144edo: Difference between revisions

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144edo's step size is called a '''farab''' when used as an [[interval size unit]].<ref>http://tonalsoft.com/enc/f/farab.aspx</ref>

== 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. It [[support]]s [[hemisecordite]], the 41 & 103 temperament, though [[103edo]] is better suited for this purpose.

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 {{nowrap|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 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.

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 {{nowrap|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.

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

=== Prime harmonics ===

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=== Approximation to φ ===

144edo is the 12th Fibonacci edo. As a consequence of being a Fibonacci edo, it ~~can produce~~ extremely precise approximation of the [[Logarithmic phi|logarithmic golden ratio]] at 89 steps. Coincidentally, it ''also'' excellently represents the [[Acoustic phi|acoustic golden ratio]] by 100 steps.

144edo is the 12th Fibonacci edo. As a consequence of being a Fibonacci edo, it produces an extremely precise approximation of the [[Logarithmic phi|logarithmic golden ratio]] at 89 steps. Coincidentally, it ''also'' excellently represents the [[Acoustic phi|acoustic golden ratio]] by 100 steps.

== Regular temperament properties ==

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| [[Substitute harmonic#Dotcom|Dotcom]]

|}

<nowiki />* [[Normal ~~lists~~|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~|minimal form]] in parentheses if ~~it is~~ distinct

<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct

== Music ==

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|144}}
+{{ED intro}}
 edo's step size is called a '''farab''' when used as an [[interval size unit]].<ref>http://tonalsoft.com/enc/f/farab.aspx</ref>
 == 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. It [[support]]s [[hemisecordite]], the 41 & 103 temperament, though [[103edo]] is better suited for this purpose.
+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 {{nowrap|41 &amp; 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 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.
+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 {{nowrap|62 &amp; 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.
+Besides all these, the 144eff val supports hemimiracle, the {{nowrap|41 &amp; 103e}} temperament. 144ee supports oracle, the {{nowrap|31 &amp; 113e}} temperament. 144cf supports necromanteion, the {{nowrap|31 &amp; 113cf}} temperament.
 === Prime harmonics ===
@@ Line 20: / Line 20: @@
 === Approximation to φ ===
-edo is the 12th Fibonacci edo. As a consequence of being a Fibonacci edo, it can produce extremely precise approximation of the [[Logarithmic phi|logarithmic golden ratio]] at 89 steps. Coincidentally, it ''also'' excellently represents the [[Acoustic phi|acoustic golden ratio]] by 100 steps.
+edo is the 12th Fibonacci edo. As a consequence of being a Fibonacci edo, it produces an extremely precise approximation of the [[Logarithmic phi|logarithmic golden ratio]] at 89 steps. Coincidentally, it ''also'' excellently represents the [[Acoustic phi|acoustic golden ratio]] by 100 steps.
 == Regular temperament properties ==
@@ Line 84: / Line 84: @@
 | [[Substitute harmonic#Dotcom|Dotcom]]
 |}
-<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
 == Music ==