complexity formulae & fuzzy notes

Perhaps the total relative harmonic entropies
of all the notes in a chord "explain" the chord's
"tonalness", in the following way:

Imagine that each of the tones in the chord acts as
a local 1/1 for the purpose of determining harmonic
entropies, so that every identity of a sounded
chord would have its own particular set of
harmonic entropy minima and maxima.

Now superimpose all those graphs on top of
each other, and what is that telling us?

Would the minima describe a subset of the
harmonic series that is the determinant of
the most likely implied fundamental of
"tonalness"?

Would they describe a range of possibilities
for fundamentals that conflict, with varying
degrees of strength, for dominance?

- Monzo
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----------
>From: Joseph L Monzo <monz@juno.com>
>To: tuning@onelist.com
>Subject: [tuning] complexity formulae & fuzzy notes
>Date: zat, 20 maa 1999 05:12
>

> From: Joseph L Monzo <monz@juno.com>
>
>
> Perhaps the total relative harmonic entropies
> of all the notes in a chord "explain" the chord's
> "tonalness", in the following way:
>
> Imagine that each of the tones in the chord acts as
> a local 1/1 for the purpose of determining harmonic
> entropies, so that every identity of a sounded
> chord would have its own particular set of
> harmonic entropy minima and maxima.
>
> Now superimpose all those graphs on top of
> each other, and what is that telling us?
>
> Would the minima describe a subset of the
> harmonic series that is the determinant of
> the most likely implied fundamental of
> "tonalness"?
>
> Would they describe a range of possibilities
> for fundamentals that conflict, with varying
> degrees of strength, for dominance?
>
> - Monzo

What do you exactly mean with an harmonic entropy minima?.
I could be wrong but, I have a strange feeling you're
touching here some ideas that are mine as well.
Do you remember my question about inversionally identical
chords? Do you remember my other point of view (common
harmonics and common subharmonics)?
Actually, two tones don't fit because they "behave" like
overtones, It's because of the fitting overtones themselves.

Peter Mulkers

Hey Paul,

Does this:

> [me, monz]
> http://www.egroups.com/message/tuning/1893
>
> Perhaps the total relative harmonic entropies
> of all the notes in a chord "explain" the chord's
> "tonalness", in the following way:
>
> Imagine that each of the tones in the chord acts as
> a local 1/1 for the purpose of determining harmonic
> entropies, so that every identity of a sounded
> chord would have its own particular set of
> harmonic entropy minima and maxima.
>
> Now superimpose all those graphs on top of
> each other, and what is that telling us?
>
> Would the minima describe a subset of the
> harmonic series that is the determinant of
> the most likely implied fundamental of
> "tonalness"?
>
> Would they describe a range of possibilities
> for fundamentals that conflict, with varying
> degrees of strength, for dominance?

... have anything at all to do with the triadic and tetradic
harmonic entropy stuff you're doing now? I think I dimly see
a connection, but am not sure that I completely understand
your current work.

-monz
http://www.ixpres.com/interval/monzo/homepage.html