3edo: Difference between revisions

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~~'''~~3 ~~equal divisions of the octave''' ('''3edo''') is the [[tuning system]] derived by dividing the [[octave]] into 3 equal steps of 400 [[cent]]s each.~~

== Theory ==

Some would argue that 3edo is more chord than scale on the basis that as it is identical for what [[12edo]] uses as an augmented triad, it is familiar in that capacity. However, it is nonetheless possible to make music in it. Specifically, tonality is actually established with only two notes at a time as opposed to three — aside from octave reduplications of the Tonic that is — and the two notes directly above the Tonic are used together as a contrast chord. However, it also has real significance in the theoretical realm as well. Its associated 5-limit [[mapping]], or [[Vals and Tuning Space|val]], is {{val|3 5 7}}, meaning octaves are mapped to 3 steps (hence 3edo), the 3rd harmonic to 5 steps and the fifth harmonic to 7 steps. It represents the [[5-limit]] [[consistent]]ly and modulo three, the mappings of 2, 3, and 5 are distinct, and both of 1-5/4-3/2 and 1-6/5-3/2 are mapped to 0-1-2. 3edo therefore erases the distinction between major and minor, and between the root, third and fifth of the chord, while keeping the basic outline of the triad.

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 {{Infobox ET}}
-'''3 equal divisions of the octave''' ('''3edo''') is the [[tuning system]] derived by dividing the [[octave]] into 3 equal steps of 400 [[cent]]s each.
+{{EDO intro|3}}
 == Theory ==
 Some would argue that 3edo is more chord than scale on the basis that as it is identical for what [[12edo]] uses as an augmented triad, it is familiar in that capacity. However, it is nonetheless possible to make music in it.  Specifically, tonality is actually established with only two notes at a time as opposed to three — aside from octave reduplications of the Tonic that is — and the two notes directly above the Tonic are used together as a contrast chord. However, it also has real significance in the theoretical realm as well. Its associated 5-limit [[mapping]], or [[Vals and Tuning Space|val]], is {{val|3 5 7}}, meaning octaves are mapped to 3 steps (hence 3edo), the 3rd harmonic to 5 steps and the fifth harmonic to 7 steps. It represents the [[5-limit]] [[consistent]]ly and modulo three, the mappings of 2, 3, and 5 are distinct, and both of 1-5/4-3/2 and 1-6/5-3/2 are mapped to 0-1-2. 3edo therefore erases the distinction between major and minor, and between the root, third and fifth of the chord, while keeping the basic outline of the triad.