130edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
m Cleanup
Move temperament generator info to RTT section and add ratios instead
Line 13: Line 13:
! Degree
! Degree
! Cents
! Cents
! Associated Temperament
! Approximate Ratios
|-
|-
| 0
| 0
| 0.000
| 0.000
|  
| 1/1
|-
|-
| 1
| 1
| 9.231
| 9.231
|  
| 126/125, 225/224
|-
|-
| 2
| 2
| 18.462
| 18.462
|  
| 81/80
|-
|-
| 3
| 3
| 27.692
| 27.692
|  
| 64/63
|-
|-
| 4
| 4
| 36.923
| 36.923
|  
| 49/48, 50/49
|-
|-
| 5
| 5
| 46.154
| 46.154
|  
| 36/35
|-
|-
| 6
| 6
| 55.385
| 55.385
|  
| 33/32
|-
|-
| 7
| 7
| 64.615
| 64.615
|  
| 28/27, 27/26
|-
|-
| 8
| 8
| 73.846
| 73.846
|  
| 25/24
|-
|-
| 9
| 9
| 83.077
| 83.077
| [[Harry]]
| 21/20, 22/21
|-
|-
| 10
| 10
| 92.308
| 92.308
|  
| 135/128
|-
|-
| 11
| 11
| 101.538
| 101.538
|  
| 35/33
|-
|-
| 12
| 12
| 110.769
| 110.769
|  
| 16/15
|-
|-
| 13
| 13
| 120.000
| 120.000
|  
| 15/14
|-
|-
| 14
| 14
| 129.231
| 129.231
|  
| 14/13
|-
|-
| 15
| 15
| 138.462
| 138.462
|  
| 13/12
|-
|-
| 16
| 16
| 147.692
| 147.692
|  
| 12/11
|-
|-
| 17
| 17
| 156.923
| 156.923
|  
| 35/32
|-
|-
| 18
| 18
| 166.154
| 166.154
|  
| 11/10
|-
|-
| 19
| 19
| 175.385
| 175.385
| [[Schismatic_family #Sesquiquartififths|Sesquart]]
| 72/65
|-
|-
| 20
| 20
| 184.615
| 184.615
|  
| 10/9
|-
|-
| 21
| 21
| 193.846
| 193.846
| [[Hemiwürschmidt]]
| 28/25
|-
|-
| 22
| 22
| 203.077
| 203.077
|  
| 9/8
|-
|-
| 23
| 23
| 212.308
| 212.308
|  
| 44/39
|-
|-
| 24
| 24
| 221.538
| 221.538
|  
| 25/22
|-
|-
| 25
| 25
| 230.769
| 230.769
|  
| 8/7
|-
|-
| 26
| 26
| 240.000
| 240.000
|  
| 55/48
|-
|-
| 27
| 27
| 249.231
| 249.231
| [[Hemischismic]]
| 15/13
|-
|-
| 28
| 28
| 258.462
| 258.462
|  
| 64/55
|-
|-
| 29
| 29
| 267.692
| 267.692
|  
| 7/6
|-
|-
| 30
| 30
| 276.923
| 276.923
|  
| 75/64
|-
|-
| 31
| 31
| 286.154
| 286.154
|  
| 13/11
|-
|-
| 32
| 32
| 295.385
| 295.385
|  
| 32/27
|-
|-
| 33
| 33
| 304.615
| 304.615
|  
| 25/21
|-
|-
| 34
| 34
| 313.846
| 313.846
|  
| 6/5
|-
|-
| 35
| 35
| 323.077
| 323.077
|  
| 65/54
|-
|-
| 36
| 36
| 332.308
| 332.308
|  
| 40/33
|-
|-
| 37
| 37
| 341.538
| 341.538
|  
| 39/32
|-
|-
| 38
| 38
| 350.769
| 350.769
|  
| 11/9, 27/22
|-
|-
| 39
| 39
| 360.000
| 360.000
|  
| 16/13
|-
|-
| 40
| 40
| 369.231
| 369.231
|  
| 26/21
|-
|-
| 41
| 41
| 378.462
| 378.462
|  
| 56/45
|-
|-
| 42
| 42
| 387.692
| 387.692
|  
| 5/4
|-
|-
| 43
| 43
| 396.923
| 396.923
|  
| 63/50
|-
|-
| 44
| 44
| 406.154
| 406.154
|  
| 81/64
|-
|-
| 45
| 45
| 415.385
| 415.385
|  
| 14/11
|-
|-
| 46
| 46
| 424.615
| 424.615
|  
| 32/25
|-
|-
| 47
| 47
| 433.846
| 433.846
|  
| 9/7
|-
|-
| 48
| 48
| 443.077
| 443.077
|  
| 128/99
|-
|-
| 49
| 49
| 452.308
| 452.308
|  
| 13/10
|-
|-
| 50
| 50
| 461.538
| 461.538
|  
| 72/55
|-
|-
| 51
| 51
| 470.769
| 470.769
|  
| 21/16
|-
|-
| 52
| 52
| 480.000
| 480.000
|  
| 33/25
|-
|-
| 53
| 53
| 489.231
| 489.231
|  
| 250/189
|-
|-
| 54
| 54
| 498.462
| 498.462
|  
| 4/3
|-
|-
| 55
| 55
| 507.692
| 507.692
|  
| 75/56
|-
|-
| 56
| 56
| 516.923
| 516.923
|  
| 27/20
|-
|-
| 57
| 57
| 526.154
| 526.154
|  
| 65/48
|-
|-
| 58
| 58
| 535.385
| 535.385
|  
| 15/11
|-
|-
| 59
| 59
| 544.615
| 544.615
|  
| 48/35
|-
|-
| 60
| 60
| 553.846
| 553.846
|  
| 11/8
|-
|-
| 61
| 61
| 563.077
| 563.077
|  
| 18/13
|-
|-
| 62
| 62
| 572.308
| 572.308
|  
| 25/18
|-
|-
| 63
| 63
| 581.538
| 581.538
|  
| 7/5
|-
|-
| 64
| 64
| 590.769
| 590.769
|  
| 45/32
|-
|-
| 65
| 65
| 600.000
| 600.000
|  
| 99/70, 140/99
|-
|-
|…
|…
Line 293: Line 293:


17-limit commas: 221/220, 364/363, 442/441, 595/594, 1275/1274, 4913/4875
17-limit commas: 221/220, 364/363, 442/441, 595/594, 1275/1274, 4913/4875
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per octave
! Generator<br>(reduced)
! Cents<br>(reduced)
! Associated<br>ratio
! Temperaments
|-
| 1
| 19\130
| 175.38
| 72/65
| [[Sesquiquartififths]] / [[sesquart]]
|-
| 1
| 21\130
| 193.85
| 28/25
| [[Didacus]] / [[hemiwürschmidt]]
|-
| 1
| 27\130
| 249.23
| 15/13
| [[Hemischis]]
|-
| 2
| 9\130
| 83.08
| [[21/20]]
| [[Harry]]
|}


== Scales ==
== Scales ==

Revision as of 10:42, 30 June 2021

130edo divides the octave into 130 parts of size 9.231 cents each.

Theory

130edo is a zeta peak edo, a zeta peak integer edo, and a zeta integral edo but not a gap edo. It can be used to tune a variety of temperaments, including hemiwürschmidt, sesquiquartififths, harry and hemischis. It also can be used to tune the rank-three temperament jove, tempering out 243/242 and 441/440, plus 364/363 for the 13-limit and 595/594 for the 17-limit. It gives the optimal patent val for 11-limit hemiwürschmidt and sesquart and 13-limit harry temperaments.

Prime harmonics

Script error: No such module "primes_in_edo".

Intervals

Degree Cents Approximate Ratios
0 0.000 1/1
1 9.231 126/125, 225/224
2 18.462 81/80
3 27.692 64/63
4 36.923 49/48, 50/49
5 46.154 36/35
6 55.385 33/32
7 64.615 28/27, 27/26
8 73.846 25/24
9 83.077 21/20, 22/21
10 92.308 135/128
11 101.538 35/33
12 110.769 16/15
13 120.000 15/14
14 129.231 14/13
15 138.462 13/12
16 147.692 12/11
17 156.923 35/32
18 166.154 11/10
19 175.385 72/65
20 184.615 10/9
21 193.846 28/25
22 203.077 9/8
23 212.308 44/39
24 221.538 25/22
25 230.769 8/7
26 240.000 55/48
27 249.231 15/13
28 258.462 64/55
29 267.692 7/6
30 276.923 75/64
31 286.154 13/11
32 295.385 32/27
33 304.615 25/21
34 313.846 6/5
35 323.077 65/54
36 332.308 40/33
37 341.538 39/32
38 350.769 11/9, 27/22
39 360.000 16/13
40 369.231 26/21
41 378.462 56/45
42 387.692 5/4
43 396.923 63/50
44 406.154 81/64
45 415.385 14/11
46 424.615 32/25
47 433.846 9/7
48 443.077 128/99
49 452.308 13/10
50 461.538 72/55
51 470.769 21/16
52 480.000 33/25
53 489.231 250/189
54 498.462 4/3
55 507.692 75/56
56 516.923 27/20
57 526.154 65/48
58 535.385 15/11
59 544.615 48/35
60 553.846 11/8
61 563.077 18/13
62 572.308 25/18
63 581.538 7/5
64 590.769 45/32
65 600.000 99/70, 140/99
… … …

Regular temperament properties

Commas

7-limit commas: 2401/2400, 3136/3125, 19683/19600

11-limit commas: 441/440, 540/539, 3136/3125, 4000/3993

13-limit commas: 3136/3125, 243/242, 441/440, 351/350, 364/363

17-limit commas: 221/220, 364/363, 442/441, 595/594, 1275/1274, 4913/4875

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per octave 		Generator
(reduced) 		Cents
(reduced) 		Associated
ratio 		Temperaments
1 19\130 175.38 72/65 Sesquiquartififths / sesquart
1 21\130 193.85 28/25 Didacus / hemiwürschmidt
1 27\130 249.23 15/13 Hemischis
2 9\130 83.08 21/20 Harry

Scales

14-tone temperament of "Narrative Wars"
as an example of using 130-EDO:
Step Cents Distance to the nearest JI interval
(selected ratios)
13 (13/130) 120.000 15/14 (+0.557 ¢)
7 (20/130) 184.615 10/9 (+2.211 ¢)
9 (29/130) 267.692 7/6 (+0,821 ¢)
9 (38/130) 350.769 11/9 (+3.361 ¢)
9 (47/130) 433.846 9/7 (-1.238 ¢)
7 (54/130) 498.462 4/3 (+0.417 ¢)
13 (67/130) 618.462 10/7 (+0.974 ¢)
9 (76/130) 701.538 3/2 (-0.417 ¢)
7 (83/130) 766.154 14/9 (+1.238 ¢)
13 (96/130) 886.154 5/3 (+1.795 ¢)
5 (101/130) 932.308 12/7 (-0.821 ¢)
13 (114/130) 1052.308 11/6 (+2.945 ¢)
7 (121/130) 1116.923 21/11 (-2.540 ¢)
9 (130/130) 1200.000 Octave (2/1, ±0 ¢)

Music

Retrieved from "https://en.xen.wiki/index.php?title=130edo&oldid=73452"