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Relative complexity for <385/384, 441/440>

🔗Gene Ward Smith <genewardsmith@juno.com> <genewardsmith@juno.com>

12/11/2002 12:52:15 AM

This is one of the best 11-limit planar temperaments; it is of course related to Miracle, but we can with some advantage use 190-et instead of 72-et for it.

Here is a list of octave equivalence class representatives between 1 and sqrt(2), in order of ascending relative complexity:

8/7, 21/16, 4/3, 21/20, 12/11, 6/5, 5/4, 7/6, 11/8,
7/5, 14/11, 49/48, 11/9, 10/9, ...

Here are vectors representing 7 and 5/3, which can be used as a basis for the 11-limit equivalence classes when reduced mod 385/384 and 441/440. Plotting the classes when so reduced gives the lattice corresponding to this temperament.

7 ~ [2.921751858, -4.929080722]

5/3 ~ [20.89259427, 3.844797215]