84ed5: Difference between revisions

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!comments
!comments
|-
|-
|0||0.0000||exact 1/1
|0||0.0000||exact [[1/1]]
|
|
|-
|-
|1||33.1704||1990656/1953125
|1||33.1704||1990656/1953125,
[[64/63]], 52/51
|Valentine comma
|Valentine comma
|-
|-
|2||66.3408||
|2||66.3408||80/77
|
|
|-
|-
| 3 |3
| 3 |3
|99.5112
|99.5112
|256/243
|[[256/243]], [[18/17]]
|limma
|limma
|-
|-
| 4 |4
| 4 |4
|132.6816
|132.6816
|27/25
|[[14/13]], [[27/25]]
|large limma, BP small semitone, Zarlino semitone
|large limma, BP small semitone, Zarlino semitone
|-
|-
| 5 |5
| 5 |5
|165.8520
|165.8520
|
|[[11/10]]
|
|
|-
|-
| 6 |6
| 6 |6
|199.0224
|199.0224
|
|[[28/25]]
|pseudo-9/8
|pseudo-[[9/8]]
|-
|-
| 7 |7
| 7 |7
|232.1928
|232.1928
|
|[[8/7]]
|
|
|-
|-
| 8 |8
| 8 |8
|265.3632
|265.3632
|
|[[7/6]]
|
|
|-
|-
|9
|9
|298.5336
|298.5336
|
|1215/1024
|pseudo-32/27
|pseudo-[[32/27]]
|-
|-
|10
|10
|331.7040
|331.7040
|
|[[40/33]]
|
|
|-
|-
|11
|11
|364.8744
|364.8744
|100/81
|[[100/81]]
|grave major third
|grave major third
|-
|-
|12
|12
|398.0448
|398.0448
|
|[[34/27]]
|pseudo-81/64
|pseudo-[[81/64]]
|-
|-
|13
|13
|431.2152
|431.2152
|
|[[32/25]]
|
|
|-
|-
|14
|14
|464.3856
|464.3856
|
|[[17/13]]
|
|
|-
|-
|15
|15
|497.5560
|497.5560
|[[4/3]]
|
|
|pseudo-4/3
|-
|-
|16
|16
|530.7264
|530.7264
|
|[[34/25]]
|
|
|-
|-
|17
|17
|563.8968
|563.8968
|
|[[18/13]]
|
|
|-
|-
|18
|18
|597.0672
|597.0672
|
|[[24/17]]
|
|
|-
|-
|19
|19
|630.2376
|630.2376
|
|[[36/25]]
|
|
|-
|-
|20
|20
|663.4080
|663.4080
|
|[[22/15]]
|
|
|-
|-
|21
|21
|696.5784
|696.5784
|
|765/512
|pseudo-3/2
|pseudo-[[3/2]]
|-
|-
|22
|22
|729.7488
|729.7488
|
|[[32/21]]
|
|
|-
|-
|23
|23
|762.9192
|762.9192
|
|[[14/9]]
|
|
|-
|-
|24
|24
|796.0896
|796.0896
|
|405/256
|pseudo-128/81
|pseudo-[[128/81]]
|-
|-
|25
|25
|829.2600
|829.2600
|
|[[21/13]]
|
|
|-
|-
|26
|26
|862.4304
|862.4304
|400/243
|[[28/17]], 400/243
|grave major sixth
|grave major sixth
|-
|-
|27
|27
|895.6008
|895.6008
|
|256/153
|pseudo-27/16
|pseudo-[[27/16]]
|-
|-
|28
|28
|928.7712
|928.7712
|
|[[128/75]]
|
|
|-
|-
|29
|29
|961.9416
|961.9416
|
|256/147
|
|
|-
|-
|30
|30
|995.1120
|995.1120
|[[16/9]]
|
|
|pseudo-16/9
|-
|-
|31
|31
|1028.2824
|1028.2824
|
|136/75
|
|
|-
|-
|32
|32
|1061.4528
|1061.4528
|
|[[24/13]]
|
|
|-
|-
|33
|33
|1094.6232
|1094.6232
|
|[[32/17]]
|
|
|-
|-
|34
|34
|1127.7936
|1127.7936
|
|[[48/25]]
|
|
|-
|-
|35
|35
|1160.9640
|1160.9640
|
|125/64
|
|
|-
|-
|36
|36
|1194.1344
|1194.1344
|
|255/128
|pseudo-2/1
|pseudo-[[2/1]]
|-
|-
|37
|37
Line 424: Line 425:
|84
|84
|2786.3137
|2786.3137
|exact 5/1
|exact [[5/1]]
|just major third plus two octaves
|just major third plus two octaves
|}
|}

Revision as of 11:57, 21 March 2023

Division of the 5th harmonic into 84 equal parts (84ed5) is related to 36edo but the 5/1 rather than the 2/1 being just. The octave is compressed (about 5.8656 cents) and the step size is about 33.1704 cents.

← 83ed5 84ed5 85ed5 →
Prime factorization 22 × 3 × 7
Step size 33.1704 ¢ 
Octave 36\84ed5 (1194.13 ¢) (→ 3\7ed5)
Twelfth 57\84ed5 (1890.71 ¢) (→ 19\28ed5)
Consistency limit 5
Distinct consistency limit 5

Intervals

degree cents value corresponding

JI intervals

comments
0 0.0000 exact 1/1
1 33.1704 1990656/1953125,

64/63, 52/51

Valentine comma
2 66.3408 80/77
3 99.5112 256/243, 18/17 limma
4 132.6816 14/13, 27/25 large limma, BP small semitone, Zarlino semitone
5 165.8520 11/10
6 199.0224 28/25 pseudo-9/8
7 232.1928 8/7
8 265.3632 7/6
9 298.5336 1215/1024 pseudo-32/27
10 331.7040 40/33
11 364.8744 100/81 grave major third
12 398.0448 34/27 pseudo-81/64
13 431.2152 32/25
14 464.3856 17/13
15 497.5560 4/3
16 530.7264 34/25
17 563.8968 18/13
18 597.0672 24/17
19 630.2376 36/25
20 663.4080 22/15
21 696.5784 765/512 pseudo-3/2
22 729.7488 32/21
23 762.9192 14/9
24 796.0896 405/256 pseudo-128/81
25 829.2600 21/13
26 862.4304 28/17, 400/243 grave major sixth
27 895.6008 256/153 pseudo-27/16
28 928.7712 128/75
29 961.9416 256/147
30 995.1120 16/9
31 1028.2824 136/75
32 1061.4528 24/13
33 1094.6232 32/17
34 1127.7936 48/25
35 1160.9640 125/64
36 1194.1344 255/128 pseudo-2/1
37 1227.3049 128/63 septimal comma, Archytas' comma plus one octave
38 1260.4753 524288/253125 Passion comma plus one octave
39 1293.6457
40 1326.8161
41 1359.9865
42 1393.1569
43 1426.3273 729/320 acute major second plus one octave
44 1459.4977
45 1492.6681
46 1525.8385
47 1559.0089
48 1592.1793
49 1625.3497
50 1658.5201
51 1691.6905
52 1724.8609
53 1758.0313
54 1791.2017
55 1824.3721
56 1857.5425
57 1890.7129
58 1923.8833 243/80 acute fifth plus one octave
59 1957.0537
60 1990.2241
61 2023.3945
62 2056.5649
63 2089.7353
64 2122.9057
65 2156.0761
66 2189.2465
67 2222.4169
68 2255.5873
69 2288.7577
70 2321.9281
71 2355.0985
72 2388.2689
73 2421.4393 81/20 syntonic comma, Didymus comma plus two octaves
74 2454.6097
75 2487.7801
76 2520.9505
77 2554.1209 2187/500 Gorgo limma plus two octaves
78 2587.2913
79 2620.4617
80 2653.6321
81 2686.8025
82 2719.9729
83 2753.1433
84 2786.3137 exact 5/1 just major third plus two octaves

Music

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