82 2405.0287 pseudo-4/1
83 2434.3583 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
91 2668.9952
92 2698.3249 385/81
93 2727.6545
94 2756.9841
95 2786.3137 exact 5/1 just major third plus two octaves

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. The small chroma interval between adjacent notes in each cluster is very versatile, representing 64/63 ~ 12100/11907 ~ 295245/290521 ~ 273375/268912 ~ 16807/16500 all tempered together. This temperament is supported by 41edo, 491edo (491e val), and 532edo (532d val) among others.

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