Marvel temperaments: Difference between revisions
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→Wizard: +intro, CTE tunings, and error maps |
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== Wizard == | == Wizard == | ||
{{Main| Wizard }} | {{Main| Wizard }} | ||
: ''For the 5-limit version of this temperament, see [[ | : ''For the 5-limit version of this temperament, see [[Miscellaneous 5-limit temperaments #Wizard]].'' | ||
Wizard has a semi-octave period and is generated by an interval that is best treated as ~17/15. The semi-octave complement of this interval is ~5/4. Wizard can be described as 22 & 72. Its ploidacot is diploid alpha-hexacot, so six generator steps plus a semi-octave period gives the [[3/1|perfect twelfth]]. [[72edo]], [[94edo]], and especially [[166edo]] are good tunings for it. | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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{{Multival|legend=1| 12 -2 20 -31 -2 52 }} | {{Multival|legend=1| 12 -2 20 -31 -2 52 }} | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[CTE]]: ~1225/864 = 600.000, ~245/216 = 216.919 | |||
: [[error map]]: {{val| 0.000 -0.443 -3.232 +0.361 }} | |||
* [[POTE]]: ~1225/864 = 600.000, ~245/216 = 216.744 | |||
: error map: {{val| 0.000 -1.492 -3.057 -1.388 }} | |||
{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 382c }} | {{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c, 382c }} | ||
[[Badness]]: 0.040846 | [[Badness]] (Smith): 0.040846 | ||
=== 11-limit === | === 11-limit === | ||
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Mapping: {{mapping| 2 1 5 2 8 | 0 6 -1 10 -3 }} | Mapping: {{mapping| 2 1 5 2 8 | 0 6 -1 10 -3 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~99/70 = 600.000, ~25/22 = 216.900 | |||
* POTE: ~99/70 = 600.000, ~25/22 = 216.768 | |||
{{Optimal ET sequence|legend=0| 22, 50, 72, 166, 238c, 310c }} | |||
Badness (Smith): 0.018539 | |||
==== Lizard ==== | ==== Lizard ==== | ||
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Mapping: {{mapping| 2 1 5 2 8 11 | 0 6 -1 10 -3 -10 }} | Mapping: {{mapping| 2 1 5 2 8 11 | 0 6 -1 10 -3 -10 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~55/39 = 600.000, ~25/22 = 216.703 | |||
* POTE: ~55/39 = 600.000, ~25/22 = 216.711 | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 22, 50, 72, 122, 194df }} | ||
Badness: 0.021781 | Badness (Smith): 0.021781 | ||
===== 17-limit ===== | ===== 17-limit ===== | ||
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Mapping: {{mapping| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }} | Mapping: {{mapping| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~17/12 = 600.000, ~17/15 = 216.748 | |||
* POTE: ~17/12 = 600.000, ~17/15 = 216.619 | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 22, 50, 72, 122g, 194dfg }} | ||
Badness: 0.014536 | Badness (Smith): 0.014536 | ||
===== 19-limit ===== | ===== 19-limit ===== | ||
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Mapping: {{mapping| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }} | Mapping: {{mapping| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~17/12 = 600.000, ~17/15 = 216.677 | |||
* POTE: ~17/12 = 600.000, ~17/15 = 216.523 | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 22h, 50, 72, 122g, 194dfg }} | ||
Badness: 0.015702 | Badness (Smith): 0.015702 | ||
==== Gizzard ==== | ==== Gizzard ==== | ||
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Mapping: {{mapping| 2 1 5 2 8 -2 | 0 6 -1 10 -3 26 }} | Mapping: {{mapping| 2 1 5 2 8 -2 | 0 6 -1 10 -3 26 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~99/70 = 600.000, ~25/22 = 216.928 | |||
* POTE: ~99/70 = 600.000, ~25/22 = 216.830 | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 22f, 72, 166, 238cf }} | ||
Badness: 0.020252 | Badness (Smith): 0.020252 | ||
===== 17-limit ===== | ===== 17-limit ===== | ||
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Mapping: {{mapping| 2 1 5 2 8 -2 6 | 0 6 -1 10 -3 26 6 }} | Mapping: {{mapping| 2 1 5 2 8 -2 6 | 0 6 -1 10 -3 26 6 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~17/12 = 600.000, ~17/15 = 216.943 | |||
* POTE: ~17/12 = 600.000, ~17/15 = 216.825 | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 22f, 72, 166g, 238cfg }} | ||
Badness: 0.013624 | Badness (Smith): 0.013624 | ||
===== 19-limit ===== | ===== 19-limit ===== | ||
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Mapping: {{mapping| 2 1 5 2 8 -2 6 15 | 0 6 -1 10 -3 26 6 -18 }} | Mapping: {{mapping| 2 1 5 2 8 -2 6 15 | 0 6 -1 10 -3 26 6 -18 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~17/12 = 600.000, ~17/15 = 216.918 | |||
* POTE: ~17/12 = 600.000, ~17/15 = 216.862 | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 72, 94, 166g }} | ||
Badness: 0.014810 | Badness (Smith): 0.014810 | ||
=== Mage === | === Mage === | ||
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Mapping: {{mapping| 2 1 5 2 4 | 0 6 -1 10 8 }} | Mapping: {{mapping| 2 1 5 2 4 | 0 6 -1 10 8 }} | ||
Optimal | Optimal tunings: | ||
* CTE: ~77/54 = 600.000, ~55/48 = 217.247 | |||
* POTE: ~77/54 = 600.000, ~55/48 = 216.876 | |||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 22, 50e, 72ee }} | ||
Badness: 0.057799 | Badness (Smith): 0.057799 | ||
== Tritonic == | == Tritonic == |