144edo: Difference between revisions

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== Theory ==

144edo is closely related to [[72edo]], but the [[patent val]]s differ on the mapping for [[13/1|13]] and [[17/1|17]]. It is [[enfactoring|enfactored]] in the 11-limit, [[tempering out]] [[225/224]], [[243/242]], [[385/384]], [[441/440]], and [[4000/3993]]. Using the [[patent val]], it tempers out [[847/845]], [[1188/1183]], 1701/1690, 1875/1859, and [[4225/4224]] in the 13-limit.

144edo is closely related to [[72edo]], but the [[patent val]]s differ on the mapping for [[13/1|13]] and [[17/1|17]]. It is [[enfactoring|enfactored]] in the 11-limit, [[tempering out]] [[225/224]], [[243/242]], [[385/384]], [[441/440]], and [[4000/3993]]. Using the [[patent val]], it tempers out [[847/845]], [[1188/1183]], 1701/1690, 1875/1859, and [[4225/4224]] in the 13-limit. It [[support]]s [[hemisecordite]], the 41 & 103 temperament, though [[103edo]] is better suited for this purpose.

Although the patent val comes out on top accuracy in the 13-limit, in the 17-limit 144 falls behind to 144g. The 144g val tempers out [[170/169]], [[289/288]], [[375/374]], [[561/560]], [[595/594]]. It ~~[[support]]s~~ [[semihemisecordite]], the 62 & 82f temperament. The patent val tempers out [[273/272]], [[715/714]], [[833/832]], 875/867, 891/884, and [[1275/1274]]~~. It supports [[~~hemisecordite~~]], the 41 & 103 temperament, though [[103edo]] is better suited for this purpose~~. In the 19-limit the patent val tempers out 210/209, 325/323, [[343/342]], [[363/361]], [[400/399]], [[513/512]], and 665/663.

Although the patent val comes out on top accuracy in the 13-limit, in the 17-limit 144 falls behind to 144g. The 144g val tempers out [[170/169]], [[289/288]], [[375/374]], [[561/560]], [[595/594]]. It supports [[semihemisecordite]], the 62 & 82f temperament. The patent val tempers out [[273/272]], [[715/714]], [[833/832]], 875/867, 891/884, and [[1275/1274]], supporting 17-limit hemisecordite. In the 19-limit the patent val tempers out 210/209, 325/323, [[343/342]], [[363/361]], [[400/399]], [[513/512]], and 665/663.

Besides all these, the 144eff val supports hemimiracle, the 41 & 103e temperament. 144ee supports oracle, the 31 & 113e temperament. 144cf supports necromanteion, the 31 & 113cf temperament.

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 == Theory ==
-edo is closely related to [[72edo]], but the [[patent val]]s differ on the mapping for [[13/1|13]] and [[17/1|17]]. It is [[enfactoring|enfactored]] in the 11-limit, [[tempering out]] [[225/224]], [[243/242]], [[385/384]], [[441/440]], and [[4000/3993]]. Using the [[patent val]], it tempers out [[847/845]], [[1188/1183]], 1701/1690, 1875/1859, and [[4225/4224]] in the 13-limit.
+edo is closely related to [[72edo]], but the [[patent val]]s differ on the mapping for [[13/1|13]] and [[17/1|17]]. It is [[enfactoring|enfactored]] in the 11-limit, [[tempering out]] [[225/224]], [[243/242]], [[385/384]], [[441/440]], and [[4000/3993]]. Using the [[patent val]], it tempers out [[847/845]], [[1188/1183]], 1701/1690, 1875/1859, and [[4225/4224]] in the 13-limit. It [[support]]s [[hemisecordite]], the 41 & 103 temperament, though [[103edo]] is better suited for this purpose.
-Although the patent val comes out on top accuracy in the 13-limit, in the 17-limit 144 falls behind to 144g. The 144g val tempers out [[170/169]], [[289/288]], [[375/374]], [[561/560]], [[595/594]]. It [[support]]s [[semihemisecordite]], the 62 & 82f temperament. The patent val tempers out [[273/272]], [[715/714]], [[833/832]], 875/867, 891/884, and [[1275/1274]]. It supports [[hemisecordite]], the 41 & 103 temperament, though [[103edo]] is better suited for this purpose. In the 19-limit the patent val tempers out 210/209, 325/323, [[343/342]], [[363/361]], [[400/399]], [[513/512]], and 665/663.
+Although the patent val comes out on top accuracy in the 13-limit, in the 17-limit 144 falls behind to 144g. The 144g val tempers out [[170/169]], [[289/288]], [[375/374]], [[561/560]], [[595/594]]. It supports [[semihemisecordite]], the 62 & 82f temperament. The patent val tempers out [[273/272]], [[715/714]], [[833/832]], 875/867, 891/884, and [[1275/1274]], supporting 17-limit hemisecordite. In the 19-limit the patent val tempers out 210/209, 325/323, [[343/342]], [[363/361]], [[400/399]], [[513/512]], and 665/663.
 Besides all these, the 144eff val supports hemimiracle, the 41 & 103e temperament. 144ee supports oracle, the 31 & 113e temperament. 144cf supports necromanteion, the 31 & 113cf temperament.