Marvel temperaments: Difference between revisions

m Update linking
Wizard: +intro, CTE tunings, and error maps
Line 40: Line 40:
== Wizard ==
== Wizard ==
{{Main| Wizard }}
{{Main| Wizard }}
: ''For the 5-limit version of this temperament, see [[High badness temperaments #Wizard]].''
: ''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
Line 52: Line 54:
{{Multival|legend=1| 12 -2 20 -31 -2 52 }}
{{Multival|legend=1| 12 -2 20 -31 -2 52 }}


[[Optimal tuning]] ([[POTE]]): ~1225/864 = 1\2, ~5/4 = 383.256 (~245/216 = 216.744)
[[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
 
Scales: [[wizard22]]


=== 11-limit ===
=== 11-limit ===
Line 67: Line 71:
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 tuning (POTE): ~99/70 = 1\2, ~5/4 = 383.232 (~25/22 = 216.768)
Optimal tunings:
 
* CTE: ~99/70 = 600.000, ~25/22 = 216.900
{{Optimal ET sequence|legend=1| 22, 50, 72, 166, 238c, 310c }}
* POTE: ~99/70 = 600.000, ~25/22 = 216.768


Badness: 0.018539
{{Optimal ET sequence|legend=0| 22, 50, 72, 166, 238c, 310c }}


Scales: [[wizard22]]
Badness (Smith): 0.018539


==== Lizard ====
==== Lizard ====
Line 82: Line 86:
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 tuning (POTE): ~55/39 = 1\2, ~5/4 = 383.389 (~25/22 = 216.711)
Optimal tunings:
* CTE: ~55/39 = 600.000, ~25/22 = 216.703
* POTE: ~55/39 = 600.000, ~25/22 = 216.711


{{Optimal ET sequence|legend=1| 22, 50, 72, 122, 194df }}
{{Optimal ET sequence|legend=0| 22, 50, 72, 122, 194df }}


Badness: 0.021781
Badness (Smith): 0.021781


===== 17-limit =====
===== 17-limit =====
Line 95: Line 101:
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 tuning (POTE): ~17/12 = 1\2, ~5/4 = 383.381 (~17/15 = 216.619)
Optimal tunings:
* CTE: ~17/12 = 600.000, ~17/15 = 216.748
* POTE: ~17/12 = 600.000, ~17/15 = 216.619


{{Optimal ET sequence|legend=1| 22, 50, 72, 122g, 194dfg }}
{{Optimal ET sequence|legend=0| 22, 50, 72, 122g, 194dfg }}


Badness: 0.014536
Badness (Smith): 0.014536


===== 19-limit =====
===== 19-limit =====
Line 108: Line 116:
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 tuning (POTE): ~17/12 = 1\2, ~5/4 = 383.477 (~17/15 = 216.523)
Optimal tunings:
* CTE: ~17/12 = 600.000, ~17/15 = 216.677
* POTE: ~17/12 = 600.000, ~17/15 = 216.523


{{Optimal ET sequence|legend=1| 22h, 50, 72, 122g, 194dfg }}
{{Optimal ET sequence|legend=0| 22h, 50, 72, 122g, 194dfg }}


Badness: 0.015702
Badness (Smith): 0.015702


==== Gizzard ====
==== Gizzard ====
Line 121: Line 131:
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 tuning (POTE): ~99/70 = 1\2, ~5/4 = 383.170 (~25/22 = 216.830)
Optimal tunings:
* CTE: ~99/70 = 600.000, ~25/22 = 216.928
* POTE: ~99/70 = 600.000, ~25/22 = 216.830


{{Optimal ET sequence|legend=1| 72, 166, 238cf }}
{{Optimal ET sequence|legend=0| 22f, 72, 166, 238cf }}


Badness: 0.020252
Badness (Smith): 0.020252


===== 17-limit =====
===== 17-limit =====
Line 134: Line 146:
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 tuning (POTE): ~17/12 = 1\2, ~5/4 = 383.175 (~25/22 = 216.825)
Optimal tunings:
* CTE: ~17/12 = 600.000, ~17/15 = 216.943
* POTE: ~17/12 = 600.000, ~17/15 = 216.825


{{Optimal ET sequence|legend=1| 72, 166g, 238cfg }}
{{Optimal ET sequence|legend=0| 22f, 72, 166g, 238cfg }}


Badness: 0.013624
Badness (Smith): 0.013624


===== 19-limit =====
===== 19-limit =====
Line 147: Line 161:
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 tuning (POTE): ~17/12 = 1\2, ~5/4 = 383.138 (~17/15 = 216.862)
Optimal tunings:
* CTE: ~17/12 = 600.000, ~17/15 = 216.918
* POTE: ~17/12 = 600.000, ~17/15 = 216.862


{{Optimal ET sequence|legend=1| 72, 94, 166g }}
{{Optimal ET sequence|legend=0| 72, 94, 166g }}


Badness: 0.014810
Badness (Smith): 0.014810


=== Mage ===
=== Mage ===
Line 160: Line 176:
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 tuning (POTE): ~77/54 = 1\2, ~5/4 = 383.124 (~55/48 = 216.876)
Optimal tunings:
* CTE: ~77/54 = 600.000, ~55/48 = 217.247
* POTE: ~77/54 = 600.000, ~55/48 = 216.876


{{Optimal ET sequence|legend=1| 22, 50e, 72ee, 94ee }}
{{Optimal ET sequence|legend=0| 22, 50e, 72ee }}


Badness: 0.057799
Badness (Smith): 0.057799


== Tritonic ==
== Tritonic ==