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The unison family

🔗Gene Ward Smith <gwsmith@svpal.org>

6/13/2004 12:34:10 AM

The null or unison temperament is the "temperament" which maps
everything to 1; in the 7-limit, it has wedgie <<0 0 0 0 0 0||. If we
take nexial adjustemnts to it, we get temperaments of the DoubleO type:

null+5 <<0 0 5 0 8 12|| DoubleO 5 {16/15, 27/25}

null+7 <<0 0 7 0 11 16|| Jamesbond = DoubleO 7 {25/24, 81/80}

null+12 <<0 0 12 0 19 28|| DoubleO 12 {81/80, 128/125}

null+19 <<0 0 19 0 30 44|| DoubleO 19 {81/80, 3125/3072}

Like other families, if we enforce a badness limit we get only a
finite number of members of the family. The complexity is O(n) and the
error O(n^(-3/2)), so logflat badness is O(sqrt(n)), and we get
finiteness. Nothing beyond DoubleO 19 seems very interesting from a
badness viewpont, despite the steady decrease of error to zero, which
doesn't happen with other families.