130edo: Difference between revisions

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m Cleanup since there's actually an interval table
m General cleanup
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''130edo'' divides the octave into 130 parts of size 9.231 cents each. It is the tenth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] but not a gap edo. It can be used to tune a variety of temperaments, including hemiwürschmidt, sesquiquartififths, harry and hemischismic. It also can be used to tune the rank-three temperament [[Breed_family#Jove, aka Wonder|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|optimal patent val]] for 11-limit [[Würschmidt_family#Hemiwürschmidt|hemiwürschmidt]] and [[Schismatic_family#Sesquiquartififths|sesquart]] and 13-limit [[Breedsmic_temperaments#Harry|harry]] temperaments.
'''130edo''' divides the octave into 130 parts of size 9.231 cents each.  
 
130edo is the tenth [[The_Riemann_Zeta_Function_and_Tuning #Zeta EDO lists|zeta integral edo]] but not a gap edo. It can be used to tune a variety of temperaments, including [[hemiwürschmidt]], [[sesquiquartififths]], [[harry]] and [[hemischismic]]. It also can be used to tune the rank-three temperament [[Breed_family#Jove, aka Wonder|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 [[Würschmidt_family #Hemiwürschmidt|hemiwürschmidt]] and [[Schismatic_family #Sesquiquartififths|sesquart]] and 13-limit [[Breedsmic_temperaments #Harry|harry]] temperaments.


7-limit commas: 2401/2400, 3136/3125, 19683/19600
7-limit commas: 2401/2400, 3136/3125, 19683/19600
Line 17: Line 19:
! Associated Temperament
! Associated Temperament
|-
|-
| | 0
| 0
| | 0.000
| 0.000
| |  
|  
|-
|-
| | 1
| 1
| | 9.231
| 9.231
| |  
|  
|-
|-
| | 2
| 2
| | 18.462
| 18.462
| |  
|  
|-
|-
| | 3
| 3
| | 27.692
| 27.692
| |  
|  
|-
|-
| | 4
| 4
| | 36.923
| 36.923
| |  
|  
|-
|-
| | 5
| 5
| | 46.154
| 46.154
| |  
|  
|-
|-
| | 6
| 6
| | 55.385
| 55.385
| |  
|  
|-
|-
| | 7
| 7
| | 64.615
| 64.615
| |  
|  
|-
|-
| | 8
| 8
| | 73.846
| 73.846
| |  
|  
|-
|-
| | 9
| 9
| | 83.077
| 83.077
| | [[Breedsmic_temperaments#Harry|Harry]]
| [[Harry]]
|-
|-
| | 10
| 10
| | 92.308
| 92.308
| |  
|  
|-
|-
| | 11
| 11
| | 101.538
| 101.538
| |  
|  
|-
|-
| | 12
| | 12
Line 69: Line 71:
| |  
| |  
|-
|-
| | 13
| 13
| | 120.000
| 120.000
| |  
|  
|-
|-
| | 14
| 14
| | 129.231
| 129.231
| |  
|  
|-
|-
| | 15
| 15
| | 138.462
| 138.462
| |  
|  
|-
|-
| | 16
| 16
| | 147.692
| 147.692
| |  
|  
|-
|-
| | 17
| 17
| | 156.923
| 156.923
| |  
|  
|-
|-
| | 18
| 18
| | 166.154
| 166.154
| |  
|  
|-
|-
| | 19
| 19
| | 175.385
| 175.385
| | [[Schismatic_family#Sesquiquartififths|Sesquart]]
| [[Schismatic_family #Sesquiquartififths|Sesquart]]
|-
|-
| | 20
| 20
| | 184.615
| 184.615
| |  
|  
|-
|-
| | 21
| 21
| | 193.846
| 193.846
| | Hemiwürschmidt
| [[Hemiwürschmidt]]
|-
|-
| | 22
| 22
| | 203.077
| 203.077
| |  
|  
|-
|-
| | 23
| 23
| | 212.308
| 212.308
| |  
|  
|-
|-
| | 24
| 24
| | 221.538
| 221.538
| |  
|  
|-
|-
| | 25
| 25
| | 230.769
| 230.769
| |  
|  
|-
|-
| | 26
| 26
| | 240.000
| 240.000
| |  
|  
|-
|-
| | 27
| 27
| | 249.231
| 249.231
| | Hemischismic
| [[Hemischismic]]
|-
|-
| | 28
| 28
| | 258.462
| 258.462
| |  
|  
|-
|-
| | 29
| 29
| | 267.692
| 267.692
| |  
|  
|-
|-
| | 30
| 30
| | 276.923
| 276.923
| |  
|  
|-
|-
| | 31
| 31
| | 286.154
| 286.154
| |  
|  
|-
|-
| | 32
| 32
| | 295.385
| 295.385
| |  
|  
|-
|-
| | 33
| 33
| | 304.615
| 304.615
| |  
|  
|-
|-
| | 34
| 34
| | 313.846
| 313.846
| |  
|  
|-
|-
| | 35
| 35
| | 323.077
| 323.077
| |  
|  
|-
|-
| | 36
| 36
| | 332.308
| 332.308
| |  
|  
|-
|-
| | 37
| 37
| | 341.538
| 341.538
| |  
|  
|-
|-
| | 38
| 38
| | 350.769
| 350.769
| |  
|  
|-
|-
| | 39
| 39
| | 360.000
| 360.000
| |  
|  
|-
|-
| | 40
| 40
| | 369.231
| 369.231
| |  
|  
|-
|-
| | 41
| 41
| | 378.462
| 378.462
| |  
|  
|-
|-
| | 42
| 42
| | 387.692
| 387.692
| |  
|  
|-
|-
| | 43
| 43
| | 396.923
| 396.923
| |  
|  
|-
|-
| | 44
| 44
| | 406.154
| 406.154
| |  
|  
|-
|-
| | 45
| 45
| | 415.385
| 415.385
| |  
|  
|-
|-
| | 46
| 46
| | 424.615
| 424.615
| |  
|  
|-
|-
| | 47
| 47
| | 433.846
| 433.846
| |  
|  
|-
|-
| | 48
| 48
| | 443.077
| 443.077
| |  
|  
|-
|-
| | 49
| 49
| | 452.308
| 452.308
| |  
|  
|-
|-
| | 50
| 50
| | 461.538
| 461.538
| |  
|  
|-
|-
| | 51
| 51
| | 470.769
| 470.769
| |  
|  
|-
|-
| | 52
| 52
| | 480.000
| 480.000
| |  
|  
|-
|-
| | 53
| 53
| | 489.231
| 489.231
| |  
|  
|-
|-
| | 54
| 54
| | 498.462
| 498.462
| |  
|  
|-
|-
| | 55
| 55
| | 507.692
| 507.692
| |  
|  
|-
|-
| | 56
| 56
| | 516.923
| 516.923
| |  
|  
|-
|-
| | 57
| 57
| | 526.154
| 526.154
| |  
|  
|-
|-
| | 58
| 58
| | 535.385
| 535.385
| |  
|  
|-
|-
| | 59
| 59
| | 544.615
| 544.615
| |  
|  
|-
|-
| | 60
| 60
| | 553.846
| 553.846
| |  
|  
|-
|-
| | 61
| 61
| | 563.077
| 563.077
| |  
|  
|-
|-
| | 62
| 62
| | 572.308
| 572.308
| |  
|  
|-
|-
| | 63
| 63
| | 581.538
| 581.538
| |  
|  
|-
|-
| | 64
| 64
| | 590.769
| 590.769
| |  
|  
|-
|-
| | 65
| 65
| | 600.000
| 600.000
| |  
|  
|-
|-
|…
|…
Line 287: Line 289:


== Music ==
== Music ==
[http://www.archive.org/details/TheParadiseOfCantor The Paradise of Cantor] [http://www.archive.org/download/TheParadiseOfCantor/cantor.mp3 play] by [[Gene_Ward_Smith|Gene Ward Smith]]       
[http://www.archive.org/details/TheParadiseOfCantor The Paradise of Cantor] [http://www.archive.org/download/TheParadiseOfCantor/cantor.mp3 play] by [[Gene Ward Smith]]       


[[Category:edo]]
[[Category:Edo]]
[[Category:harry]]
[[Category:Harry]]
[[Category:hemischismic]]
[[Category:Hemischismic]]
[[Category:hemiwuerschmidt]]
[[Category:Hemiwuerschmidt]]
[[Category:listen]]
[[Category:Listen]]
[[Category:sesquiquartififths]]
[[Category:Sesquiquartififths]]
[[Category:zeta]]
[[Category:Zeta]]

Revision as of 10:56, 10 September 2020

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

130edo is the tenth zeta integral edo but not a gap edo. It can be used to tune a variety of temperaments, including hemiwürschmidt, sesquiquartififths, harry and hemischismic. 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.

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

Intervals

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

Music

The Paradise of Cantor play by Gene Ward Smith

Retrieved from "https://en.xen.wiki/index.php?title=130edo&oldid=49078"