Xenharmonic Wiki

Gamelismic clan: Difference between revisions

← Older editNewer edit →
VisualWikitext
Switch to Sintel's badness, WE & CWE tunings, per community consensus (6/)
Switch to Sintel's badness, WE & CWE tunings, per community consensus (7/7)
Line 1,947: Line 1,947:


Badness (Sintel): 0.595
Badness (Sintel): 0.595
== Lagaca ==
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 1029/1024, 11529602/11390625
{{Mapping|legend=1| 2 -4 15 8 | 0 9 -13 -3 }}
: mapping generators: ~3375/2401, ~450/343
[[Optimal tuning]]s:
* [[WE]]: ~3375/2401 = 600.1355{{c}}, ~450/343 = 478.0813{{c}}
: [[error map]]: {{val| +0.271 +0.235 +0.662 -1.986 }}
* [[CWE]]: ~3375/2401 = 600.000{{c}}, ~450/343 = 477.9725{{c}}
: error map: {{val| 0.000 -0.202 +0.043 -2.743 }}
<!-- * [[CTE]]: ~3375/2401 = 600.000{{c}}, ~450/343 = 477.969{{c}}
: [[error map]]: {{val| 0.000 -0.232 +0.087 -2.734 }}
* [[POTE]]: ~3375/2401 = 600.000{{c}}, ~450/343 = 477.973{{c}}
: error map: {{val| 0.000 -0.195 +0.033 -2.746 }} -->
{{Optimal ET sequence|legend=1| 10, 98, 108, 118 }}
[[Badness]] (Sintel): 3.65


== Necromanteion ==
== Necromanteion ==
Line 1,975: Line 1,953:
[[Comma list]]: 1029/1024, 5103/5000
[[Comma list]]: 1029/1024, 5103/5000


{{Mapping|legend=1| 1 7 10 1 | 0 -12 -17 4 }}
{{Mapping|legend=1| 1 -5 -7 5 | 0 12 17 -4 }}
: mapping generators: ~2, ~48/35
: mapping generators: ~2, ~35/24


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~48/35 = 541.743{{c}}
* [[WE]]: ~2 = 1200.2959{{c}}, ~35/24 = 658.3833{{c}}
: [[error map]]: {{val| +0.296 -2.835 +4.130 -0.879 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~35/24 = 658.2313{{c}}
: error map: {{val| 0.000 -3.179 +3.619 -1.751 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~35/24 = 658.257{{c}}
: [[error map]]: {{val| 0.000 -2.872 +4.053 -1.853 }}
: [[error map]]: {{val| 0.000 -2.872 +4.053 -1.853 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~48/35 = 541.779{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~35/24 = 658.221{{c}}
: error map: {{val| 0.000 -3.304 +3.442 -1.710 }}
: error map: {{val| 0.000 -3.304 +3.442 -1.710 }} -->


{{Optimal ET sequence|legend=1| 11c, 20c, 31, 144c, 175c }}
{{Optimal ET sequence|legend=1| 11c, 20c, 31, 144c, 175c }}


[[Badness]] (Smith): 0.117680
[[Badness]] (Sintel): 2.98


=== 11-limit ===
=== 11-limit ===
Line 1,993: Line 1,975:
Comma list: 176/175, 243/242, 1029/1024
Comma list: 176/175, 243/242, 1029/1024


Mapping: {{mapping| 1 7 10 1 17 | 0 -12 -17 4 -30 }}
Mapping: {{mapping| 1 -5 -7 5 -13 | 0 12 17 -4 30 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~15/11 = 541.695{{c}}
* WE: ~2 = 1200.2862{{c}}, ~22/15 = 658.4276{{c}}
* POTE: ~2 = 1200.000{{c}}, ~15/11 = 541.729{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 658.2805{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~22/15 = 658.305{{c}}
* POTE: ~2 = 1200.000{{c}}, ~22/15 = 658.271{{c}} -->


{{Optimal ET sequence|legend=0| 20ce, 31, 113c, 144c }}
{{Optimal ET sequence|legend=0| 20ce, 31, 113c, 144c }}


Badness (Smith): 0.053459
Badness (Sintel): 1.77


=== 13-limit ===
=== 13-limit ===
Line 2,008: Line 1,992:
Comma list: 144/143, 176/175, 243/242, 343/338
Comma list: 144/143, 176/175, 243/242, 343/338


Mapping: {{mapping| 1 7 10 1 17 1 | 0 -12 -17 4 -30 6 }}
Mapping: {{mapping| 1 -5 -7 5 -13 7 | 0 12 17 -4 30 -6 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~15/11 = 541.673{{c}}
* WE: ~2 = 1199.3663{{c}}, ~22/15 = 658.0465{{c}}
* POTE: ~2 = 1200.000{{c}}, ~15/11 = 541.606{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/15 = 658.3800{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~22/15 = 541.673{{c}}
* POTE: ~2 = 1200.000{{c}}, ~22/15 = 541.606{{c}} -->


{{Optimal ET sequence|legend=0| 20ce, 31, 82cf, 113cf }}
{{Optimal ET sequence|legend=0| 20ce, 31, 82cf, 113cf }}


Badness (Smith): 0.047015
Badness (Sintel): 1.94


== Restles ==
== Restles ==
Line 2,029: Line 2,015:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~315/256 = 358.548{{c}}
* [[WE]]: ~2 = 1200.0322{{c}}, ~315/256 = 358.5581{{c}}
: [[error map]]: {{val| +0.032 +0.678 +1.340 -2.930 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~315/256 = 358.5484{{c}}
: error map: {{val| 0.000 +0.626 +1.267 -3.019 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~315/256 = 358.548{{c}}
: [[error map]]: {{val| 0.000 +0.620 +1.275 -3.018 }}
: [[error map]]: {{val| 0.000 +0.620 +1.275 -3.018 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~315/256 = 358.548{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~315/256 = 358.548{{c}}
: error map: {{val| 0.000 +0.627 +1.265 -3.020 }}
: error map: {{val| 0.000 +0.627 +1.265 -3.020 }} -->


{{Optimal ET sequence|legend=1| 77, 87, 164 }}
{{Optimal ET sequence|legend=1| 77, 87, 164 }}


[[Badness]] (Smith): 0.108011
[[Badness]] (Sintel): 2.73


=== 11-limit ===
=== 11-limit ===
Line 2,046: Line 2,036:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~27/22 = 358.575{{c}}
* WE: ~2 = 1200.1110{{c}}, ~27/22 = 358.6045{{c}}
* POTE: ~2 = 1200.000{{c}}, ~27/22 = 358.571{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~27/22 = 358.5720{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~27/22 = 358.575{{c}}
* POTE: ~2 = 1200.000{{c}}, ~27/22 = 358.571{{c}} -->


{{Optimal ET sequence|legend=0| 77, 87, 164, 251d }}
{{Optimal ET sequence|legend=0| 77, 87, 164, 251d }}


Badness (Smith): 0.054655
Badness (Sintel): 1.81


=== 13-limit ===
=== 13-limit ===
Line 2,061: Line 2,053:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~16/13 = 358.576{{c}}
* WE: ~2 = 1200.0482{{c}}, ~~16/13 = 358.5883{{c}}
* POTE: ~2 = 1200.000{{c}}, ~16/13 = 358.574{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/13 = 358.5741{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~16/13 = 358.576{{c}}
* POTE: ~2 = 1200.000{{c}}, ~16/13 = 358.574{{c}} -->


{{Optimal ET sequence|legend=0| 77, 87, 164, 251d }}
{{Optimal ET sequence|legend=0| 77, 87, 164, 251d }}


Badness (Smith): 0.028187
Badness (Sintel): 1.16
 
== Lagaca ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 1029/1024, 11529602/11390625
 
{{Mapping|legend=1| 2 -4 15 8 | 0 9 -13 -3 }}
: mapping generators: ~3375/2401, ~450/343
 
[[Optimal tuning]]s:
* [[WE]]: ~3375/2401 = 600.1355{{c}}, ~450/343 = 478.0813{{c}}
: [[error map]]: {{val| +0.271 +0.235 +0.662 -1.986 }}
* [[CWE]]: ~3375/2401 = 600.000{{c}}, ~450/343 = 477.9725{{c}}
: error map: {{val| 0.000 -0.202 +0.043 -2.743 }}
<!-- * [[CTE]]: ~3375/2401 = 600.000{{c}}, ~450/343 = 477.969{{c}}
: [[error map]]: {{val| 0.000 -0.232 +0.087 -2.734 }}
* [[POTE]]: ~3375/2401 = 600.000{{c}}, ~450/343 = 477.973{{c}}
: error map: {{val| 0.000 -0.195 +0.033 -2.746 }} -->
 
{{Optimal ET sequence|legend=1| 10, 98, 108, 118 }}
 
[[Badness]] (Sintel): 3.65


== Quartemka ==
== Quartemka ==
Line 2,075: Line 2,091:
[[Comma list]]: 1029/1024, 1250000/1240029
[[Comma list]]: 1029/1024, 1250000/1240029


{{Mapping|legend=1| 1 4 6 2 | 0 -21 -32 7 }}
{{Mapping|legend=1| 1 -17 -26 9 | 0 21 32 -7 }}
: mapping generators: ~2, ~27/25
: mapping generators: ~2, ~50/27


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~27/25 = 137.971{{c}}
* [[WE]]: ~2 = 1200.5278{{c}}, ~50/27 = 1062.4614{{c}}
: [[error map]]: {{val| +0.528 +0.762 -1.272 -1.305 }}
* [[CWE]]: ~21 = 1200.0000{{c}}, ~50/27 = 1062.0046{{c}}
: error map: {{val| 0.000 +0.142 -2.167 -2.858 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~50/27 = 1062.029{{c}}
: [[error map]]: {{val| 0.000 +0.658 -1.380 -3.030 }}
: [[error map]]: {{val| 0.000 +0.658 -1.380 -3.030 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~27/25 = 138.006{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~50/27 = 1061.994{{c}}
: error map: {{val| 0.000 -0.075 -2.496 -2.786 }}
: error map: {{val| 0.000 -0.075 -2.496 -2.786 }} -->


{{Optimal ET sequence|legend=1| 26, 61, 87, 113, 200 }}
{{Optimal ET sequence|legend=1| 26, 61, 87, 113, 200 }}


[[Badness]] (Smith): 0.152287
[[Badness]] (Sintel): 3.85


=== 11-limit ===
=== 11-limit ===
Line 2,093: Line 2,113:
Comma list: 385/384, 441/440, 800000/793881
Comma list: 385/384, 441/440, 800000/793881


Mapping: {{mapping| 1 4 6 2 3 | 0 -21 -32 7 4 }}
Mapping: {{mapping| 1 -17 -26 9 7 | 0 21 32 -7 -4 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~27/25 = 137.970{{c}}
* WE: ~2 = 1200.3051{{c}}, ~50/27 = 1062.2805{{c}}
* POTE: ~2 = 1200.000{{c}}, ~27/25 = 137.990{{c}}
* CWE: ~21 = 1200.0000{{c}}, ~50/27 = 1062.0147{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~50/27 = 1062.030{{c}}
* POTE: ~2 = 1200.000{{c}}, ~50/27 = 1062.010{{c}} -->


{{Optimal ET sequence|legend=0| 26, 61, 87, 200, 287d }}
{{Optimal ET sequence|legend=0| 26, 61, 87, 200, 287d }}


Badness (Smith): 0.057307
Badness (Sintel): 1.89


=== 13-limit ===
=== 13-limit ===
Line 2,108: Line 2,130:
Comma list: 325/324, 364/363, 385/384, 2200/2197
Comma list: 325/324, 364/363, 385/384, 2200/2197


Mapping: {{mapping| 1 4 6 2 3 6 | 0 -21 -32 7 4 -20 }}
Mapping: {{mapping| 1 -17 -26 9 7 -14 | 0 21 32 -7 -4 20 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~13/12 = 137.971{{c}}
* WE: ~2 = 1200.2708{{c}}, ~24/13 = 1062.2496{{c}}
* POTE: ~2 = 1200.000{{c}}, ~13/12 = 137.990{{c}}
* CWE: ~21 = 1200.0000{{c}}, ~24/13 = 1062.0139{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~24/13 = 1062.029{{c}}
* POTE: ~2 = 1200.000{{c}}, ~24/13 = 1062.010{{c}} -->


{{Optimal ET sequence|legend=0| 26, 61, 87, 200 }}
{{Optimal ET sequence|legend=0| 26, 61, 87, 200 }}


Badness (Smith): 0.028393
Badness (Sintel): 1.17


== Tritriple ==
== Tritriple ==
Line 2,129: Line 2,153:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~864/625 = 559.320{{c}}
* [[WE]]: ~2 = 1200.4239{{c}}, ~864/625 = 559.4921{{c}}
: [[error map]]: {{val| +0.424 -0.331 +0.561 -1.287 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~864/625 = 559.3015{{c}}
: error map: {{val| 0.000 -0.815 -0.284 -2.539 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~864/625 = 559.320{{c}}
: [[error map]]: {{val| 0.000 -0.317 +0.085 -2.705 }}
: [[error map]]: {{val| 0.000 -0.317 +0.085 -2.705 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~864/625 = 559.295{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~864/625 = 559.295{{c}}
: error map: {{val| 0.000 -1.003 -0.423 -2.477 }}
: error map: {{val| 0.000 -1.003 -0.423 -2.477 }} -->


{{Optimal ET sequence|legend=1| 15, …, 88, 103, 118, 221, 339d }}
{{Optimal ET sequence|legend=1| 15, …, 88, 103, 118, 221, 339d }}


[[Badness]] (Smith): 0.118640
[[Badness]] (Sintel): 3.00


=== 11-limit ===
=== 11-limit ===
Line 2,146: Line 2,174:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~242/175 = 559.327{{c}}
* WE: ~2 = 1200.4953{{c}}, ~242/175 = 559.5243{{c}}
* POTE: ~2 = 1200.000{{c}}, ~242/175 = 559.293{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~242/175 = 559.3016{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~242/175 = 559.327{{c}}
* POTE: ~2 = 1200.000{{c}}, ~242/175 = 559.293{{c}} -->


{{Optimal ET sequence|legend=0| 15, …, 88, 103, 118, 221e, 339de }}
{{Optimal ET sequence|legend=0| 15, …, 88, 103, 118, 221e, 339de }}


Badness (Smith): 0.035350
Badness (Sintel): 1.17


== Widefourth ==
== Widefourth ==
Line 2,158: Line 2,188:
[[Comma list]]: 1029/1024, 48828125/48771072
[[Comma list]]: 1029/1024, 48828125/48771072


{{Mapping|legend=1| 1 16 8 -2 | 0 -33 -13 11 }}
{{Mapping|legend=1| 1 -17 -5 9 | 0 33 13 -11 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~3125/2304 = 524.188{{c}}
* [[WE]]: ~2 = 1200.4770{{c}}, ~4608/3125 = 676.0584{{c}}
: [[error map]]: {{val| +0.477 -0.137 +0.061 -1.175 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~4608/3125 = 675.7954{{c}}
: error map: {{val| 0.000 -0.705 -0.973 -2.576 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~4608/3125 = 675.812{{c}}
: [[error map]]: {{val| 0.000 -0.154 -0.756 -2.759 }}
: [[error map]]: {{val| 0.000 -0.154 -0.756 -2.759 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~3125/2304 = 524.210{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~4608/3125 = 675.790{{c}}
: error map: {{val| 0.000 -0.892 -1.047 -2.513 }}
: error map: {{val| 0.000 -0.892 -1.047 -2.513 }} -->


{{Optimal ET sequence|legend=1| 16, 71, 87, 103, 190 }}
{{Optimal ET sequence|legend=1| 16, 71, 87, 103, 190 }}


[[Badness]] (Smith): 0.154117
[[Badness]] (Sintel): 3.90


=== 11-limit ===
=== 11-limit ===
Line 2,178: Line 2,212:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~847/625 = 524.183{{c}}
* WE: ~2 = 1200.4852{{c}}, ~1250/847 = 676.0634{{c}}
* POTE: ~2 = 1200.000{{c}}, ~847/625 = 524.210{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~1250/847 = 675.7966{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~1250/847 = 675.817{{c}}
* POTE: ~2 = 1200.000{{c}}, ~1250/847 = 675.790{{c}} -->


{{Optimal ET sequence|legend=0| 16, 71, 87, 103, 190 }}
{{Optimal ET sequence|legend=0| 16, 71, 87, 103, 190 }}


Badness (Smith): 0.040785
Badness (Sintel): 1.35


=== 13-limit ===
=== 13-limit ===
Line 2,193: Line 2,229:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~65/48 = 524.183{{c}}
* WE: ~2 = 1200.4217{{c}}, ~77/52 = 676.0286{{c}}
* POTE: ~2 = 1200.000{{c}}, ~65/48 = 524.209{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~77/52 = 675.7967{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~77/52 = 675.817{{c}}
* POTE: ~2 = 1200.000{{c}}, ~77/52 = 675.791{{c}} -->


{{Optimal ET sequence|legend=0| 16, 71, 87, 103, 190 }}
{{Optimal ET sequence|legend=0| 16, 71, 87, 103, 190 }}


Badness (Smith): 0.021636
Badness (Sintel): 0.894


== References ==
== References ==
Retrieved from "https://en.xen.wiki/w/Gamelismic_clan"