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Another way to look at Tenney-weighted max error

🔗Kalle Aho <kalleaho@mappi.helsinki.fi>

8/11/2006 12:13:16 PM

Draw a triangle wave so that its valleys are at integers and tops are
at half-integers.

Draw a second triangle wave with a period and an amplitude which are
ln(3)/ln(2) times smaller than the first one.

Draw a third triangle wave with a period and an amplitude which are
ln(5)/ln(2) times smaller than the first one.

You can continue the this until you have drawn triangle waves for all
the primes you want.

The triangle waves represent tenney-weighted errors of primes in all
divisions of octave starting from 0. The errors are proportional to
step size. The max error is the "mountain range" that results from the
superimposed lines of all these triangle waves. The good ETs are at
the valleys of the mountain silhouette.

I think that the max error function is quasiperiodic at periods that
correspond to good ETs. At these points the function seems almost
mirror symmetric.

Kalle