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Line 1: Line 1:
{{Infobox ET
{{Infobox ET}}
| Prime factorization = 2 × 5 × 13
{{ED intro}}
| Step size = 9.231¢
| Fifth = 76\130 (701.538¢) (→ [[65edo|38\65]])
| Major 2nd = 22\130 (203¢)
| Semitones = 12:10 (111¢ : 92¢)
| Consistency = 15
}}
 
The '''130 equal divisions of the octave''' ('''130edo'''), or the '''130(-tone) equal temperament''' ('''130tet''', '''130et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 130 parts of size about 9.23 [[cent]]s each.


== Theory ==
== 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 [[Schismatic family #Sesquiquartififths|sesquart]] and 13-limit [[Breedsmic temperaments #Harry|harry]] temperaments.
130edo is a [[zeta peak edo]], a [[zeta peak integer edo]], and a [[zeta integral edo]] but not a gap edo. It is [[distinctly consistent]] to the [[15-odd-limit]] and is the first [[trivial temperament|nontrivial edo]] to be consistent in the 14-[[odd prime sum limit|odd-prime-sum-limit]]. As an equal temperament, it [[tempering out|tempers out]] [[2401/2400]], [[3136/3125]], [[6144/6125]], and [[19683/19600]] in the 7-limit; [[243/242]], [[441/440]], [[540/539]], and [[4000/3993]] in the 11-limit; and [[351/350]], [[364/363]], [[676/675]], [[729/728]], [[1001/1000]], [[1575/1573]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit. 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-3 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 [[Schismatic family #Sesquiquartififths|sesquart]] and 13-limit [[harry]].  


=== Prime harmonics ===
=== Prime harmonics ===
{{Primes in edo|130|columns=11}}
{{Harmonics in equal|130|columns=9}}
{{Harmonics in equal|130|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 130edo (continued)}}
 
=== Subsets and supersets ===
Since 130 factors into 2 × 5 × 13, 130edo has subset edos {{EDOs| 2, 5, 10, 13, 26, and 65 }}.
 
[[260edo]], which divides the edostep in two, provides a strong correction for the 29th harmonic.


== Intervals ==
== Intervals ==
Line 21: Line 19:
! Degree
! Degree
! Cents
! Cents
! Approximate Ratios
! Approximate ratios
|-
|-
| 0
| 0
| 0.000
| 0.00
| 1/1
| 1/1
|-
|-
| 1
| 1
| 9.231
| 9.23
| 126/125, 225/224
| ''126/125'', 144/143, 169/168, 176/175, 196/195, 225/224
|-
|-
| 2
| 2
| 18.462
| 18.46
| 81/80
| 78/77, 81/80, 91/90, 99/98, 100/99, 105/104, 121/120
|-
|-
| 3
| 3
| 27.692
| 27.69
| 64/63
| 56/55, 64/63, 65/64, 66/65
|-
|-
| 4
| 4
| 36.923
| 36.92
| 49/48, 50/49
| 45/44, 49/48, 50/49, ''55/54''
|-
|-
| 5
| 5
| 46.154
| 46.15
| 36/35
| 36/35, 40/39
|-
|-
| 6
| 6
| 55.385
| 55.38
| 33/32
| 33/32
|-
|-
| 7
| 7
| 64.615
| 64.62
| 28/27, 27/26
| 27/26, 28/27
|-
|-
| 8
| 8
| 73.846
| 73.85
| 25/24
| 25/24, 26/25
|-
|-
| 9
| 9
| 83.077
| 83.08
| 21/20, 22/21
| 21/20, 22/21
|-
|-
| 10
| 10
| 92.308
| 92.31
| 135/128
| 135/128
|-
|-
| 11
| 11
| 101.538
| 101.54
| 35/33
| 35/33
|-
|-
| 12
| 12
| 110.769
| 110.77
| 16/15
| 16/15
|-
|-
| 13
| 13
| 120.000
| 120.00
| 15/14
| 15/14
|-
|-
| 14
| 14
| 129.231
| 129.23
| 14/13
| 14/13
|-
|-
| 15
| 15
| 138.462
| 138.46
| 13/12
| 13/12
|-
|-
| 16
| 16
| 147.692
| 147.69
| 12/11
| 12/11
|-
|-
| 17
| 17
| 156.923
| 156.92
| 35/32
| 35/32
|-
|-
| 18
| 18
| 166.154
| 166.15
| 11/10
| 11/10
|-
|-
| 19
| 19
| 175.385
| 175.38
| 72/65
| 72/65
|-
|-
| 20
| 20
| 184.615
| 184.62
| 10/9
| 10/9
|-
|-
| 21
| 21
| 193.846
| 193.85
| 28/25
| 28/25
|-
|-
| 22
| 22
| 203.077
| 203.08
| 9/8
| 9/8
|-
|-
| 23
| 23
| 212.308
| 212.31
| 44/39
| 44/39
|-
|-
| 24
| 24
| 221.538
| 221.54
| 25/22
| 25/22
|-
|-
| 25
| 25
| 230.769
| 230.77
| 8/7
| 8/7
|-
|-
| 26
| 26
| 240.000
| 240.00
| 55/48
| 55/48
|-
|-
| 27
| 27
| 249.231
| 249.23
| 15/13
| 15/13
|-
|-
| 28
| 28
| 258.462
| 258.46
| 64/55
| 64/55
|-
|-
| 29
| 29
| 267.692
| 267.69
| 7/6
| 7/6
|-
|-
| 30
| 30
| 276.923
| 276.92
| 75/64
| 75/64
|-
|-
| 31
| 31
| 286.154
| 286.15
| 13/11
| 13/11
|-
|-
| 32
| 32
| 295.385
| 295.38
| 32/27
| 32/27
|-
|-
| 33
| 33
| 304.615
| 304.62
| 25/21
| 25/21
|-
|-
| 34
| 34
| 313.846
| 313.85
| 6/5
| 6/5
|-
|-
| 35
| 35
| 323.077
| 323.08
| 65/54
| 65/54
|-
|-
| 36
| 36
| 332.308
| 332.31
| 40/33
| 40/33
|-
|-
| 37
| 37
| 341.538
| 341.54
| 39/32
| 39/32
|-
|-
| 38
| 38
| 350.769
| 350.77
| 11/9, 27/22
| 11/9, 27/22
|-
|-
| 39
| 39
| 360.000
| 360.00
| 16/13
| 16/13
|-
|-
| 40
| 40
| 369.231
| 369.23
| 26/21
| 26/21
|-
|-
| 41
| 41
| 378.462
| 378.46
| 56/45
| 56/45
|-
|-
| 42
| 42
| 387.692
| 387.69
| 5/4
| 5/4
|-
|-
| 43
| 43
| 396.923
| 396.92
| 63/50
| 44/35
|-
|-
| 44
| 44
| 406.154
| 406.15
| 81/64
| 81/64
|-
|-
| 45
| 45
| 415.385
| 415.38
| 14/11
| 14/11
|-
|-
| 46
| 46
| 424.615
| 424.62
| 32/25
| 32/25
|-
|-
| 47
| 47
| 433.846
| 433.85
| 9/7
| 9/7
|-
|-
| 48
| 48
| 443.077
| 443.08
| 128/99
| 84/65, 128/99
|-
|-
| 49
| 49
| 452.308
| 452.31
| 13/10
| 13/10
|-
|-
| 50
| 50
| 461.538
| 461.54
| 72/55
| 64/49, ''72/55''
|-
|-
| 51
| 51
| 470.769
| 470.77
| 21/16
| 21/16
|-
|-
| 52
| 52
| 480.000
| 480.00
| 33/25
| 33/25
|-
|-
| 53
| 53
| 489.231
| 489.23
| 250/189
| 65/49
|-
|-
| 54
| 54
| 498.462
| 498.46
| 4/3
| 4/3
|-
|-
| 55
| 55
| 507.692
| 507.69
| 75/56
| 75/56
|-
|-
| 56
| 56
| 516.923
| 516.92
| 27/20
| 27/20
|-
|-
| 57
| 57
| 526.154
| 526.15
| 65/48
| 65/48
|-
|-
| 58
| 58
| 535.385
| 535.38
| 15/11
| 15/11
|-
|-
| 59
| 59
| 544.615
| 544.62
| 48/35
| 48/35
|-
|-
| 60
| 60
| 553.846
| 553.85
| 11/8
| 11/8
|-
|-
| 61
| 61
| 563.077
| 563.08
| 18/13
| 18/13
|-
|-
| 62
| 62
| 572.308
| 572.31
| 25/18
| 25/18
|-
|-
| 63
| 63
| 581.538
| 581.54
| 7/5
| 7/5
|-
|-
| 64
| 64
| 590.769
| 590.77
| 45/32
| 45/32
|-
|-
| 65
| 65
| 600.000
| 600.00
| 99/70, 140/99
| 99/70, 140/99
|-
|-
Line 291: Line 289:
|…
|…
|}
|}
== Notation ==
=== Sagittal notation ===
{| class="wikitable center-all"
! Steps
| 0
| 1
| 2
| 3
| 4
| 5
| 6
| 7
| 8
| 9
| 10
| 11
| 12
|-
! Symbol
| [[File:Sagittal natural.png]]
| [[File:Sagittal nai.png]]
| [[File:Sagittal pai.png]]
| [[File:Sagittal tai.png]]
| [[File:Sagittal phai.png]]
| [[File:Sagittal patai.png]]
| [[File:Sagittal pakai.png]]
| [[File:Sagittal jakai.png]]
| [[File:Sagittal sharp phao.png]]
| [[File:Sagittal sharp tao.png]]
| [[File:Sagittal sharp pao.png]]
| [[File:Sagittal sharp nao.png]]
| [[File:Sagittal sharp.png]]
|}
== Approximation to JI ==
=== Zeta peak index ===
{{ZPI
| zpi = 796
| steps = 130.003910460506
| step size = 9.23049157328654
| tempered height = 10.355108
| pure height = 10.339572
| integral = 1.634018
| gap = 19.594551
| octave = 1199.96390452725
| consistent = 16
| distinct = 16
}}


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | Subgroup
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
Line 305: Line 353:
| 2.3.5.7
| 2.3.5.7
| 2401/2400, 3136/3125, 19683/19600
| 2401/2400, 3136/3125, 19683/19600
| [{{val| 130 206 302 365 }}]
| {{Mapping| 130 206 302 365 }}
| -0.119
| −0.119
| 0.311
| 0.311
| 3.37
| 3.37
Line 312: Line 360:
| 2.3.5.7.11
| 2.3.5.7.11
| 243/242, 441/440, 3136/3125, 4000/3993
| 243/242, 441/440, 3136/3125, 4000/3993
| [{{val| 130 206 302 365 450 }}]
| {{Mapping| 130 206 302 365 450 }}
| -0.241
| −0.241
| 0.370
| 0.370
| 4.02
| 4.02
Line 319: Line 367:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 243/242, 351/350, 364/363, 441/440, 3136/3125
| 243/242, 351/350, 364/363, 441/440, 3136/3125
| [{{val| 130 206 302 365 450 481 }}]
| {{Mapping| 130 206 302 365 450 481 }}
| -0.177
| −0.177
| 0.367
| 0.367
| 3.98
| 3.98
Line 329: Line 377:


{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
! Periods<br>per octave
|-
! Generator<br>(reduced)
! Periods<br>per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! Temperaments
! Associated<br>ratio*
! Temperament
|-
|-
| 1
| 1
Line 341: Line 390:
| 64/63
| 64/63
| [[Arch]]
| [[Arch]]
|-
| 1
| 7\130
| 64.62
| 26/25
| [[Rectified hebrew]]
|-
|-
| 1
| 1
Line 346: Line 401:
| 83.08
| 83.08
| 21/20
| 21/20
| [[Sextilififths]]
| [[Sextilifourths]]
|-
|-
| 1
| 1
Line 358: Line 413:
| 193.85
| 193.85
| 28/25
| 28/25
| [[Didacus]] / [[hemiwürschmidt]]
| [[Hemiwürschmidt]]
|-
|-
| 1
| 1
Line 376: Line 431:
| 55.38
| 55.38
| 33/32
| 33/32
| [[Biscapade]]
| [[Septisuperfourth]]
|-
|-
| 2
| 2
Line 406: Line 461:
| 249.23<br>(9.23)
| 249.23<br>(9.23)
| 81/70<br>(176/175)
| 81/70<br>(176/175)
| [[Hemipental]]
| [[Hemiquintile]]
|-
|-
| 10
| 10
Line 418: Line 473:
| 498.46<br>(18.46)
| 498.46<br>(18.46)
| 4/3<br>(81/80)
| 4/3<br>(81/80)
| [[Decal]]
| [[Decile]]
|-
|-
| 26
| 26
Line 426: Line 481:
| [[Bosonic]]
| [[Bosonic]]
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct


== Scales ==
== Scales ==
{| class="wikitable"
{| class="wikitable"
|+14-tone temperament of "Narrative Wars"<br>as an example of using 130edo:
|+ style="font-size: 105%;" | 14-tone temperament of "Narrative Wars"<br />as an example of using 130edo:
|-
! Step
! Step
! Cents
! Cents
! Distance to the nearest JI interval<br>(selected ratios)
! Distance to the nearest JI interval<br />(selected ratios)
|-
|-
| 13 (13/130)
| 13 (13/130)
| 120.000
| 120.000
| [[15/14]] (+0.557 ¢)
| [[15/14]] (+0.557{{c}})
|-
|-
| 7 (20/130)
| 7 (20/130)
| 184.615
| 184.615
| [[10/9]] (+2.211 ¢)
| [[10/9]] (+2.211{{c}})
|-
|-
| 9 (29/130)
| 9 (29/130)
| 267.692
| 267.692
| [[7/6]] (+0,821 ¢)
| [[7/6]] (+0,821{{c}})
|-
|-
| 9 (38/130)
| 9 (38/130)
| 350.769
| 350.769
| [[11/9]] (+3.361 ¢)
| [[11/9]] (+3.361{{c}})
|-
|-
| 9 (47/130)
| 9 (47/130)
| 433.846
| 433.846
| [[9/7]] (-1.238 ¢)
| [[9/7]] (−1.238{{c}})
|-
|-
| 7 (54/130)
| 7 (54/130)
| 498.462
| 498.462
| [[4/3]] (+0.417 ¢)
| [[4/3]] (+0.417{{c}})
|-
|-
| 13 (67/130)
| 13 (67/130)
| 618.462
| 618.462
| [[10/7]] (+0.974 ¢)
| [[10/7]] (+0.974{{c}})
|-
|-
| 9 (76/130)
| 9 (76/130)
| 701.538
| 701.538
| [[3/2]] (-0.417 ¢)
| [[3/2]] (−0.417{{c}})
|-
|-
| 7 (83/130)
| 7 (83/130)
| 766.154
| 766.154
| [[14/9]] (+1.238 ¢)
| [[14/9]] (+1.238{{c}})
|-
|-
| 13 (96/130)
| 13 (96/130)
| 886.154
| 886.154
| [[5/3]] (+1.795 ¢)
| [[5/3]] (+1.795{{c}})
|-
|-
| 5 (101/130)
| 5 (101/130)
| 932.308
| 932.308
| [[12/7]] (-0.821 ¢)
| [[12/7]] (−0.821{{c}})
|-
|-
| 13 (114/130)
| 13 (114/130)
| 1052.308
| 1052.308
| [[11/6]] (+2.945 ¢)
| [[11/6]] (+2.945{{c}})
|-
|-
| 7 (121/130)
| 7 (121/130)
| 1116.923
| 1116.923
| [[21/11]] (-2.540 ¢)
| [[21/11]] (−2.540{{c}})
|-
|-
| 9 (130/130)
| 9 (130/130)
| 1200.000
| 1200.000
| [[Octave]] (2/1, ±0 ¢)
| [[Octave]] (2/1, 0{{c}})
|}
|}
== Instruments ==
[[Lumatone mapping for 130edo]]


== Music ==
== Music ==
{{See also|:Category:130edo tracks}}
{{Catrel|130edo tracks}}
* [http://www.archive.org/details/TheParadiseOfCantor The Paradise of Cantor] [http://www.archive.org/download/TheParadiseOfCantor/cantor.mp3 play] by [[Gene Ward Smith]]
 
; [[birdshite stalactite]]
* [https://www.youtube.com/watch?v=q41n5XI6YA4 ''wazzock''] (2024)
 
; [[Sevish]]
* [https://www.youtube.com/watch?v=30UQVYWnsDU Narrative Wars]
 
; [[Gene Ward Smith]]
* [https://www.archive.org/details/TheParadiseOfCantor ''The Paradise of Cantor''] [https://www.archive.org/download/TheParadiseOfCantor/cantor.mp3 play] (2006)


[[Category:130edo|130edo]] <!-- main article -->
[[Category:Equal divisions of the octave]]
[[Category:Harry]]
[[Category:Harry]]
[[Category:Hemischis]]
[[Category:Hemischis]]
[[Category:Hemiwürschmidt]]
[[Category:Hemiwürschmidt]]
[[Category:Listen]]
[[Category:Sesquiquartififths]]
[[Category:Sesquiquartififths]]
[[Category:Zeta]]
[[Category:Listen]]

Latest revision as of 10:27, 11 May 2025

← 129edo 130edo 131edo →
Prime factorization 2 × 5 × 13
Step size 9.23077 ¢ 
Fifth 76\130 (701.538 ¢) (→ 38\65)
Semitones (A1:m2) 12:10 (110.8 ¢ : 92.31 ¢)
Consistency limit 15
Distinct consistency limit 15

130 equal divisions of the octave (abbreviated 130edo or 130ed2), also called 130-tone equal temperament (130tet) or 130 equal temperament (130et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 130 equal parts of about 9.23 ¢ each. Each step represents a frequency ratio of 21/130, or the 130th root of 2.

Theory

130edo is a zeta peak edo, a zeta peak integer edo, and a zeta integral edo but not a gap edo. It is distinctly consistent to the 15-odd-limit and is the first nontrivial edo to be consistent in the 14-odd-prime-sum-limit. As an equal temperament, it tempers out 2401/2400, 3136/3125, 6144/6125, and 19683/19600 in the 7-limit; 243/242, 441/440, 540/539, and 4000/3993 in the 11-limit; and 351/350, 364/363, 676/675, 729/728, 1001/1000, 1575/1573, 1716/1715, 2080/2079, 4096/4095, and 4225/4224 in the 13-limit. 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-3 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.

Prime harmonics

Approximation of prime harmonics in 130edo
Harmonic 2 3 5 7 11 13 17 19 23
Error Absolute (¢) +0.00 -0.42 +1.38 +0.40 +2.53 -0.53 -3.42 -2.13 -0.58
Relative (%) +0.0 -4.5 +14.9 +4.4 +27.4 -5.7 -37.0 -23.1 -6.3
Steps
(reduced) 		130
(0) 		206
(76) 		302
(42) 		365
(105) 		450
(60) 		481
(91) 		531
(11) 		552
(32) 		588
(68)
Approximation of prime harmonics in 130edo (continued)
Harmonic 29 31 37 41 43 47 53 59 61
Error Absolute (¢) +4.27 -0.42 -2.11 -4.45 -3.83 -0.89 +3.42 +2.37 +0.04
Relative (%) +46.2 -4.6 -22.9 -48.2 -41.4 -9.7 +37.0 +25.6 +0.4
Steps
(reduced) 		632
(112) 		644
(124) 		677
(27) 		696
(46) 		705
(55) 		722
(72) 		745
(95) 		765
(115) 		771
(121)

Subsets and supersets

Since 130 factors into 2 × 5 × 13, 130edo has subset edos 2, 5, 10, 13, 26, and 65.

260edo, which divides the edostep in two, provides a strong correction for the 29th harmonic.

Intervals

Degree Cents Approximate ratios
0 0.00 1/1
1 9.23 126/125, 144/143, 169/168, 176/175, 196/195, 225/224
2 18.46 78/77, 81/80, 91/90, 99/98, 100/99, 105/104, 121/120
3 27.69 56/55, 64/63, 65/64, 66/65
4 36.92 45/44, 49/48, 50/49, 55/54
5 46.15 36/35, 40/39
6 55.38 33/32
7 64.62 27/26, 28/27
8 73.85 25/24, 26/25
9 83.08 21/20, 22/21
10 92.31 135/128
11 101.54 35/33
12 110.77 16/15
13 120.00 15/14
14 129.23 14/13
15 138.46 13/12
16 147.69 12/11
17 156.92 35/32
18 166.15 11/10
19 175.38 72/65
20 184.62 10/9
21 193.85 28/25
22 203.08 9/8
23 212.31 44/39
24 221.54 25/22
25 230.77 8/7
26 240.00 55/48
27 249.23 15/13
28 258.46 64/55
29 267.69 7/6
30 276.92 75/64
31 286.15 13/11
32 295.38 32/27
33 304.62 25/21
34 313.85 6/5
35 323.08 65/54
36 332.31 40/33
37 341.54 39/32
38 350.77 11/9, 27/22
39 360.00 16/13
40 369.23 26/21
41 378.46 56/45
42 387.69 5/4
43 396.92 44/35
44 406.15 81/64
45 415.38 14/11
46 424.62 32/25
47 433.85 9/7
48 443.08 84/65, 128/99
49 452.31 13/10
50 461.54 64/49, 72/55
51 470.77 21/16
52 480.00 33/25
53 489.23 65/49
54 498.46 4/3
55 507.69 75/56
56 516.92 27/20
57 526.15 65/48
58 535.38 15/11
59 544.62 48/35
60 553.85 11/8
61 563.08 18/13
62 572.31 25/18
63 581.54 7/5
64 590.77 45/32
65 600.00 99/70, 140/99
… … …

Notation

Sagittal notation

Steps 0 1 2 3 4 5 6 7 8 9 10 11 12
Symbol

Approximation to JI

Zeta peak index

Tuning Strength Octave (cents) Integer limit
ZPI Steps
per 8ve 		Step size
(cents) 		Height Integral Gap Size Stretch Consistent Distinct
Tempered Pure
796zpi 130.00391 9.230492 10.355108 10.339572 1.634018 19.594551 1199.963905 −0.036095 16 16

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3.5.7 2401/2400, 3136/3125, 19683/19600 [⟨130 206 302 365]] −0.119 0.311 3.37
2.3.5.7.11 243/242, 441/440, 3136/3125, 4000/3993 [⟨130 206 302 365 450]] −0.241 0.370 4.02
2.3.5.7.11.13 243/242, 351/350, 364/363, 441/440, 3136/3125 [⟨130 206 302 365 450 481]] −0.177 0.367 3.98

Rank-2 temperaments

Note: temperaments supported by 65et are not included.

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperament
1 3\130 27.69 64/63 Arch
1 7\130 64.62 26/25 Rectified hebrew
1 9\130 83.08 21/20 Sextilifourths
1 19\130 175.38 72/65 Sesquiquartififths / sesquart
1 21\130 193.85 28/25 Hemiwürschmidt
1 27\130 249.23 15/13 Hemischis
1 41\130 378.46 56/45 Subpental
2 6\130 55.38 33/32 Septisuperfourth
2 9\130 83.08 21/20 Harry
2 17\130 156.92 35/32 Bison
2 19\130 175.38 448/405 Bisesqui
2 54\130
(11\130) 		498.46
(101.54) 		4/3
(35/33) 		Bischismic
5 27\130
(1\130) 		249.23
(9.23) 		81/70
(176/175) 		Hemiquintile
10 27\130
(1\130) 		249.23
(9.23) 		15/13
(176/175) 		Decoid
10 54\130
(2\130) 		498.46
(18.46) 		4/3
(81/80) 		Decile
26 54\130
(1\130) 		498.46
(9.23) 		4/3
(225/224) 		Bosonic

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct

Scales

14-tone temperament of "Narrative Wars"
as an example of using 130edo:
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 ¢)

Instruments

Lumatone mapping for 130edo

Music

See also: Category:130edo tracks
birdshite stalactite
Sevish
Gene Ward Smith
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