4edo: Difference between revisions

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~~'''~~4 ~~equal divisions of the octave''' ('''4edo''') is the [[tuning system]] derived by dividing the [[octave]] into 4 equal steps of 300 [[cent]]s each.~~

== Theory ==

Like [[3edo]], 4edo is already familiar as a chord of [[12edo]]. Not only that, but 4edo establishes tonality in much the same ways that 3edo does — with only two notes at a time as opposed to three aside from octave reduplications of the tonic, though the Tonic-Antitonic contrast from [[2edo]] also works. Also like with 3edo, it has a theoretical interest in that it preserves a kind of outline, or skeleton, of melodic movement while erasing key distinctions concerning harmony. The 7-limit [[mapping]], or [[Vals and_Tuning Space|val]], for 4edo goes {{val|4 6 9 11}}, all of which are distinct modulo 4. It therefore goes with tetradic harmony in much the same way that 3edo goes with triadic harmony, mapping the [[7-limit]] [[consistent]]ly, and sending 15/14, 21/20, 25/24, and 36/35 to the unison. Somewhat confusingly, the patent mapping of 4edo sees 9/8 mapped to the unison also, leading to [[Very low accuracy temperaments #Antitonic|antitonic]], though this can be traced to both 3/2 and 4/3 being mapped to 2\4.

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 {{Infobox ET}}
-'''4 equal divisions of the octave''' ('''4edo''') is the [[tuning system]] derived by dividing the [[octave]] into 4 equal steps of 300 [[cent]]s each.
+{{EDO intro|4}}
 == Theory ==
 Like [[3edo]], 4edo is already familiar as a chord of [[12edo]].  Not only that, but 4edo establishes tonality in much the same ways that 3edo does — with only two notes at a time as opposed to three aside from octave reduplications of the tonic, though the Tonic-Antitonic contrast from [[2edo]] also works.  Also like with 3edo, it has a theoretical interest in that it preserves a kind of outline, or skeleton, of melodic movement while erasing key distinctions concerning harmony. The 7-limit [[mapping]], or [[Vals and_Tuning Space|val]], for 4edo goes {{val|4 6 9 11}}, all of which are distinct modulo 4. It therefore goes with tetradic harmony in much the same way that 3edo goes with triadic harmony, mapping the [[7-limit]] [[consistent]]ly, and sending 15/14, 21/20, 25/24, and 36/35 to the unison. Somewhat confusingly, the patent mapping of 4edo sees 9/8 mapped to the unison also, leading to [[Very low accuracy temperaments #Antitonic|antitonic]], though this can be traced to both 3/2 and 4/3 being mapped to 2\4.