Chordal harmonic entropy

Hi Paul! In Monz' c. 1997 interview with you about harmonic entropy,
where you wrote that it is "unclear how to weigh the various subsets'
contributrions to the probabilities of particular fundamentals in the
overall analysis", is there any new data suggesting exactly which
chords higher in the series (eg, 10-12-15) become overpowered by the
low entropy of their constituent intervals?

THanks, - Kelly

--- In harmonic_entropy@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
>
> Hi Paul! In Monz' c. 1997 interview with you about harmonic entropy,
> where you wrote that it is "unclear how to weigh the various subsets'
> contributrions to the probabilities of particular fundamentals in the
> overall analysis", is there any new data suggesting exactly which
> chords higher in the series (eg, 10-12-15) become overpowered by the
> low entropy of their constituent intervals?
>
> THanks, - Kelly

Not that I know of, although I'm pretty confident saying it's not a
question of "which" but rather "to what extent" for a given chord.
Meanwhile, many chords high in the harmonic series don't have any low-
entropy consitutent intervals . . .

Hi Paul.

"traktus5" wrote: > > is there any new data suggesting exactly which
> > chords higher in the series (eg, 10-12-15) become overpowered by
the low entropy of their constituent intervals?

>Paul wrote: > Not that I know of, although I'm pretty confident
saying it's not a > question of "which" but rather "to what extent"
for a given chord.

I ask, because I've been wondering if chords like 8-10-15 (5/4 x 3/2 =
15/8), 9-15-20 (5/3 x 4/3 = 20/9) and 25-30-48 (6/5 x 8/5 = 48/25)--
which are already reduced in their outer interval-- have a special
balance between the (higher-in-the-series) chordal-, and (low-in-the-
series dyadic) 'harmonic-entropy'-values.

When I look at all the 5-limit chords in that procedure I do (where I
look at which two numbers, of the conjoining intervals, are present
for each note, so the the first chord, from the top note down, would
be 15/3, 5/2, and 8/4, or 5, 5/2, 2)...the 'reduced chords' all boil
down to just one interval (5,5/2, 2; 3, 4/3, 3; etc.) All the other
chords boil down, with this procedure, to either whole numbers (ie,
the otonal chords like 4-5-7), or fractions (the utonal chords, like
1/4:5:6).

(THere's also the appeal for me that a simplified ratio is to an
interval what a prime number is to an integer!)

> Meanwhile, many chords high in the harmonic series don't have any
low-> entropy consitutent intervals . . .

What would be an example of one of these?

thanks, Kelly

--- In harmonic_entropy@yahoogroups.com, "traktus5" <kj4321@h...>
wrote:
>
> Hi Paul.
>
> "traktus5" wrote: > > is there any new data suggesting exactly
which
> > > chords higher in the series (eg, 10-12-15) become overpowered
by
> the low entropy of their constituent intervals?
>
> >Paul wrote: > Not that I know of, although I'm pretty confident
> saying it's not a > question of "which" but rather "to what extent"
> for a given chord.
>
> I ask, because I've been wondering if chords like 8-10-15 (5/4 x
3/2 =
> 15/8), 9-15-20 (5/3 x 4/3 = 20/9) and 25-30-48 (6/5 x 8/5 = 48/25)--
> which are already reduced in their outer interval-- have a special
> balance between the (higher-in-the-series) chordal-, and (low-in-
the-
> series dyadic) 'harmonic-entropy'-values.
>
> When I look at all the 5-limit chords in that procedure I do (where
I
> look at which two numbers, of the conjoining intervals, are present
> for each note, so the the first chord, from the top note down,
would
> be 15/3, 5/2, and 8/4, or 5, 5/2, 2)

I don't get it.

> > Meanwhile, many chords high in the harmonic series don't have any
> low-> entropy consitutent intervals . . .
>
> What would be an example of one of these?

8:11:13, or 9:11:13, or 9:11:14, or 10:13:17, or 11:13:15, etc.

Hi Paul. May I re-phrase that? From what I"ve read at this list,
there is the high-number ambiguity of chords (where the high number of
the series approximates other chords' numbers), and there is the low
number quality of chords where the dyads are a stronger signal than
the whole chord. So, I was merely postulating that some chords (the
ones I mentioned) may have the unique property of containing a measure
of both qualities, and perhaps in a way which both forces are
balanced!

Also, per our ealier discussion of that interesting min 9th chord e2-
g3-f#4, where you pointed out how the difference tones need to be
calculated from the high-number-in-the-series version of the chord,
and not from the dyads. I had pointed out how the difference of each
individual interval was 7. (12-5, 15-8, 9-2). So, is the dyad
element strong in this chord? And if the individual dyads are
prominant, does the ear then perform a difference tone calculation on
the individual dyads? Furthermore, could the equalness of the dyads'
difference values, in itself, increase the strenght of the dyad-ness
of this chord, over it's higher number quality?

thanks for listening! - Kelly

--- In harmonic_entropy@yahoogroups.com, "traktus5" <kj4321@h...>
wrote:

> Also, per our ealier discussion of that interesting min 9th chord
e2-
> g3-f#4,

10:24:45?

> where you pointed out how the difference tones need to be
> calculated from the high-number-in-the-series version of the chord,
> and not from the dyads. I had pointed out how the difference of
each
> individual interval was 7. (12-5, 15-8, 9-2). So, is the dyad
> element strong in this chord?

Not particularly, though the 9:2 may be simple enough to influence
the perceived root.

> And if the individual dyads are
> prominant, does the ear then perform a difference tone calculation
on
> the individual dyads?

I'm not clear on what you're asking -- difference tones are
difference tones, and their calculation is the same regardless of how
well any individual dyads approximate simple ratios. In order to know
their pitches, you have to know the pitches of the original notes.

> Furthermore, could the equalness of the dyads'
> difference values, in itself, increase the strenght of the dyad-
ness
> of this chord, over it's higher number quality?

No, I don't think so.