back to list

Metameantones

🔗Gene Ward Smith <gwsmith@svpal.org>

9/8/2005 2:43:44 AM

Wilson's idea of having a recurrence relationship such that the ratios
converge to a meantone with a particular brat, giving scales along the
way, works if and only if the polynomial for the meantone fifth, which
is the characteristic polynomial of the recurrence relationship, has
the meantone fifth as the unique solution of greatest absolute value.
This happens if and only if the brat is negative. Hence, the Wilson
fifth of -1 will do, but so would, for instance, -6 or -3/8.