User:Dummy index/Heuristics for picking a nonstandard basis of JI subgroup
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Just intonation subgroup #Normalization
Why not normalize a subgroup?
- Nonoctave gang:
- One says it should be a strict no-twos subgroup for tritave temperament. Another says it might be useful to include 4 for avoiding interval become near-octave (get help from odd-numbered-ed4s).
- Combined with the convention of putting equave at the first base, it is 3.4.….
- One says it should be a strict no-twos subgroup for tritave temperament. Another says it might be useful to include 4 for avoiding interval become near-octave (get help from odd-numbered-ed4s).
- There is also a style in which the bases are arranged in ascending order without distinction between prime and composite numbers.
- The desire to choose the basis so that the error is as small as possible.
- e.g. 2.3.5 12&19 [⟨1 0 -4], ⟨0 1 4]] is intended to 1/4-comma meantone, whereas 2.3.5/3 12&19 [⟨1 0 -4], ⟨0 1 3]] is intended to 1/3-comma meantone.