RE: [tuning] Harmonic Entropy Made Audible!

Joseph wrote,

>Could we say that the experiment is a comprehensive investigation of
>concordance across the full audible spectrum,

Uh -- I don't think so. We've ignored the effects of register in the theory
and I've ignored the vast majority of the audible spectrum in practice by
using the same bass note for all the chords.

>finding pairs of notes
>within tetrads that most closely approximate low integer ratios (??)

As you know, some of the chords agree with this description, and others do
not.

I'd say this (though it's not "populist"): using a simple model that simply
sums the individual discordances of the 6 diads within each tetrad, and
ignores any 3- or 4- note synergies, I calculated the total discordance for
a host of tetrads: those with all three intervals between adjacent tones
lying within the 150¢ - 550¢ range, in 2¢ increments. Among these chords, I
found the local minima of discordance -- those chords that cannot be
improved by moving any notes 2¢ in any direction. The 15 most concordant of
these had a perfect octave, then the next 36 are the ones I made sound files
for, and there were 89 others. Remember that the diadic discordance function
I used is inherently biased against smaller intervals and hence the overall
rankings are biased against close-voiced chords.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/12812

>using a simple model that
>simply sums the individual discordances of the 6 diads within each
>tetrad, and ignores any 3- or 4- note synergies, I calculated the
>total discordance for a host of tetrads: those with all three
>intervals between adjacent tones lying within the 150¢ - 550¢
range, in 2¢ increments. Among these chords, I found the local
minima
of discordance -- those chords that cannot be improved by moving any
>notes 2¢ in any direction. The 15 most concordant of these had a
>perfect octave, then the next 36 are the ones I made sound files
for, and there were 89 others. Remember that the diadic discordance
>function I used is inherently biased against smaller intervals and
>hence the overall rankings are biased against close-voiced chords.

Thanks Paul!

I'm not sure that Kyle Gann is going to be publishing this in the
"Voice" anytime soon... but it works for me!

Thanks!

JP
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Joseph Pehrson