Gamelismic clan: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 46: / Line 46: @@
 ==== 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 ===
@@ Line 2,060: / Line 2,060: @@
 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 [[portent]] or [[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=3| 3 0 10 5 | 0 3 -1 -1 }}
+: mapping generators: ~44/35, ~175/121
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 400.000{{c}}, ~175/121 = 633.742{{c}}
+{{Optimal ET sequence|legend=1| 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=3| 3 0 10 5 0 | 0 3 -1 -1 7 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~44/35 = 400.000{{c}}, ~13/9 = 633.918{{c}}
+{{Optimal ET sequence|legend=1| 15, 21f, 36, 87, 123, 159 }}
+==== 2.3.7.11/5.13.17 subgroup ====
+[[Subgroup]]: 2.3.7.11/5.13.17
+[[Comma list]]: 273/272, 833/832, 1575/1573, 2080/2079
+{{Mapping|legend=3| 3 0 10 5 0 -2 | 0 3 -1 -1 7 9 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 400.000{{c}}, ~13/9 = 633.820{{c}}
+{{Optimal ET sequence|legend=1| 15, 21fg, 36, 123, 159 }}
+===== Trisector =====
+[[Subgroup]]: 2.3.7.11/5.13.17.19
+[[Comma list]]: 210/209, 273/272, 286/285, 595/594, 2080/2079
+{{Mapping|legend=3| 3 0 10 5 0 -2 8 | 0 3 -1 -1 7 9 3 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 400.000{{c}}, ~13/9 = 633.894{{c}}
+{{Optimal ET sequence|legend=1| 15, 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]]: 210/209, 231/230, 273/272, 286/285, 595/594, 2080/2079
+{{Mapping|legend=3| 3 0 10 5 0 -2 8 12 | 0 3 -1 -1 7 9 3 1 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~34/27 = 400.000{{c}}, ~13/9 = 634.038{{c}}
+{{Optimal ET sequence|legend=1| 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]]: 210/209, 231/230, 273/272, 286/285, 320/319, 595/594, 2080/2079
+{{Mapping|legend=3| 3 0 10 5 0 -2 8 12 13 | 0 3 -1 -1 7 9 3 1 1 }}
+[[Optimal tuning]] ([[Tp tuning|subgroup POTE]]): ~29/23 = 400.000{{c}}, ~13/9 = 634.102{{c}}
+{{Optimal ET sequence|legend=1| 15g, 21fg, 36, 87, 123hi }}
 === Gigapyth (2.3.7.85) ===