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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|130}}
{{ED intro}}


== Theory ==
== Theory ==
Line 6: Line 6:


=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|130|columns=12}}
{{Harmonics in equal|130|columns=9}}
{{Harmonics in equal|130|columns=12|start=13|collapsed=true|title=Approximation of prime harmonics in 130edo (continued)}}
{{Harmonics in equal|130|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 130edo (continued)}}


=== Subsets and supersets ===
=== Subsets and supersets ===
Since 130 factors into {{Factorisation|130}}, 130edo has subset edos {{EDOs| 2, 5, 10, 13, 26, and 65 }}.
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.
[[260edo]], which divides the edostep in two, provides a strong correction for the 29th harmonic.
Line 19: 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'', 144/143, 169/168, 176/175, 196/195, 225/224
| ''126/125'', 144/143, 169/168, 176/175, 196/195, 225/224
|-
|-
| 2
| 2
| 18.462
| 18.46
| 78/77, 81/80, 91/90, 99/98, 100/99, 105/104, 121/120
| 78/77, 81/80, 91/90, 99/98, 100/99, 105/104, 121/120
|-
|-
| 3
| 3
| 27.692
| 27.69
| 56/55, 64/63, 65/64, 66/65
| 56/55, 64/63, 65/64, 66/65
|-
|-
| 4
| 4
| 36.923
| 36.92
| 45/44, 49/48, 50/49, ''55/54''
| 45/44, 49/48, 50/49, ''55/54''
|-
|-
| 5
| 5
| 46.154
| 46.15
| 36/35, 40/39
| 36/35, 40/39
|-
|-
| 6
| 6
| 55.385
| 55.38
| 33/32
| 33/32
|-
|-
| 7
| 7
| 64.615
| 64.62
| 27/26, 28/27
| 27/26, 28/27
|-
|-
| 8
| 8
| 73.846
| 73.85
| 25/24, 26/25
| 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
| 44/35
| 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
| 84/65, 128/99
| 84/65, 128/99
|-
|-
| 49
| 49
| 452.308
| 452.31
| 13/10
| 13/10
|-
|-
| 50
| 50
| 461.538
| 461.54
| 64/49, ''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
| 65/49
| 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 323: Line 323:
| [[File:Sagittal sharp.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 ==
Line 330: Line 345:
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
! colspan="2" | Tuning error
|-
|-
Line 338: Line 353:
| 2.3.5.7
| 2.3.5.7
| 2401/2400, 3136/3125, 19683/19600
| 2401/2400, 3136/3125, 19683/19600
| {{mapping| 130 206 302 365 }}
| {{Mapping| 130 206 302 365 }}
| −0.119
| −0.119
| 0.311
| 0.311
Line 345: 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
| {{mapping| 130 206 302 365 450 }}
| {{Mapping| 130 206 302 365 450 }}
| −0.241
| −0.241
| 0.370
| 0.370
Line 352: 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
| {{mapping| 130 206 302 365 450 481 }}
| {{Mapping| 130 206 302 365 450 481 }}
| −0.177
| −0.177
| 0.367
| 0.367
Line 364: Line 379:
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
! Periods<br />per 8ve
! Periods<br>per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br />ratio*
! Associated<br>ratio*
! Temperament
! Temperament
|-
|-
Line 386: Line 401:
| 83.08
| 83.08
| 21/20
| 21/20
| [[Sextilififths]]
| [[Sextilifourths]]
|-
|-
| 1
| 1
Line 437: Line 452:
|-
|-
| 2
| 2
| 54\130<br />(11\130)
| 54\130<br>(11\130)
| 498.46<br />(101.54)
| 498.46<br>(101.54)
| 4/3<br />(35/33)
| 4/3<br>(35/33)
| [[Bischismic]]
| [[Bischismic]]
|-
|-
| 5
| 5
| 27\130<br />(1\130)
| 27\130<br>(1\130)
| 249.23<br />(9.23)
| 249.23<br>(9.23)
| 81/70<br />(176/175)
| 81/70<br>(176/175)
| [[Hemipental]]
| [[Hemiquintile]]
|-
|-
| 10
| 10
| 27\130<br />(1\130)
| 27\130<br>(1\130)
| 249.23<br />(9.23)
| 249.23<br>(9.23)
| 15/13<br />(176/175)
| 15/13<br>(176/175)
| [[Decoid]]
| [[Decoid]]
|-
|-
| 10
| 10
| 54\130<br />(2\130)
| 54\130<br>(2\130)
| 498.46<br />(18.46)
| 498.46<br>(18.46)
| 4/3<br />(81/80)
| 4/3<br>(81/80)
| [[Decal]]
| [[Decile]]
|-
|-
| 26
| 26
| 54\130<br />(1\130)
| 54\130<br>(1\130)
| 498.46<br />(9.23)
| 498.46<br>(9.23)
| 4/3<br />(225/224)
| 4/3<br>(225/224)
| [[Bosonic]]
| [[Bosonic]]
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 
== Zeta properties ==
=== Zeta peak index ===
{| class="wikitable"
|-
! colspan="3" | Tuning
! colspan="3" | Strength
! colspan="2" | Closest EDO
! colspan="2" | Integer limit
|-
! ZPI
! Steps per octave
! Step size (cents)
! Height
! Integral
! Gap
! EDO
! Octave (cents)
! Consistent
! Distinct
|-
| [[796zpi]]
| 130.003910460506
| 9.23049157328654
| 10.355108
| 1.634018
| 19.594551
| 130edo
| 1199.96390452725
| 16
| 16
|}


== Scales ==
== Scales ==
Line 564: Line 547:
| [[Octave]] (2/1, 0{{c}})
| [[Octave]] (2/1, 0{{c}})
|}
|}
== Instruments ==
[[Lumatone mapping for 130edo]]


== Music ==
== Music ==
Retrieved from "https://en.xen.wiki/w/130edo"