Survey of efficient temperaments by subgroup: Difference between revisions

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Other subgroups: Add explanation.
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=== Other subgroups ===
=== Other subgroups ===
Subgroups ''without'' a "2" don't have octaves (similar to the [[Bohlen-Pierce scale]]).
Subgroups ''without'' a "2" ''don't have'' multiple of 2 intervals (eg the 2/1 octave, the 3/2 perfect fifth, the 5/4 major third).


Subgroups ''without'' a "3" don't have perfect fifths or perfect fourths.
Subgroups ''without'' a "3" ''don't have'' multiple of 3 intervals (eg the 3/1 perfect twelfth, the 3/2 perfect fifth, the 5/3 major sixth).


Subgroups ''without'' a "5" don't have conventional major and minor thirds or sixths.
Subgroups ''without'' a "5" ''don't have'' multiple of 3 intervals (eg the 5/3 major sixth, the 5/4 major third, the 6/5 minor third).


Subgroups ''with'' a "7", "11", or "other ''n''" include new [[xenharmonic]] consonant intervals that can't be found in common [[12edo]] tuning.
Subgroups ''with'' a "7", "11", or "other ''n''" include new [[xenharmonic]] consonant intervals that can't be found in common [[12edo]] tuning.