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Quince clan: Difference between revisions

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Lériendil (talk | contribs)
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added countermiracle, which is the alternative mapping of 3 for quince on the other side of 31edo
Sorting, units & misc. cleanup
Line 21: Line 21:
{{Mapping|legend=3| 1 0 3 3 | 0 0 -7 -2 }}
{{Mapping|legend=3| 1 0 3 3 | 0 0 -7 -2 }}


: gencom: [2 343/320; 823543/819200]
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~343/320 = 116.291{{c}}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/320 = 116.291


{{Optimal ET sequence|legend=1| 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd }}
{{Optimal ET sequence|legend=1| 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd }}


==== 2.5.7.13 subgroup ====
== Countermiracle ==
Subgroup: 2.5.7.13
The ''countermiracle'' temperament ({{nowrap| 31 & 145 }}) tempers out the trimyna, 50421/50000 and the [[quince comma]], 823543/819200.
 
Comma list: 343/338, 640/637
 
Sval mapping: {{mapping| 1 3 3 4 | 0 -7 -2 -3 }}
 
Gencom mapping: {{mapping| 1 0 3 3 0 4 | 0 0 -7 -2 0 -3 }}
 
: gencom: [2 14/13; 343/338 640/637]
 
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 116.094
 
{{Optimal ET sequence|legend=1| 10, 21, 31}}
 
==== 2.5.7.13.17 subgroup ====
Subgroup: 2.5.7.13.17
 
Comma list: 170/169, 224/221, 640/637
 
Sval mapping: {{mapping| 1 3 3 4 4 | 0 -7 -2 -3 1 }}
 
Gencom mapping: {{mapping| 1 0 3 3 0 4 4 | 0 0 -7 -2 0 -3 1 }}
 
: gencom: [2 14/13; 170/169 224/221 640/637]
 
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 115.769
 
{{Optimal ET sequence|legend=1| 10, 21, 31 }}
 
==== 2.5.7.13.17.19 subgroup ====
Subgroup: 2.5.7.13.17.19
 
Comma list: 170/169, 343/338, 640/637, 16384/16055
 
Sval mapping: {{mapping| 1 3 3 4 4 3 | 0 -7 -2 -3 1 13 }}
 
Gencom mapping: {{mapping| 1 0 3 3 0 4 4 3 | 0 0 -7 -2 0 -3 1 13 }}
 
: gencom: [2 14/13; 170/169 343/338 640/637 16384/16055]
 
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 115.716
 
{{Optimal ET sequence|legend=1| 10, 21, 31, 52f }}


== Countermiracle ==
{{Todo|inline=1|expand|comment=Explain relationship to miracle. There's clearly ''some'' relationship, since the extensions are named the same way, but the nature of that relationship isn't obvious from looking at this page.}}
The ''countermiracle'' temperament (31 & 145) tempers out the trimyna, 50421/50000 and the [[quince comma]], 823543/819200.
{{todo|inline=1|explain relationship to miracle|comment=There's clearly ''some'' relationship, since the extensions are named the same way, but the nature of that relationship isn't obvious from looking at this page.}}


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 81: Line 35:


{{Mapping|legend=1| 1 4 3 3 | 0 -25 -7 -2 }}
{{Mapping|legend=1| 1 4 3 3 | 0 -25 -7 -2 }}
: mapping generators: ~2, ~343/320


: Mapping generators: ~2, ~343/320
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~343/320 = 115.9169{{c}}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/320 = 115.9169


{{Optimal ET sequence|legend=1| 31, 114, 145, 176, 559cc, 735cc }}
{{Optimal ET sequence|legend=1| 31, 114, 145, 176, 559cc, 735cc }}


[[Badness]]: 0.102326
[[Badness]] (Smith): 0.102326


=== 11-limit ===
=== 11-limit ===
Line 97: Line 50:
Mapping: {{mapping| 1 4 3 3 8 | 0 -25 -7 -2 -47 }}
Mapping: {{mapping| 1 4 3 3 8 | 0 -25 -7 -2 -47 }}


Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.9158
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~77/72 = 115.9158{{c}}


{{Optimal ET sequence|legend=1| 31, 114e, 145, 176 }}
{{Optimal ET sequence|legend=0| 31, 114e, 145, 176 }}


Badness: 0.039162
Badness (Smith): 0.039162


==== Countermiraculous ====
==== Countermiraculous ====
Line 110: Line 63:
Mapping: {{mapping| 1 4 3 3 8 1 | 0 -25 -7 -2 -47 28 }}
Mapping: {{mapping| 1 4 3 3 8 1 | 0 -25 -7 -2 -47 28 }}


Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8803
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~77/72 = 115.8803{{c}}


{{Optimal ET sequence|legend=1| 31, 83e, 114e, 145, 321ceff }}
{{Optimal ET sequence|legend=0| 31, 83e, 114e, 145, 321ceff }}


Badness: 0.039271
Badness (Smith): 0.039271


===== 17-limit =====
===== 17-limit =====
Line 123: Line 76:
Mapping: {{mapping| 1 4 3 3 8 1 1 | 0 -25 -7 -2 -47 28 32 }}
Mapping: {{mapping| 1 4 3 3 8 1 1 | 0 -25 -7 -2 -47 28 32 }}


Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8756
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~77/72 = 115.8756{{c}}


{{Optimal ET sequence|legend=1| 31, 83e, 114e, 145 }}
{{Optimal ET sequence|legend=0| 31, 83e, 114e, 145 }}


Badness: 0.029496
Badness (Smith): 0.029496


==== Counterbenediction ====
==== Counterbenediction ====
Line 136: Line 89:
Mapping: {{mapping| 1 4 3 3 8 -2 | 0 -25 -7 -2 -47 59 }}
Mapping: {{mapping| 1 4 3 3 8 -2 | 0 -25 -7 -2 -47 59 }}


Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.9335
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~77/72 = 115.9335{{c}}


{{Optimal ET sequence|legend=1| 31, 114ef, 145f, 176, 207, 383c, 590cc }}
{{Optimal ET sequence|legend=0| 31, 114ef, 145f, 176, 207, 383c, 590cc }}


Badness: 0.045569
Badness (Smith): 0.045569


===== 17-limit =====
===== 17-limit =====
Line 149: Line 102:
Mapping: {{mapping| 1 4 3 3 8 -2 -2 | 0 -25 -7 -2 -47 59 63 }}
Mapping: {{mapping| 1 4 3 3 8 -2 -2 | 0 -25 -7 -2 -47 59 63 }}


Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.9391
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~77/72 = 115.9391{{c}}


{{Optimal ET sequence|legend=1| 31, 114efg, 145fg, 176, 207 }}
{{Optimal ET sequence|legend=0| 31, 114efg, 145fg, 176, 207 }}


Badness: 0.036289
Badness (Smith): 0.036289


==== Countermanna ====
==== Countermanna ====
Line 162: Line 115:
Mapping: {{mapping| 1 4 3 3 8 15 | 0 -25 -7 -2 -47 -117 }}
Mapping: {{mapping| 1 4 3 3 8 15 | 0 -25 -7 -2 -47 -117 }}


Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8898
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~77/72 = 115.8898{{c}}


{{Optimal ET sequence|legend=1| 145, 176, 321ce }}
{{Optimal ET sequence|legend=0| 145, 176, 321ce }}


Badness: 0.053409
Badness (Smith): 0.053409


===== 17-limit =====
===== 17-limit =====
Line 175: Line 128:
Mapping: {{mapping| 1 4 3 3 8 15 15 | 0 -25 -7 -2 -47 -117 -113 }}
Mapping: {{mapping| 1 4 3 3 8 15 15 | 0 -25 -7 -2 -47 -117 -113 }}


Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8832
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~77/72 = 115.8832{{c}}


{{Optimal ET sequence|legend=1| 145, 321ce }}
{{Optimal ET sequence|legend=0| 145, 321ce }}


Badness: 0.040898
Badness (Smith): 0.040898


=== Counterrevelation ===
=== Counterrevelation ===
Line 188: Line 141:
Mapping: {{mapping| 1 4 3 3 5 | 0 -25 -7 -2 -16 }}
Mapping: {{mapping| 1 4 3 3 5 | 0 -25 -7 -2 -16 }}


Optimal tuning (POTE): ~2 = 1\1, ~343/320 = 115.9192
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~343/320 = 115.9192{{c}}


{{Optimal ET sequence|legend=1| 31, 114, 145e, 176e }}
{{Optimal ET sequence|legend=0| 31, 114, 145e, 176e }}


Badness: 0.064070
Badness (Smith): 0.064070


==== 13-limit ====
==== 13-limit ====
Line 201: Line 154:
Mapping: {{mapping| 1 4 3 3 5 1 | 0 -25 -7 -2 -16 28 }}
Mapping: {{mapping| 1 4 3 3 5 1 | 0 -25 -7 -2 -16 28 }}


Optimal tuning (POTE): ~2 = 1\1, ~273/256 = 115.8624
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~273/256 = 115.8624{{c}}


{{Optimal ET sequence|legend=1| 31, 83, 114, 145e }}
{{Optimal ET sequence|legend=0| 31, 83, 114, 145e }}


Badness: 0.057497
Badness (Smith): 0.057497


==== 17-limit ====
==== 17-limit ====
Line 214: Line 167:
Mapping: {{mapping| 1 4 3 3 5 1 1 | 0 -25 -7 -2 -16 28 32 }}
Mapping: {{mapping| 1 4 3 3 5 1 1 | 0 -25 -7 -2 -16 28 32 }}


Optimal tuning (POTE): ~2 = 1\1, ~91/85 = 115.8527
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~91/85 = 115.8527{{c}}
 
{{Optimal ET sequence|legend=0| 31, 83, 114, 145e }}
 
Badness (Smith): 0.044043
 
== Subgroup extensions ==
=== Mercy (2.5.7.13) ===
Subgroup: 2.5.7.13
 
Comma list: 343/338, 640/637
 
Subgroup-val mapping: {{mapping| 1 3 3 4 | 0 -7 -2 -3 }}
 
Gencom mapping: {{mapping| 1 0 3 3 0 4 | 0 0 -7 -2 0 -3 }}
 
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~14/13 = 116.094{{c}}
 
{{Optimal ET sequence|legend=0| 10, 21, 31}}
 
==== 2.5.7.13.17 subgroup ====
Subgroup: 2.5.7.13.17
 
Comma list: 170/169, 224/221, 640/637
 
Subgroup-val mapping: {{mapping| 1 3 3 4 4 | 0 -7 -2 -3 1 }}
 
Gencom mapping: {{mapping| 1 0 3 3 0 4 4 | 0 0 -7 -2 0 -3 1 }}
 
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~14/13 = 115.769{{c}}
 
{{Optimal ET sequence|legend=0| 10, 21, 31 }}
 
==== 2.5.7.13.17.19 subgroup ====
Subgroup: 2.5.7.13.17.19
 
Comma list: 170/169, 343/338, 640/637, 16384/16055
 
Subgroup-val mapping: {{mapping| 1 3 3 4 4 3 | 0 -7 -2 -3 1 13 }}
 
Gencom mapping: {{mapping| 1 0 3 3 0 4 4 3 | 0 0 -7 -2 0 -3 1 13 }}


{{Optimal ET sequence|legend=1| 31, 83, 114, 145e }}
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~14/13 = 115.716{{c}}


Badness: 0.044043
{{Optimal ET sequence|legend=0| 10, 21, 31, 52f }}


[[Category:Temperament clans]]
[[Category:Temperament clans]]
Retrieved from "https://en.xen.wiki/w/Quince_clan"