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5L 2s/Temperaments: Difference between revisions

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[[Comma list]]: 169/168, 352/351, 364/363
[[Comma list]]: 169/168, 352/351, 364/363


[[Gencom]]: [2 3/2; 169/169 352/351 364/363]
[[Gencom]]: [2 3/2; 169/168 352/351 364/363]


[[Gencom]] [[mapping]]: [{{val| 1 1 -6 -3 -1 }}, {{val| 0 1 15 11 8 }}]
[[Gencom]] [[mapping]]: [{{val| 1 1 -6 -3 -1 }}, {{val| 0 1 15 11 8 }}]
Line 779: Line 779:
[[Comma list]]: 64/63, 245/243
[[Comma list]]: 64/63, 245/243


[[Mapping]]: [{{val|1 0 -12 6}}, {{val|0 1 9 -2}}]
[[Mapping]]: [{{val|1 1 -3 4}}, {{val|0 1 9 -2}}]


[[Wedgie]]: {{wedgie|1 9 -2 12 -6 -30}}
[[Wedgie]]: {{wedgie|1 9 -2 12 -6 -30}}
Line 788: Line 788:


=== Ultrapyth ===
=== Ultrapyth ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.13


Period: 1\1
Period: 1\1


Optimal ([[POTE]]) generator: ~3/2 = 713.500
Optimal ([[POTE]]) generator: ~3/2 = 713.745


EDO generators: [[32edo|19\32]], [[37edo|22\37]]
EDO generators: [[32edo|19\32]], [[37edo|22\37]]


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Interval table (32-note MOS, 2.3.5.7.11.13 POTE tuning)</div>
<div style="line-height:1.6;">Interval table (22-note MOS, 2.3.5.7.13 POTE tuning)</div>
<div class="mw-collapsible-content">
<div class="mw-collapsible-content">
{| class="wikitable right-1 right-2 sortable"
{| class="wikitable right-1 right-2 sortable"
Line 804: Line 804:
! #Gens up
! #Gens up
! Cents <ref>octave-reduced</ref>
! Cents <ref>octave-reduced</ref>
! class="unsortable"| Approximate ratios<ref>2.3.5.7.11.13, odd limit ≤ 15</ref>
! class="unsortable"| Approximate ratios<ref>2.3.5.7.13, odd limit ≤ 15</ref>
|-
|-
| 0
| 0
Line 811: Line 811:
|-
|-
| 1
| 1
| 713.5
| 713.7
| 3/2
| 3/2
|-
|-
| 2
| 2
| 227.0
| 227.5
| 9/8, 8/7
| 9/8, 8/7
|-
|-
| 3
| 3
| 940.5
| 941.2
| 12/7, 26/15
| 12/7, 26/15
|-
|-
| 4
| 4
| 454.0
| 455.0
| 9/7, 13/10
| 9/7, 13/10
|-
|-
| 5
| 5
| 1167.5
| 1168.7
|  
|  
|-
|-
| 6
| 6
| 681.0
| 682.5
|  
|  
|-
|-
| 7
| 7
| 194.5
| 196.2
|  
|  
|-
|-
| 8
| 8
| 908.0
| 910.0
|  
|  
|-
|-
| 9
| 9
| 421.5
| 423.7
| 14/11
|  
|-
|-
| 10
| 10
| 1135.0
| 1137.5
|  
|  
|-
|-
| 11
| 11
| 648.5
| 651.2
| 16/11
|  
|-
|-
| 12
| 12
| 162.0
| 164.9
| 12/11, 10/9
| 10/9
|-
|-
| 13
| 13
| 875.5
| 878.7
| 18/11, 5/3
| 5/3
|-
|-
| 14
| 14
| 389.0
| 392.4
| 5/4
| 5/4
|-
|-
| 15
| 15
| 1102.5
| 1106.2
| 15/8
| 15/8
|-
|-
| 16
| 16
| 616.0
| 619.9
| 10/7, 13/9
| 10/7, 13/9
|-
|-
| 17
| 17
| 129.5
| 133.7
| 15/14, 13/12
| 15/14, 13/12
|-
|-
| 18
| 18
| 843.0
| 847.4
| 13/8
| 13/8
|-
|-
| 19
| 19
| 356.5
| 361.2
|  
|  
|-
|-
| 20
| 20
| 1070.0
| 1074.9
| 13/7
| 13/7
|-
|-
| 21
| 21
| 583.5
| 588.7
|
|-
| 22
| 97.0
|
|-
| 23
| 810.5
|
|-
| 24
| 324.0
|
|-
| 25
| 1037.5
| 20/11
|-
| 26
| 551.0
| 15/11
|-
| 27
| 64.5
|
|-
| 28
| 778.0
|
|-
| 29
| 291.5
| 13/11
|-
| 30
| 1005.0
|
|-
| 31
| 518.5
|  
|  
|}
|}
<references/></div></div>
<references/></div></div>
[[Comma list]]: 55/54, 64/63, 91/90, 1573/1568
Comma list: 64/63, 91/90, 4394/4375
 
Gencom: [2 3/2; 64/63 91/90 4394/4375]


[[Mapping]]: [{{val|1 0 -20 6 21 -25}}, {{val|0 1 14 -2 -11 18}}]
Gencom mapping: [{{val| 1 1 -6 4 -7 }}, {{val| 0 1 14 -2 18 }}]


[[Val]]s: {{Val list| 5, 32, 37 }}
Vals: {{Val list| 5, 32, 37 }}


[[Badness]]: 0.049172
RMS error: 2.318 cents


[[Category:Scales]]
[[Category:Scales]]
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