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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")       
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