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Gamelismic clan: Difference between revisions

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==== Subgroup extensions ====
==== Subgroup extensions ====
No-five subgroup extensions of slendric include radon, a 2.3.7.11-subgroup extension that may be viewed as no-five rodan, considered below, euslendric, a 2.3.7.13-subgroup extension, baladic, a weak 2.3.7.13.17-subgroup extension, and gigapyth, a 2.3.7.85-subgroup extension, considered in [[#Other subgroup extensions]]. Dicussed elsewhere is [[Subgroup temperaments #Trisect|trisect]] in the 2.3.7.11/5 subgroup.
No-5 subgroup extensions of slendric include radon, a 2.3.7.11-subgroup extension that may be viewed as no-5 rodan, considered below, euslendric, a 2.3.7.13-subgroup extension, baladic, a weak 2.3.7.13-subgroup extension, trisect, a weak 2.3.7.11/5-subgroup extension, and gigapyth, a 2.3.7.85-subgroup extension, considered in [[#Other subgroup extensions]].  


=== Radon ===
=== Radon ===
Line 57: Line 57:
Comma list: 896/891, 1029/1024
Comma list: 896/891, 1029/1024


Subgroup-val mapping: {{mapping| 1 1 3 6 | 0 3 -1 -13 }}
{{Mapping|legend=2| 1 1 3 6 | 0 3 -1 -13 }}


{{Mapping|legend=4| 1 1 0 3 6 | 0 3 0 -1 -13 }}
{{Mapping|legend=4| 1 1 0 3 6 | 0 3 0 -1 -13 }}
Line 1,944: Line 1,944:
Comma list: 729/728, 1029/1024
Comma list: 729/728, 1029/1024


Subgroup-val mapping: {{mapping| 1 1 3 0 | 0 3 -1 19 }}
{{Mapping|legend=2| 1 1 3 0 | 0 3 -1 19 }}


{{Mapping|legend=4| 1 1 0 3 0 0 | 0 3 0 -1 0 19 }}
{{Mapping|legend=4| 1 1 0 3 0 0 | 0 3 0 -1 0 19 }}
Line 1,961: Line 1,961:
Comma list: 273/272, 729/728, 833/832
Comma list: 273/272, 729/728, 833/832


Subgroup-val mapping: {{mapping| 1 1 3 0 0 | 0 3 -1 19 21 }}
{{Mapping|legend=2| 1 1 3 0 0 | 0 3 -1 19 21 }}


{{Mapping|legend=4| 1 1 0 3 0 0 0 | 0 3 0 -1 0 19 21 }}
{{Mapping|legend=4| 1 1 0 3 0 0 0 | 0 3 0 -1 0 19 21 }}
Line 1,978: Line 1,978:
Comma list: 273/272, 343/342, 513/512, 729/728
Comma list: 273/272, 343/342, 513/512, 729/728


Subgroup-val mapping: {{mapping| 1 1 3 0 0 6 | 0 3 -1 19 21 -9 }}
{{Mapping|legend=2| 1 1 3 0 0 6 | 0 3 -1 19 21 -9 }}


{{Mapping|legend=4| 1 1 0 3 0 0 0 6 | 0 3 0 -1 0 19 21 -9 }}
{{Mapping|legend=4| 1 1 0 3 0 0 0 6 | 0 3 0 -1 0 19 21 -9 }}
Line 1,995: Line 1,995:
Comma list: 273/272, 343/342, 392/391, 513/512, 729/728
Comma list: 273/272, 343/342, 392/391, 513/512, 729/728


Subgroup-val mapping: {{mapping| 1 1 3 0 0 6 9 | 0 3 -1 19 21 -9 -23 }}
{{Mapping|legend=2| 1 1 3 0 0 6 9 | 0 3 -1 19 21 -9 -23 }}


{{Mapping|legend=4| 1 1 0 3 0 0 0 6 9 | 0 3 0 -1 0 19 21 -9 -23 }}
{{Mapping|legend=4| 1 1 0 3 0 0 0 6 9 | 0 3 0 -1 0 19 21 -9 -23 }}
Line 2,012: Line 2,012:
Comma list: 273/272, 343/342, 378/377, 392/391, 513/512, 609/608
Comma list: 273/272, 343/342, 378/377, 392/391, 513/512, 609/608


Subgroup-val mapping: {{mapping| 1 1 3 0 0 6 9 7 | 0 3 -1 19 21 -9 -23 -11 }}
{{Mapping|legend=2| 1 1 3 0 0 6 9 7 | 0 3 -1 19 21 -9 -23 -11 }}


{{Mapping|legend=4| 1 1 0 3 0 0 0 6 9 7 | 0 3 0 -1 0 19 21 -9 -23 -11 }}
{{Mapping|legend=4| 1 1 0 3 0 0 0 6 9 7 | 0 3 0 -1 0 19 21 -9 -23 -11 }}
Line 2,031: Line 2,031:
Comma list: 169/168, 1029/1024
Comma list: 169/168, 1029/1024


Subgroup-val mapping: {{mapping| 2 2 6 7 | 0 3 -1 1 }}
{{Mapping|legend=2| 2 2 6 7 | 0 3 -1 1 }}


{{Mapping|legend=4| 2 2 0 6 0 7 | 0 3 0 -1 0 1 }}
{{Mapping|legend=4| 2 2 0 6 0 7 | 0 3 0 -1 0 1 }}
Line 2,049: Line 2,049:
Comma list: 169/168, 273/272, 289/288
Comma list: 169/168, 273/272, 289/288


Subgroup-val mapping: {{mapping| 2 2 6 7 7 | 0 3 -1 1 3 }}
{{Mapping|legend=2| 2 2 6 7 7 | 0 3 -1 1 3 }}


{{Mapping|legend=4| 2 2 0 6 0 7 7 | 0 3 0 -1 0 1 3 }}
{{Mapping|legend=4| 2 2 0 6 0 7 7 | 0 3 0 -1 0 1 3 }}
Line 2,060: Line 2,060:


Badness (Sintel): 0.253
Badness (Sintel): 0.253
=== Trisect (2.3.7.11/5) ===
Trisect divides every Pythagorean interval into three, and is the much more accurate subgroup [[restriction]] of [[augmented family #Trisected|trisected]].
Extending this temperament to the full [[11-limit|11-]], [[13-limit|13-]], or [[17-limit]] through [[gamelismic family #Portent|portent]] or [[landscape family #Landscape|landscape]] results in the [[weak extension]] known as [[kleismic family #Tritikleismic|tritikleismic]].
Subgroup: 2.3.7.11/5
Comma list: 1029/1024, 4000/3993
{{Mapping|legend=2| 3 0 10 5 | 0 3 -1 -1 }}
: mapping generators: ~44/35, ~175/121
Optimal tunings:
* Subgroup WE: ~44/35 = 400.1400{{c}}, ~175/121 = 633.9635{{c}}
* Subgroup CWE: ~44/35 = 400.0000{{c}}, ~175/121 = 633.7885{{c}}
{{Optimal ET sequence|legend=0| 15, 21, 36, 123, 159, 195, 231 }}
==== 2.3.7.11/5.13 subgroup ====
Subgroup: 2.3.7.11/5.13
Comma list: 1029/1024, 1575/1573, 2080/2079
{{Mapping|legend=2| 3 0 10 5 0 | 0 3 -1 -1 7 }}
Optimal tunings:
* Subgroup WE: ~44/35 = 400.1532{{c}}, ~13/9 = 634.1597{{c}}
* Subgroup CWE: ~44/35 = 400.0000{{c}}, ~13/9 = 633.9765{{c}}
{{Optimal ET sequence|legend=1| 15, 21f, 36, 87, 123, 159, 354df }}
==== 2.3.7.11/5.13.17 subgroup ====
Subgroup: 2.3.7.11/5.13.17
Comma list: 273/272, 595/594, 833/832, 1575/1573
{{Mapping|legend=2| 3 0 10 5 0 -2 | 0 3 -1 -1 7 9 }}
Optimal tunings:
* Subgroup WE: ~34/27 = 400.1534{{c}}, ~13/9 = 634.0635{{c}}
* Subgroup CWE: ~34/27 = 400.0000{{c}}, ~13/9 = 633.8797{{c}}
{{Optimal ET sequence|legend=0| 15g, 21fg, 36, 123, 159, 195f }}
===== Trisector =====
Subgroup: 2.3.7.11/5.13.17.19
Comma list: 210/209, 273/272, 286/285, 595/594, 833/832
{{Mapping|legend=2| 3 0 10 5 0 -2 8 | 0 3 -1 -1 7 9 3 }}
Optimal tunings:
* Subgroup WE: ~34/27 = 400.0514{{c}}, ~13/9 = 633.9749{{c}}
* Subgroup CWE: ~34/27 = 400.0000{{c}}, ~13/9 = 633.9126{{c}}
{{Optimal ET sequence|legend=0| 15g, 21fg, 36, 123h, 159h }}
===== 2.3.7.11/5.13.17.19.23 subgroup =====
Subgroup: 2.3.7.11/5.13.17.19.23
Comma list: 208/207, 210/209, 231/230, 273/272, 286/285, 595/594
{{Mapping|legend=2| 3 0 10 5 0 -2 8 12 | 0 3 -1 -1 7 9 3 1 }}
Optimal tunings:
* Subgroup WE: ~34/27 = 399.9410{{c}}, ~13/9 = 633.9438{{c}}
* Subgroup CWE: ~34/27 = 400.0000{{c}}, ~13/9 = 634.0183{{c}}
{{Optimal ET sequence|legend=0| 15g, 21fg, 36, 87, 123hi }}
===== 2.3.7.11/5.13.17.19.23.29 subgroup =====
Subgroup: 2.3.7.11/5.13.17.19.23.29
Comma list: 208/207, 210/209, 231/230, 273/272, 286/285, 320/319, 595/594
{{Mapping|legend=2| 3 0 10 5 0 -2 8 12 13 | 0 3 -1 -1 7 9 3 1 1 }}
Optimal tunings:
* Subgroup WE: ~29/23 = 399.8924{{c}}, ~13/9 = 633.9310{{c}}
* Subgroup CWE: ~29/23 = 400.0000{{c}}, ~13/9 = 634.0711{{c}}
{{Optimal ET sequence|legend=0| 15g, 21fg, 36, 87, 123hi }}


=== Gigapyth (2.3.7.85) ===
=== Gigapyth (2.3.7.85) ===
Line 2,066: Line 2,149:
Comma list: 1029/1024, 7225/7203
Comma list: 1029/1024, 7225/7203


Subgroup-val mapping: {{mapping| 1 -2 4 7 | 0 6 -2 -1 }}
{{Mapping|legend=2| 1 -2 4 7 | 0 6 -2 -1 }}


Optimal tunings:  
Optimal tunings:  
Line 2,079: Line 2,162:


[[Category:Gamelismic clan| ]] <!-- main article -->
[[Category:Gamelismic clan| ]] <!-- main article -->
[[Category:Gamelismic| ]] <!-- key article -->
[[Category:Temperament clans]]
[[Category:Temperament clans]]
[[Category:Catalogs of rank-2 temperaments]]
[[Category:Catalogs of rank-2 temperaments]]
[[Category:Listen]]
[[Category:Listen]]
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