H.E. minima/ inversionally identical chords

[Erlich, TD93:]
> the minima [calculated from the Harmonic Entropy
> formula] are not really a scale, except that they
> represent the points you might stop at if tuning
> one note against a fixed pitch.

I had a feeling you were going to say that.

> They are not conceived in relation to one another,
> although many of them happen to be quite consonant
> with one another. Lattice diagrams are useful when
> trying to grasp _all_ the interrelationships within
> a scale. The harmonic entropy concept can be applied
> to all those interrelationships, not just the ones
> formed with a single tonic. So if you were really going
> to derive a scale (for a type of music in which a
> lattice is relevant) from the harmonic entropy concept,
> you would not simply take the minima and construct them
> all upwards from a single tonic.

I was thinking when I made it that a lattice of the
Harmonic Entropy minima was (for lack of a better word)
irrelevant. You confirmed it.

However, I did have the thought that a lattice would
be useful for modelling Parncutt's "tonalness" concept.
. . . ???

I've always had a problem with the idea that the
subharmonics/utonalities were exactly as valid as
the harmonics/otonalities, and Parncutt's and Erlich's
experiments seem to bear out the fact that *when we
are considering more than 2 tones*, the otonal
perception is more pronounced.

That's not to say that utonalities are not valid
musical resources, or that Partch's theories are
wrong. His utonal ideas are acoustically correct
in terms of intervals of 2 notes. I'm just saying
that I've always thought that we tend to *hear*
chords more as otonalities, even when they are
a utonal series.

This relates to the "inversionally similar" chords
I posted yesterday (actual they should be referred
to as "inversionally identical"). Perhaps utonalities
that are most favored are the ones which are
inversionally identical when described otonally.
Has anyone ever investigated this property in
chords before?

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

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Joe Monzo wrote,

>Perhaps utonalities
>that are most favored are the ones which are
>inversionally identical when described otonally.

Perhaps utonalities that are most favored are the ones which are
simplest when described otonally. If your definition of "utonalities" is
"chords not having a simpler otonal representation than utonal
repersentation", then our statements agree, trivially.

"Paul H. Erlich" wrote:

> Perhaps utonalities that are most favored are the ones which are
> simplest when described otonally. If your definition of "utonalities" is
> "chords not having a simpler otonal representation than utonal
> repersentation", then our statements agree, trivially.

I have always heard the Utonalities as being almost more introspective,
complete, and "deeper". The otonalities seem more Pointed, direct and more
introverted. Jungians need not comment!
-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

Sorry, may I ask what is Utolnality and Otonality??

:-)

Thanks.

Paul H. Erlich wrote:

> From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>
>
> Joe Monzo wrote,
>
> >Perhaps utonalities
> >that are most favored are the ones which are
> >inversionally identical when described otonally.
>
> Perhaps utonalities that are most favored are the ones which are
> simplest when described otonally. If your definition of "utonalities" is
> "chords not having a simpler otonal representation than utonal
> repersentation", then our statements agree, trivially.
>
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