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[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[Diamond monotone]] range: [685.714, 720.000] (4\7 to 3\5)
* 5-odd-limit [[diamond monotone]]: ~3/2 = [685.714, 720.000] (4\7 to 3\5)
* [[Diamond tradeoff]] range: [694.786, 701.955]
* 5-odd-limit [[diamond tradeoff]]: ~3/2 = [694.786, 701.955]
* Diamond monotone and tradeoff: [694.786, 701.955]
* 5-odd-limit diamond monotone and tradeoff: ~3/2 = [694.786, 701.955]


{{Vals|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b, 212bb, 293bb }}
{{Vals|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b, 212bb, 293bb }}
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[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[Diamond monotone]] range: [692.308, 694.737] (15\26 to 11\19)
* 7- and 9-odd-limit [[diamond monotone]]: ~3/2 = [692.308, 694.737] (15\26 to 11\19)
* 7-odd-limit [[diamond tradeoff]]: [692.353, 701.955]
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [692.353, 701.955]
* 9-odd-limit diamond tradeoff: [691.202, 701.955]
* 9-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955]
* 7-odd-limit diamond monotone and tradeoff: [692.353, 694.737]
* 7-odd-limit diamond monotone and tradeoff: ~3/2 = [692.353, 694.737]
* 9-odd-limit diamond monotone and tradeoff: [692.308, 694.737]
* 9-odd-limit diamond monotone and tradeoff: ~3/2 = [692.308, 694.737]


Algebraic generator: Squarto, the positive root of 8''x''<sup>2</sup> - 4''x'' - 9, at 506.3239 cents, equal to (1 + sqrt (19))/4.
Algebraic generator: Squarto, the positive root of 8''x''<sup>2</sup> - 4''x'' - 9, at 506.3239 cents, equal to (1 + sqrt (19))/4.
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[[Tuning ranges]]:  
[[Tuning ranges]]:  
* [[Diamond monotone]] range: [694.737, 700.000] (11\19 to 7\12)
* 7- and 9-odd-limit [[diamond monotone]]: ~3/2 = [694.737, 700.000] (11\19 to 7\12)
* 7-odd-limit [[diamond tradeoff]]: [694.786, 701.955]
* 7-odd-limit [[diamond tradeoff]]: ~3/2 = [694.786, 701.955]
* 9-odd-limit diamond tradeoff: [691.202, 701.955]
* 9-odd-limit diamond tradeoff: ~3/2 = [691.202, 701.955]
* 7-odd-limit diamond monotone and tradeoff: [694.786, 700.000]
* 7-odd-limit diamond monotone and tradeoff: ~3/2 = [694.786, 700.000]
* 9-odd-limit diamond monotone and tradeoff: [694.737, 700.000]
* 9-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 700.000]


Algebraic generator: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, which comes to 503.4257 cents. The recurrence converges quickly.
Algebraic generator: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, which comes to 503.4257 cents. The recurrence converges quickly.
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Tuning ranges:  
Tuning ranges:  
* [[Diamond monotone]] range: [694.737, 696.774] (11\19 to 18\31)
* 11-odd-limit [[diamond monotone]]: ~3/2 = [694.737, 696.774] (11\19 to 18\31)
* [[Diamond tradeoff]] range: [691.202, 701.955]
* 11-odd-limit [[diamond tradeoff]]: ~3/2 = [691.202, 701.955]
* Diamond monotone and tradeoff: [694.737, 696.774]
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 696.774]


Algebraic generator: Cybozem; or else Radieubiz, the real root of 3''x''<sup>3</sup> + 6''x'' - 19. Unlike Cybozem, the recurrence for Radieubiz does not converge.
Algebraic generator: Cybozem; or else Radieubiz, the real root of 3''x''<sup>3</sup> + 6''x'' - 19. Unlike Cybozem, the recurrence for Radieubiz does not converge.
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Tuning ranges:  
Tuning ranges:  
* [[Diamond monotone]] range: [696.774, 700.000] (18\31 to 7\12)
* 11-odd-limit [[diamond monotone]]: ~3/2 = [696.774, 700.000] (18\31 to 7\12)
* [[Diamond tradeoff]] range: [691.202, 701.955]
* 11-odd-limit [[diamond tradeoff]]: ~3/2 = [691.202, 701.955]
* Diamond monotone and tradeoff: [696.774, 700.000]
* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [696.774, 700.000]


[[Algebraic generator]]: Traverse, the positive real root of ''x''<sup>4</sup> + 2''x'' - 13, or 696.9529 cents.
[[Algebraic generator]]: Traverse, the positive real root of ''x''<sup>4</sup> + 2''x'' - 13, or 696.9529 cents.
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[[Wedgie]]: {{wedgie|1 9 -2 12 -6 -30}}
[[Wedgie]]: {{wedgie|1 9 -2 12 -6 -30}}


Vals: {{Val list| 5, 17, 22, 27, 49 }}
[[Val]]s: {{Val list| 5, 17, 22, 27, 49 }}


Badness: 0.032318
[[Badness]]: 0.032318
 
=== Ultrapyth ===
Subgroup: 2.3.5.7.11.13
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~3/2 = 713.500
 
EDO generators: [[32edo|23\32]], [[37edo|28\37]]
 
<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 class="mw-collapsible-content">
{| class="wikitable right-1 right-2 sortable"
|+
|-
! #Gens up
! Cents <ref>octave-reduced</ref>
! class="unsortable"| Approximate ratios<ref>2.3.5.7.11.13, odd limit ≤ 15</ref>
|-
| 0
| 0.00
| 1/1
|-
| 1
| 713.5
| 3/2
|-
| 2
| 227.0
| 9/8, 8/7
|-
| 3
| 940.5
| 12/7, 26/15
|-
| 4
| 454.0
| 9/7, 13/10
|-
| 5
| 1167.5
|
|-
| 6
| 681.0
|
|-
| 7
| 194.5
|
|-
| 8
| 908.0
|
|-
| 9
| 421.5
| 14/11
|-
| 10
| 1135.0
|
|-
| 11
| 648.5
| 16/11
|-
| 12
| 162.0
| 12/11, 10/9
|-
| 13
| 875.5
| 18/11, 5/3
|-
| 14
| 389.0
| 5/4
|-
| 15
| 1102.5
| 15/8
|-
| 16
| 616.0
| 10/7, 13/9
|-
| 17
| 129.5
| 15/14, 13/12
|-
| 18
| 843.0
| 13/8
|-
| 19
| 356.5
|
|-
| 20
| 1070.0
| 13/7
|-
| 21
| 583.5
|
|-
| 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>
[[Comma list]]: 55/54, 64/63, 91/90, 1573/1568
 
[[Mapping]]: [{{val|1 0 -20 6 21 -25}}, {{val|0 1 14 -2 -11 18}}]
 
[[Val]]s: {{Val list| 5, 32, 37 }}
 
[[Badness]]: 0.049172


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