Survey of efficient temperaments by subgroup: Difference between revisions

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Subgroups with no 2s, e.g. 3.5.7.11, are the most jarring break away from familiar harmony, which one may consider a good or a bad thing.
Subgroups with no 2s, e.g. 3.5.7.11, are the most jarring break away from familiar harmony, which one may consider a good or a bad thing.


Subgroups with 2s and 3s but no 5s, e.g. 2.3.7.11, preserve the most fundamental familiar intervals like the octave and the fifth, but do away with the 5-limit major and minor intervals of common practice harmony^<ref>^According to the 2.3.5 reading of common practice harmony. Alternate readings are possible.</ref>, forcing innovation while still keeping some familiarity.
Subgroups with 2s and 3s but no 5s, e.g. 2.3.7.11, preserve the most fundamental familiar intervals like the octave and the fifth, but do away with the 5-limit major and minor intervals of common practice harmony<ref>According to the 2.3.5 reading of common practice harmony. Alternate readings are possible.</ref>, forcing innovation while still keeping some familiarity.


Some theorists believe including 13, 17 or higher in a subgroup is pointless because the brain can't register such complex intervals. Others believe these intervals are registered by the brain, perhaps subtly and subconsciously in some instances, but still there.
Some theorists believe including 13, 17 or higher in a subgroup is pointless because the brain can't register such complex intervals. Others believe these intervals are registered by the brain, perhaps subtly and subconsciously in some instances, but still there.