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| Temperaments discussed elsewhere include: | | Temperaments discussed elsewhere include: |
| * ''[[Beatles]]'' (+64/63) → [[Archytas clan #Beatles|Archytas clan]] | | * ''[[Beatles]]'' (+64/63) → [[Archytas clan #Beatles|Archytas clan]] |
| | * ''[[Newt]]'' (+33554432/33480783) → [[Garischismic clan #Beatles|Garischismic clan]] |
| * [[Decimal]] (+25/24, 49/48 or 50/49) → [[Dicot family #Decimal|Dicot family]] | | * [[Decimal]] (+25/24, 49/48 or 50/49) → [[Dicot family #Decimal|Dicot family]] |
| * [[Squares]] (+81/80) → [[Meantone family #Squares|Meantone family]] | | * [[Squares]] (+81/80) → [[Meantone family #Squares|Meantone family]] |
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| * ''[[Greenwood]]'' (+405/392 or 1323/1280) → [[Whitewood family #Greenwood|Whitewood family]] | | * ''[[Greenwood]]'' (+405/392 or 1323/1280) → [[Whitewood family #Greenwood|Whitewood family]] |
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| Considered below are tertiaseptal, emmthird, hemififths, osiris, quasiorwell, quinmite, newt, septidiasemi, subneutral, maviloid, lockerbie, unthirds, neominor, catafourth, cotritone, fibo, quasimoha, mintone, gorgik, hemigoldis, and surmarvelpyth, in the order of increasing [[badness]]. | | Considered below are tertiaseptal, emmthird, hemififths, osiris, quasiorwell, quinmite, septidiasemi, subneutral, maviloid, lockerbie, unthirds, neominor, catafourth, cotritone, fibo, quasimoha, mintone, gorgik, hemigoldis, and surmarvelpyth, in the order of increasing [[badness]]. |
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| == Tertiaseptal == | | == Tertiaseptal == |
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| [[Badness]] (Sintel): 0.945 | | [[Badness]] (Sintel): 0.945 |
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| == Newt ==
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| Newt tempers out the [[garischisma]] and can be described as the {{nowrap| 41 & 270 }} temperament. It has a generator of a neutral third (0.2 cents flat of [[49/40]]) with a [[ploidacot]] signature of dicot. 41 generator steps fall short of 12 octaves by a [[schisma]]~[[aberschisma]]. From there the intervals of 5 and 7 can be derived.
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| Newt continues to be significant as an [[11-limit]] temperament. The commas it tempers out include the [[lehmerisma]] (3025/3024), the [[symbiotic comma]] (19712/19683), the [[argyria]] (41503/41472), and the [[olympia]] (131072/130977). This extends into a strong [[13-limit]] temperament and eventually a strong no-17 [[19-limit]] temperament, a.k.a. '''neonewt'''. [[270edo]] and [[311edo]] are obvious tuning choices, but [[581edo]] and especially [[851edo]] work even better.
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 2401/2400, 33554432/33480783
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| {{Mapping|legend=1| 1 1 19 11 | 0 2 -57 -28 }}
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| : mapping generators: ~2, ~49/40
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| [[Optimal tuning]]s:
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| * [[WE]]: ~2 = 1199.9315{{c}}, ~49/40 = 351.0932{{c}}
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| : [[error map]]: {{val| -0.068 +0.163 +0.075 -0.188 }}
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| * [[CWE]]: ~2 = 1200.0000{{c}}, ~49/40 = 351.1141{{c}}
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| : error map: {{val| 0.000 +0.273 +0.180 -0.022 }}
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| {{Optimal ET sequence|legend=1| 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 2201 }}
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| [[Badness]] (Sintel): 1.06
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 2401/2400, 3025/3024, 19712/19683
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| Mapping: {{mapping| 1 1 19 11 -10 | 0 2 -57 -28 46 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9603{{c}}, ~49/40 = 351.1038{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1155{{c}}
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| {{Optimal ET sequence|legend=0| 41, 188, 229, 270, 581, 851, 1121, 1972 }}
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| Badness (Sintel): 0.643
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 2080/2079, 2401/2400, 3025/3024, 4096/4095
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| Mapping: {{mapping| 1 1 19 11 -10 -20 | 0 2 -57 -28 46 81 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9747{{c}}, ~49/40 = 351.1094{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1168{{c}}
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| {{Optimal ET sequence|legend=0| 41, 229, 270, 581, 851, 2283b }}
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| Badness (Sintel): 0.571
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| === 2.3.5.7.11.13.19 subgroup (neonewt) ===
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| Subgroup: 2.3.5.7.11.13.19
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| Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2401/2400
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| Mapping: {{mapping| 1 1 19 11 -10 -20 18 | 0 2 -57 -28 46 81 -47 }}
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| Optimal tunings:
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| * WE: ~2 = 1199.9782{{c}}, ~49/40 = 351.1102{{c}}
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| * CWE: ~2 = 1200.0000{{c}}, ~49/40 = 351.1166{{c}}
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| {{Optimal ET sequence|legend=0| 41, 229, 270, 581, 851 }}
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| Badness (Sintel): 0.438
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| == Septidiasemi == | | == Septidiasemi == |