130edo: Difference between revisions

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Added table with 14-tone temperament intervals for 130-EDO (from the Sevish tune "Narrative Wars").
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'''130edo''' divides the octave into 130 parts of size 9.231 cents each.  
'''130edo''' divides the octave into 130 parts of size 9.231 cents each.  


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 [[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 [[hemiwürschmidt]] and [[Schismatic_family #Sesquiquartififths|sesquart]] and 13-limit [[Breedsmic_temperaments #Harry|harry]] temperaments.
== 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 [[Breed family #Jove|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 [[Schismatic family #Sesquiquartififths|sesquart]] and 13-limit [[Breedsmic temperaments #Harry|harry]] temperaments.


7-limit commas: 2401/2400, 3136/3125, 19683/19600
=== Prime harmonics ===
 
{{Primes in edo|130|columns=11|prec=2}}
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 ==
== Intervals ==
{{Primes in edo|130|columns=11|prec=2}}


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


== 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]]
* [http://www.archive.org/details/TheParadiseOfCantor The Paradise of Cantor] [http://www.archive.org/download/TheParadiseOfCantor/cantor.mp3 play] by [[Gene Ward Smith]]
* [https://youtu.be/30UQVYWnsDU "Narrative Wars"] by Sevish (uses a 14-tone (13 7 9 9 9 7 13 9 7 13 5 13 7 9) subset of 130-EDO, from the 2016 compilation album "Next Xen")       
* [https://youtu.be/30UQVYWnsDU "Narrative Wars"] by Sevish (uses a 14-tone (13 7 9 9 9 7 13 9 7 13 5 13 7 9) subset of 130-EDO, from the 2016 compilation album "Next Xen")       

Revision as of 10:06, 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 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
… … …

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

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

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