RE: [tuning] Re: Harmonic Entropy for the Sophisticated Ear

John deLaubenfels wrote,

>Thanks, Paul E, for the latest chart, at:

> http://www.egroups.com/files/tuning/perlich/ent_006.jpg

>The curve is detailed and interesting. But I'm having a bit of trouble
>correlating some of the entropy dips with my perception of interval
>concordance.

>Compare, for example, 5/4 and 4/3 from the first octave, to their
>counterparts, 5/2 and 8/3, in the second octave. The curve shows 4/3
>as having less entropy then 5/4, but 8/3 as having more entropy than
>5/2. What does this mean?

This certainly accords with classical theory -- a perfect eleventh
"resolves" to a major tenth. However, since octave-equivalence is so strong,
the octave-equivalent version of this curve that I keep talking about (on
the Monz page, for instance) may be more appropriate for your purposes.

>Does this really make tuning sense? That is, is it more important to
>tune 4/3 close to true than 5/4, yet LESS important to tune 8/3 close
>to true than 5/2?

Well, the slopes are not that different, but to be honest, my perception
agrees with the harmonic entropy curve here. 5:2 definitely has a stronger
pull than 5:4, and 4:3 has a stronger pull than 8:3. In particular, 8:3 does
have a minute but noticable tendency to "slip" into 11:4. Again, many
musical purposes will make it more convenient to use an octave-equivalent
formulation . . . I'll get to it when I get a chance . . .