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Ragismic microtemperaments: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings (6/). Move 5-limit quasithird away
Switch to Sintel's badness, WE & CWE tunings (7/)
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{{Mapping|legend=1| 4 0 -11 48 | 0 5 16 -29 }}
{{Mapping|legend=1| 4 0 -11 48 | 0 5 16 -29 }}
: mapping generators: ~65536/55125, ~5103/4096


[[Optimal tuning]] ([[POTE]]): ~65536/55125 = 300.000{{c}}, ~5103/4096 = 380.388 {{c}}
[[Optimal tuning]]s:
* [[WE]]: ~65536/55125 = 300.0052{{c}}, ~5103/4096 = 380.3949{{c}}
: [[error map]]: {{val| +0.021 +0.020 -0.052 -0.031 }}
* [[CWE]]: ~65536/55125 = 300.0000{{c}}, ~5103/4096 = 380.3884{{c}}
: error map: {{val| 0.000 -0.013 -0.100 -0.089 }}


{{Optimal ET sequence|legend=1| 60d, 164, 224, 388, 612, 1448, 2060 }}
{{Optimal ET sequence|legend=1| 60d, 164, 224, 388, 612, 1448, 2060 }}


[[Badness]] (Sintel): 1.564
[[Badness]] (Sintel): 1.56


=== 11-limit ===
=== 11-limit ===
Line 767: Line 772:
Mapping: {{mapping| 4 0 -11 48 43 | 0 5 16 -29 -23 }}
Mapping: {{mapping| 4 0 -11 48 43 | 0 5 16 -29 -23 }}


Optimal tuning (POTE): ~65536/51125 = 300.000{{c}}, ~5103/4096 = 380.387{{c}} (or ~22/21 = 80.387{{c}})
Optimal tunings:
* WE: ~65536/51125 = 300.0073{{c}}, ~5103/4096 = 380.3963{{c}} (or ~22/21 = 80.3890{{c}})
* CWE: ~65536/51125 = 300.0000{{c}}, ~5103/4096 = 380.3868{{c}} (or ~22/21 = 80.3868{{c}})


{{Optimal ET sequence|legend=0| 60d, 164, 224, 388, 612, 836, 1448 }}
{{Optimal ET sequence|legend=0| 60d, 164, 224, 388, 612, 836, 1448, 6404cee, 7852cee }}


Badness (Sintel): 0.698
Badness (Sintel): 0.698
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Mapping: {{mapping| 4 0 -11 48 43 11 | 0 5 16 -29 -23 3 }}
Mapping: {{mapping| 4 0 -11 48 43 11 | 0 5 16 -29 -23 3 }}


Optimal tuning (POTE): ~65536/51125 = 300.000{{c}}, ~81/65 = 380.385{{c}} (or ~22/21 = 80.385{{c}})
Optimal tunings:
* WE: ~65536/51125 = 299.9985{{c}}, ~81/65 = 380.3833{{c}} (or ~22/21 = 80.3848{{c}})
* CWE: ~65536/51125 = 300.0000{{c}}, ~81/65 = 380.3852{{c}} (or ~22/21 = 80.3852{{c}})


{{Optimal ET sequence|legend=0| 60d, 164, 224, 388, 612, 836, 1448f, 2284f }}
{{Optimal ET sequence|legend=0| 60d, 164, 224, 388, 612, 836 }}


Badness (Sintel): 1.219
Badness (Sintel): 1.22


== Deca ==
== Deca ==
: ''For 5-limit version, see [[10th-octave temperaments #Neon]].''
: ''For 5-limit version, see [[10th-octave temperaments #Neon]].''


Deca temperament has a period of 1/10 octave and tempers out the [[linus comma]], {{monzo| 11 -10 -10 10 }}, neon comma {{monzo| 21 60 -50 }} and {{monzo| 12 -3 -14 9 }} = 165288374272/164794921875 (satritrizo-asepbigu).
Deca temperament has a period of 1/10 octave and tempers out the [[linus comma]], {{monzo| 11 -10 -10 10 }}, neon comma {{monzo| 21 60 -50 }} and {{monzo| 12 -3 -14 9 }} (165288374272/164794921875).


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
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{{Mapping|legend=1| 10 4 9 2 | 0 5 6 11 }}
{{Mapping|legend=1| 10 4 9 2 | 0 5 6 11 }}
: mapping generators: ~15/14, ~6/5
: mapping generators: ~15/14, ~460992/390625


[[Optimal tuning]] ([[POTE]]): ~15/14 = 120.000{{c}}, ~6/5 = 315.577{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~15/14 = 119.9966{{c}}, ~460992/390625 = 284.4150{{c}} (5625/5488 = 44.4219{{c}})
: [[error map]]: {{val| -0.034 +0.106 +0.145 -0.268 }}
* [[CWE]]: ~15/14 = 120.0000{{c}}, ~460992/390625 = 284.4182{{c}} (5625/5488 = 44.4182{{c}})
: error map: {{val| 0.000 +0.136 +0.195 -0.226 }}


{{Optimal ET sequence|legend=1| 80, 190, 270, 1270, 1540, 1810, 2080 }}
{{Optimal ET sequence|legend=1| 80, 190, 270, 1270, 1540, 1810, 2080 }}


[[Badness]] (Sintel): 2.041
[[Badness]] (Sintel): 2.04


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 10 4 9 2 18 | 0 5 6 11 7 }}
Mapping: {{mapping| 10 4 9 2 18 | 0 5 6 11 7 }}


Optimal tuning (POTE): ~15/14 = 120.000{{c}}, ~6/5 = 315.582{{c}}
Optimal tunings:
* WE: ~15/14 = 120.0004{{c}}, ~33/28 = 284.4193{{c}} (77/75 = 44.4185{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~33/28 = 284.4189{{c}} (77/75 = 44.4189{{c}})


{{Optimal ET sequence|legend=0| 80, 190, 270, 1000, 1270, 1540e, 1810e }}
{{Optimal ET sequence|legend=0| 80, 190, 270, 1000, 1270, 1540e, 1810e }}
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Mapping: {{mapping| 10 4 9 2 18 37 | 0 5 6 11 7 0 }}
Mapping: {{mapping| 10 4 9 2 18 37 | 0 5 6 11 7 0 }}


Optimal tuning (POTE): ~15/14 = 120.000{{c}}, ~6/5 = 315.602{{c}} (~40/39 = 44.398{{c}})
Optimal tunings:
* WE: ~15/14 = 120.0067{{c}}, ~33/28 = 284.4139{{c}} (~40/39 = 44.4006{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~33/28 = 284.4048{{c}} (~40/39 = 44.4048{{c}})


{{Optimal ET sequence|legend=0| 80, 190, 270, 730, 1000 }}
{{Optimal ET sequence|legend=0| 80, 190, 270, 730, 1000 }}
Line 833: Line 850:
Subgroup: 2.3.5.7.11.13.19
Subgroup: 2.3.5.7.11.13.19


Comma list: 1001/1000, 3025/3024, 4225/4224, 4375/4374, 1521/1520
Comma list: 1001/1000, 1521/1520, 3025/3024, 4225/4224, 4375/4374


Mapping: {{mapping| 10 4 9 2 18 37 33 | 0 5 6 11 7 0 4 }}
Mapping: {{mapping| 10 4 9 2 18 37 33 | 0 5 6 11 7 0 4 }}


Optimal tuning (CTE): ~15/14 = 120.000{{c}}, ~6/5 = 315.581{{c}} (~39/38 = 44.419{{c}})
Optimal tunings:
* WE: ~15/14 = 120.0045{{c}}, ~33/28 = 284.4140{{c}} (~39/38 = 44.4050{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~33/28 = 284.4075{{c}} (~39/38 = 44.4075{{c}})


{{Optimal ET sequence|legend=0| 80, 190, 270, 730, 1000 }}
{{Optimal ET sequence|legend=0| 80, 190, 270, 730, 1000 }}
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