4edo: Difference between revisions

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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 tuning map, or [[Vals_and_Tuning_Space|val]], for 4EDO goes <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|7-limit]] [[consistent|consistent]]ly, and sending 15/14, 21/20, 25/24, and 36/35 to the unison. Somewhat confusingly, 9/8 is mapped to the unison also.

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 tuning map, or [[Vals_and_Tuning_Space|val]], for 4EDO goes <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|7-limit]] [[consistent|consistent]]ly, and sending 15/14, 21/20, 25/24, and 36/35 to the unison. Somewhat confusingly, 9/8 is mapped to the unison also.

By putting together the triples of integers which uniquely represent 7-limit tetrads in the [[The_Seven_Limit_Symmetrical_Lattices|7-limit cubic lattice of tetrads]] with the number of 4EDO steps returned by the val <4 6 9 11| we obtain a representation of the 7-limit in terms of four integers, which differs from the usual (monzo) representation in that the triple representing the chord can be swapped for another such triple, resulting in a similar note tuned to a different chord. It is even possible under some circumstances to create a sort of recombinant merging of two pieces of music by using the chords of one with the 4EDO skeletons of another.

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-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 tuning map, or [[Vals_and_Tuning_Space|val]], for 4EDO goes &lt;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|7-limit]] [[consistent|consistent]]ly, and sending 15/14, 21/20, 25/24, and 36/35 to the unison. Somewhat confusingly, 9/8 is mapped to the unison also.
+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 tuning map, or [[Vals_and_Tuning_Space|val]], for 4EDO goes &lt;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|7-limit]] [[consistent|consistent]]ly, and sending 15/14, 21/20, 25/24, and 36/35 to the unison. Somewhat confusingly, 9/8 is mapped to the unison also.
 By putting together the triples of integers which uniquely represent 7-limit tetrads in the [[The_Seven_Limit_Symmetrical_Lattices|7-limit cubic lattice of tetrads]] with the number of 4EDO steps returned by the val &lt;4 6 9 11| we obtain a representation of the 7-limit in terms of four integers, which differs from the usual (monzo) representation in that the triple representing the chord can be swapped for another such triple, resulting in a similar note tuned to a different chord. It is even possible under some circumstances to create a sort of recombinant merging of two pieces of music by using the chords of one with the 4EDO skeletons of another.