Re: [harmonic_entropy] Digest Number 146

One comment: I don't see why one would expect otonal and utonal chords
spanning the same interval to be equally consonant under either
Helmholztian or Setharean (aka Plomp-Levelt) theories. The intervals are
the same, but they occur in at different pitches and both theories take
register into account. For example, 1/1 5/4 3/2 7/4 and 1/1 7/6 7/5 7/4
are O and U chords spanning the same interval (1/1-7/4), but the
component subintervals appear at different pitches. Both the 33 hz beat
rate (helmholz's max dissonance) and the location of the critical band
are sensitive to absolute pitch.

I haven't done the computations for lack of time to rewrite Sethares's
program for 3 and 4 rather than 2 simultaneous intervals, but I suspect
there would be a difference in the total computed dissonance. Whether
it would be enough to account for the perceived difference in tonal
consonance is questionable. The lack of the 3/2 above the tonic in the
second chord, difference tones, residue pitches etc. might be involved
(I'm a bit rusty these days on psychoacoustics, having gottena away from
music theory for a couple of years).

--John

--- In harmonic_entropy@y..., John Chalmers <JHCHALMERS@U...> wrote:
> One comment: I don't see why one would expect otonal and utonal
chords
> spanning the same interval to be equally consonant under either
> Helmholztian or Setharean (aka Plomp-Levelt) theories. The
intervals are
> the same, but they occur in at different pitches and both theories
take
> register into account. For example, 1/1 5/4 3/2 7/4 and 1/1 7/6 7/5
7/4
> are O and U chords spanning the same interval (1/1-7/4), but the
> component subintervals appear at different pitches. Both the 33 hz
beat
> rate (helmholz's max dissonance) and the location of the critical
band
> are sensitive to absolute pitch.
>
> I haven't done the computations for lack of time to rewrite
Sethares's
> program for 3 and 4 rather than 2 simultaneous intervals, but I
suspect
> there would be a difference in the total computed dissonance.
Whether
> it would be enough to account for the perceived difference in tonal
> consonance is questionable. The lack of the 3/2 above the tonic in
the
> second chord, difference tones, residue pitches etc. might be
involved
> (I'm a bit rusty these days on psychoacoustics, having gottena away
from
> music theory for a couple of years).
>
> --John

The difference in consonance that I have perceived between otonal and
utonal chords spanning the same interval *regardless of register* is
so profound that I seriously doubt that differences in register for
the constituent intervals plays a major factor.

Keeping the top and bottom tones constant when converting a four-note
chord from otonal to utonal, the top interval switches places with
the bottom one, so an increased amount of disturbance for one tends
to offset a decreased amount for the other, while the middle interval
undergoes a very small change in register.

The one thing that changes significantly, however, is the
relationships between the various combinational tones, which produce
considerably more disturbance in utonal than otonal chords played in
the same register, regardless of what that particular register may be.

--George

--- In harmonic_entropy@y..., John Chalmers <JHCHALMERS@U...> wrote:
> One comment: I don't see why one would expect otonal and utonal
chords
> spanning the same interval to be equally consonant under either
> Helmholztian or Setharean (aka Plomp-Levelt) theories. The
intervals are
> the same, but they occur in at different pitches and both theories
take
> register into account. For example, 1/1 5/4 3/2 7/4 and 1/1 7/6 7/5
7/4
> are O and U chords spanning the same interval (1/1-7/4), but the
> component subintervals appear at different pitches. Both the 33 hz
beat
> rate (helmholz's max dissonance) and the location of the critical
band
> are sensitive to absolute pitch.
>
> I haven't done the computations for lack of time to rewrite
Sethares's
> program for 3 and 4 rather than 2 simultaneous intervals, but I
suspect
> there would be a difference in the total computed dissonance.
Whether
> it would be enough to account for the perceived difference in tonal
> consonance is questionable.

this was my real point, john. it's not enough, not nearly enough. all
this has been gone into more deeply in the past on this list. i've
done the calculations and we've listened to 36 tetrads. sethares's
model has an inherent scaling problem, we've found, but even being as
generous as possible, it doesn't come even close to predicting the
consonance rankings listeners gave the 36 tetrads.

--- In harmonic_entropy@y..., "gdsecor" <gdsecor@y...> wrote:
> --- In harmonic_entropy@y..., John Chalmers <JHCHALMERS@U...> wrote:
> > One comment: I don't see why one would expect otonal and utonal
> chords
> > spanning the same interval to be equally consonant under either
> > Helmholztian or Setharean (aka Plomp-Levelt) theories. The
> intervals are
> > the same, but they occur in at different pitches and both
theories
> take
> > register into account. For example, 1/1 5/4 3/2 7/4 and 1/1 7/6
7/5
> 7/4
> > are O and U chords spanning the same interval (1/1-7/4), but the
> > component subintervals appear at different pitches. Both the 33
hz
> beat
> > rate (helmholz's max dissonance) and the location of the critical
> band
> > are sensitive to absolute pitch.
> >
> > I haven't done the computations for lack of time to rewrite
> Sethares's
> > program for 3 and 4 rather than 2 simultaneous intervals, but I
> suspect
> > there would be a difference in the total computed dissonance.
> Whether
> > it would be enough to account for the perceived difference in
tonal
> > consonance is questionable. The lack of the 3/2 above the tonic
in
> the
> > second chord, difference tones, residue pitches etc. might be
> involved
> > (I'm a bit rusty these days on psychoacoustics, having gottena
away
> from
> > music theory for a couple of years).
> >
> > --John
>
> The difference in consonance that I have perceived between otonal
and
> utonal chords spanning the same interval *regardless of register*
is
> so profound that I seriously doubt that differences in register for
> the constituent intervals plays a major factor.
>
> Keeping the top and bottom tones constant when converting a four-
note
> chord from otonal to utonal, the top interval switches places with
> the bottom one, so an increased amount of disturbance for one tends
> to offset a decreased amount for the other, while the middle
interval
> undergoes a very small change in register.

i'm 100% with you so far . . .

> The one thing that changes significantly, however, is the
> relationships between the various combinational tones, which
produce
> considerably more disturbance in utonal than otonal chords played
in
> the same register, regardless of what that particular register may
be.

it's not "the one thing" that changes, either in my opinion or in the
opinion of psychoacoustical theory for the last 30 years.