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More www harmonic entropy graphs

🔗Paul H. Erlich <PErlich@xxxxxxxxxxxxx.xxxx>

4/12/1999 12:23:12 PM

The harmonic entropy in the first octave, calculated from the Farey series
of order 79, assuming an auditory accuracy of 1%, is shown (with minima and
maxima in cents) at
http://www.uq.net.au/~zzdkeena/Erlich/hentropy6.gif
Compare this with order 80
http://www.uq.net.au/~zzdkeena/Erlich/hentropy1.gif
and 81
http://www.uq.net.au/~zzdkeena/Erlich/hentropy2.gif

Note that the order 79 graph has a local minimum at 1160 cents. This is
similar to the anomalous minima (148 cents, 214 cents) found in the harmonic
entropy for the Mann series of order 112:
http://www.uq.net.au/~zzdkeena/Erlich/hentropy4.gif

A comparison of curves for different orders, for the Farey series:
http://www.uq.net.au/~zzdkeena/Erlich/hentropy3.gif
and for the Mann series:
http://www.uq.net.au/~zzdkeena/Erlich/hentropy5.gif

I am working on graphs for the "Graham series" (num.*den.<N) and some
2-octave graphs.

My discussions of the underlying concepts have been collected at:
http://www.ixpres.com/interval/td/entropy.htm