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Gamelismic clan: Difference between revisions

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m Units; -gencom (trivial); misc. cleanup
Switch to Sintel's badness, WE & CWE tunings, per community consensus (1/)
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~8/7 = 233.889{{c}}
* [[WE]]: ~2 = 1200.4859{{c}}, ~8/7 = 233.7822{{c}}
: [[error map]]: {{val| +0.486 -0.123 -1.151 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~8/7 = 233.7474{{c}}
: error map: {{val| 0.000 -0.713 -2.573 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~8/7 = 233.889{{c}}
: [[error map]]: {{val| 0.000 -0.288 -2.715 }}
: [[error map]]: {{val| 0.000 -0.288 -2.715 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~8/7 = 233.688{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~8/7 = 233.688{{c}}
: error map: {{val| 0.000 -0.892 -2.513 }}
: error map: {{val| 0.000 -0.892 -2.513 }} -->


{{Optimal ET sequence|legend=1| 36, 77, 113, 190 }}
{{Optimal ET sequence|legend=1| 36, 77, 113, 190 }}
[[Badness]] (Sintel): 0.158


=== Euslendric ===
=== Euslendric ===
Forms of slendric in the most optimal range for the 2.3.7 temperament ({{nowrap| 36 & 77 }}) lack an obvious strong mapping of prime 5 or prime 11. However, slendric can extend well to the no-fives no-elevens [[29-limit]] by tempering out [[273/272]], [[343/342]], [[378/377]], [[392/391]], [[513/512]], and [[729/728]], or a comma basis defined in terms of [[S-expression]]s as {S7/S8, S14/S16, S15/S20, S24/S26, S27, S28}. [[113edo]] is an obvious tuning.
Forms of slendric in the most optimal range for the 2.3.7 temperament ({{nowrap| 36 & 77 }}) lack an obvious strong mapping of prime 5 or prime 11. However, slendric can extend well to the no-fives no-elevens [[29-limit]] by tempering out [[273/272]], [[343/342]], [[378/377]], [[392/391]], [[513/512]], and [[729/728]], or a comma basis defined in terms of [[S-expression]]s as {S7/S8, S14/S16, S15/S20, S24/S26, S27, S28}. [[113edo]] is an obvious tuning.


==== 2.3.7.13 subgroup ====
Subgroup: 2.3.7.13
Subgroup: 2.3.7.13


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Sval mapping: {{mapping| 1 1 3 0 | 0 3 -1 19 }}
Sval mapping: {{mapping| 1 1 3 0 | 0 3 -1 19 }}
Gencom mapping: {{mapping| 1 1 0 3 0 0 | 0 3 0 -1 0 19 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~8/7 = 233.734{{c}}
* WE: ~2 = 1200.5057{{c}}, ~8/7 = 233.7200{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 233.622{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6534{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~8/7 = 233.734{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 233.622{{c}} -->


{{Optimal ET sequence|legend=0| 5, …, 31f, 36, 77, 113 }}
{{Optimal ET sequence|legend=0| 5, 31f, 36, 77, 113, 827bdddff }}


Badness (Sintel): 0.339
Badness (Sintel): 0.339
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Sval mapping: {{mapping| 1 1 3 0 0 | 0 3 -1 19 21 }}
Sval mapping: {{mapping| 1 1 3 0 0 | 0 3 -1 19 21 }}
Gencom mapping: {{mapping| 1 1 0 3 0 0 0 | 0 3 0 -1 0 19 21 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~8/7 = 233.657{{c}}
* WE: ~2 = 1200.5282{{c}}, ~8/7 = 233.6492{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 233.546{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.5776{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~8/7 = 233.657{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 233.546{{c}} -->


{{Optimal ET sequence|legend=0| 5g, …, 31fg, 36, 113, 149 }}
{{Optimal ET sequence|legend=0| 5g, 31fg, 36, 113, 149 }}


Badness (Sintel): 0.332
Badness (Sintel): 0.332
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Sval mapping: {{mapping| 1 1 3 0 0 6 | 0 3 -1 19 21 -9 }}
Sval mapping: {{mapping| 1 1 3 0 0 6 | 0 3 -1 19 21 -9 }}
Gencom mapping: {{mapping| 1 1 0 3 0 0 0 6 | 0 3 0 -1 0 19 21 -9 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~8/7 = 233.657{{c}}
* WE: ~2 = 1200.3292{{c}}, ~8/7 = 233.6651{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 233.601{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6106{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~8/7 = 233.657{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 233.601{{c}} -->


{{Optimal ET sequence|legend=0| 5g, …, 36, 77, 113 }}
{{Optimal ET sequence|legend=0| 5g, 36, 77, 113, 262df }}


Badness (Sintel): 0.380
Badness (Sintel): 0.380
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Sval mapping: {{mapping| 1 1 3 0 0 6 9 | 0 3 -1 19 21 -9 -23 }}
Sval mapping: {{mapping| 1 1 3 0 0 6 9 | 0 3 -1 19 21 -9 -23 }}
Gencom mapping: {{mapping| 1 1 0 3 0 0 0 6 9 | 0 3 0 -1 0 19 21 -9 -23 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~8/7 = 233.624{{c}}
* WE: ~2 = 1200.3127{{c}}, ~8/7 = 233.6679{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 233.607{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6091{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~8/7 = 233.624{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 233.607{{c}} -->


{{Optimal ET sequence|legend=0| 5gi, …, 36, 77, 113 }}
{{Optimal ET sequence|legend=0| 36, 77, 113, 262df }}


Badness (Sintel): 0.474
Badness (Sintel): 0.474
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Sval mapping: {{mapping| 1 1 3 0 0 6 9 7 | 0 3 -1 19 21 -9 -23 -11 }}
Sval mapping: {{mapping| 1 1 3 0 0 6 9 7 | 0 3 -1 19 21 -9 -23 -11 }}
Gencom mapping: {{mapping| 1 1 0 3 0 0 0 6 9 7 | 0 3 0 -1 0 19 21 -9 -23 -11 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~8/7 = 233.626{{c}}
* WE: ~2 = 1200.2503{{c}}, ~8/7 = 233.6688{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 233.620{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 233.6208{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~8/7 = 233.626{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 233.620{{c}} -->


{{Optimal ET sequence|legend=0| 5gi, …, 36, 77, 113 }}
{{Optimal ET sequence|legend=0| 36, 77, 113 }}


Badness (Sintel): 0.473
Badness (Sintel): 0.473
Line 132: Line 157:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~8/7 = 234.384{{c}}
* WE: ~2 = 1199.9708{{c}}, ~8/7 = 234.3748{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 234.3813{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~8/7 = 234.384{{c}}
: error map: {{val| 0.000 +1.197 -3.210 +1.691 }}
: error map: {{val| 0.000 +1.197 -3.210 +1.691 }}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 234.381{{c}}
* POTE: ~2 = 1200.000{{c}}, ~8/7 = 234.381{{c}}
: error map: {{val| 0.000 +1.187 -3.206 +1.735 }}
: error map: {{val| 0.000 +1.187 -3.206 +1.735 }} -->


{{Optimal ET sequence|legend=0| 36, 41, 87, 128 }}
{{Optimal ET sequence|legend=0| 5, …, 36, 41, 87, 128 }}
 
Badness (Sintel): 0.619


=== Baladic ===
=== Baladic ===
Baladic is a 2.3.7.13.17 subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. It tempers out {{S|13}} = [[169/168]], which splits [[7/6]] in half ([[13/12]]~[[14/13]]) and one finds that the octave is therefore split in half via the interval [[91/64]], which is then equated to [[17/12]]. 36edo is an excellent baladic tuning.
Baladic is a 2.3.7.13.17 subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. It tempers out [[169/168]] ({{S|13}}), which splits [[7/6]] in half ([[13/12]]~[[14/13]]) and one finds that the octave is therefore split in half via the interval [[91/64]], which is then equated to [[17/12]]. 36edo is an excellent baladic tuning.


==== 2.3.7.13 subgroup ====
Subgroup: 2.3.7.13
Subgroup: 2.3.7.13


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Sval mapping: {{mapping| 2 2 6 7 | 0 3 -1 1 }}
Sval mapping: {{mapping| 2 2 6 7 | 0 3 -1 1 }}
Gencom mapping: {{mapping| 2 2 0 6 0 7 | 0 3 0 -1 0 1 }}
: mapping generators: ~91/64, ~8/7
: mapping generators: ~91/64, ~8/7


Optimal tunings:  
Optimal tunings:  
* POTE: ~91/64 = 600.0000{{c}}, ~8/7 = 233.6044{{c}}
* WE: ~91/64 = 600.4315{{c}}, ~8/7 = 233.7724{{c}}
* CWE: ~91/64 = 600.0000{{c}}, ~8/7 = 233.7039{{c}}
<!-- * POTE: ~91/64 = 600.0000{{c}}, ~8/7 = 233.6044{{c}} -->


{{Optimal ET sequence|legend=0| 10, 26, 36, 154f, 190ff, 226ff, 262dfff }}
{{Optimal ET sequence|legend=0| 10, 26, 36, 154f, 190ff, 226ff, 262dfff }}


RMS error: 0.5452 cents
Badness (Sintel): 0.434


==== 2.3.7.13.17 subgroup ====
==== 2.3.7.13.17 subgroup ====
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Sval mapping: {{mapping| 2 2 6 7 7 | 0 3 -1 1 3 }}
Sval mapping: {{mapping| 2 2 6 7 7 | 0 3 -1 1 3 }}
Gencom mapping: {{mapping| 2 2 0 6 0 7 7 | 0 3 0 -1 0 1 3 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~17/12 = 600.000{{c}}, ~8/7 = 234.138{{c}}
* WE: ~17/12 = 600.4436{{c}}, ~8/7 = 233.7883{{c}}
* POTE: ~17/12 = 600.000{{c}}, ~8/7 = 233.616{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~8/7 = 233.7312{{c}}
<!-- * CTE: ~17/12 = 600.000{{c}}, ~8/7 = 234.138{{c}}
* POTE: ~17/12 = 600.000{{c}}, ~8/7 = 233.616{{c}} -->


{{Optimal ET sequence|legend=0| 10, 26, 36, 154f, 190ffg, 226ffg }}
{{Optimal ET sequence|legend=0| 10, 26, 36, 154f, 190ffg, 226ffg }}
Badness (Sintel): 0.253


== Mothra ==
== Mothra ==
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