I find 0_184_388_886 quite smooth

David Finnamore wrote,

>Take the 7-8 pair from the T
>Lab: 498 702 886, and 184 388 886. The first one seems to cause the
partials >to
>mostly line up with each other, while the second one causes them to beat
>against each
>other.
>Or it may be that they both beat, but the second one beats at a rate that
>makes it more obvious. I've noticed that this phenomenon is fairly
frequent >among
>otonal/utonal pairs in general.
>> > > >#33: [0_184__388___886]
>>
>> Warbling? I'll get back to you tomorrow. I
>> hope you aren't using "Lo-Fi Play"!

>Nooooo. D-loaded Joseph's zip file. I've listened on two different
systems, >a pair
>of pretty nice, if soft sounding, speakers at work, and Altec cubes with
sub->woofer
>at home. When I say "warbling" I mean beating.

Are you sure? See below.

This tetrad beats harder than >any
>other in the list, to my ears. It's the only one to which I had a negative
>reaction. When I listen to it and it's "partner" back to back, they don't
>even seem
>to be in the same ballpark in terms of the concordance/discordance
continuum. >I may
>be confusing pure concordance somewhat with my acculturated sense of
tonality, >do you
>think?

When I listen to the tetrads (0_184_388_886 and its partner 0_498_702_886),
I could almost call both of them "beatless", and what beating I do hear is
pretty much the same in both chords. The high guide tone of the
0_184_388_886, which is two octaves above the 388, beats about 3 times per
second -- in the 0_498_702_886 I hear a beat at about 4 times per second two
octaves above the 702, and a lower beating about 2 times per second. So in
that sense I disagree with you, but I do know what you mean by "warbling".
It is much like Joseph Pehrson's remark on September 1st about another
utonal chord:

>the utonal 1/7:1/6:1/5:1/4... which doesn't really BEAT in a timable
>fashion, but which has a certain "wobble" to it that is different
>from the otonal perception.

What is this sensation? I might even call it a "gurgle" rather than a
"wobble" or "warble". It's definitely not a beating you can count, that
happens at a regular rate, the way beating is supposed to. It almost seems
as if different notes in the chord are fighting for prominence, and the
power shifts rapidly among them, rather than achieving a nice equilibrium
the way it does in the otonal chord. Does this description make sense to
you, David and Joseph?

I think this sensation may very well be the "confusion" of harmonic entropy
-- tetradic harmonic entropy, that is, which the geometric mean ranking
gives a good ranking for, for the simpler chords. In the 0_498_702_886, the
498 is clearly heard as the root -- in fact, it's almost hard to hear the 0
as the bass note. The whole chord, despite some slight cricket-chirping due
to the slightly detuned intervals, sounds integrated in its projection of
the harmony. The 0_184_388_886 chord, though certainly what I would describe
as a very "smooth" chord, seems to be unbalanced and almost vertiginous in a
sea-sickness-inducing kind of way. I believe that this may be due, in part,
to the central pitch processor's inability to find a sure "root" for this
chord (the numbers in 36:40:45:60 may just be too high -- too many other
interpretations confuse you) -- in other words, harmonic entropy.

Another explanation is that the roughness is in fact greater for the
0_184_388_886 than for the 0_498_702_886, not because of beating upper
partials, but because of beating fundamentals -- and masking. Both chords
have a pair of fundamentals which are 184 cents apart. That corresponds, in
the 0_184_388_886 chord, to a beat rate of 33 beats per second (precisely
where Helmholtz put his dissonance maximum), and in the 0_498_702_886 chord,
to a beat rate of 50 beats per second. Both so fast they should really be
called "roughness" and not "beating". The difference is due to masking --
the phenomenon by which any frequency suppresses the apparant volume of
frequencies above it, but not those below it. So the lowest note of each
tetrads is always heard as loudest. Since, in the 0_184_388_886 chord, the
lowest note is within another note's critical band, producing prominent
roughness, while in the 0_498_702_886 chord, it isn't, the first chord sound
rougher than the second.

Neither explanation would give the 0_184_388_886 a prominent, countable rate
of beating, as opposed to 0_498_702_886. Nor do I hear one. So David, are
you sure about the statement:

>When I say "warbling" I mean beating.

? If you are, please say so, and try to time how fast this beating is taking
place. There may yet be another explanation . . .

This is fun!

Paul Erlich wrote:

> It almost seems
> as if different notes in the chord are fighting for prominence, and the
> power shifts rapidly among them, rather than achieving a nice equilibrium
> the way it does in the otonal chord. Does this description make sense to
> you, David and Joseph?

Yes, though I hadn't thought about it that way before. Hmm. Yes, I find it a very apt
description, and one that should be generally applicable, beyond the confines of Western
Common Practice theory.

> I think this sensation may very well be the "confusion" of harmonic entropy

You mean we're not just banging our heads against the wall? Oh, good. :-)

> In the 0_498_702_886, the
> 498 is clearly heard as the root -- in fact, it's almost hard to hear the 0
> as the bass note. The whole chord, despite some slight cricket-chirping due
> to the slightly detuned intervals, sounds integrated in its projection of
> the harmony.

Agreed. The crickets are sweet. I like the term "integrated."

> The 0_184_388_886 chord, though certainly what I would describe
> as a very "smooth" chord, seems to be unbalanced and almost vertiginous in a
> sea-sickness-inducing kind of way.

Bingo! Smooth but vertiginous.

> I believe that this may be due, in part,
> to the central pitch processor's inability to find a sure "root" for this
> chord (the numbers in 36:40:45:60 may just be too high -- too many other
> interpretations confuse you) -- in other words, harmonic entropy.

A ha! I love it when a plan comes together. So utonal chords really can have higher
harmonic entropy than their otonal Siamese twins?

Thanks so much for the clarification of the difference between beating and roughness, and
for the reminder about how masking factors in. Very helpful.

> Neither explanation would give the 0_184_388_886 a prominent, countable rate
> of beating, as opposed to 0_498_702_886. Nor do I hear one. So David, are
> you sure about the statement:
>
> >When I say "warbling" I mean beating.
>
> ? If you are, please say so, and try to time how fast this beating is taking
> place. There may yet be another explanation . . .

I hear several distinct rates at once. Most are slow, in the "chorusing effect" range,
like it's sibling has. The offender seems to beat somewhere in the upper teens per
second. It's too fast to get a firm count, and every time I think I've got a track on
it, it seems to mysteriously change rates. This could be related to the
vertiginousness. In general, it feels like driving on a washboarded dirt road. There's
a neutral third that seems to get implied somehow. The fiercest clash is between the
actual major third fundamental and the ghostly implied neutral third.

You're absolutely right that the chord is relatively sweet. All 36 are. We're splitting
some pretty fine hairs here, and for good reason. I find that when I listen to 0 184 388
886 "out of the blue," it sounds pleasant. When I listen to most others in the Lab
first, it suddenly grates on my nerves by comparison.

--
David J. Finnamore
Nashville, TN, USA
http://personal.bna.bellsouth.net/bna/d/f/dfin/index.html
--

Thanks David, and I'm glad harmonic
entropy is beginning to correlate well with a
perception we can hear -- whether we
choose to call it a "wobble", a "warble", or
"driving down a gravelly road", it seems to
be distinct from beating per se and yet at
least as powerful a component of
discordance.

--- In harmonic_entropy@egroups.com,
"David J. Finnamore" <daeron@b...> wrote:

> So utonal chords really can have higher
> harmonic entropy than their otonal Siamese >twins?

They always do. Again, I haven't calculated
true tetradic (or even triadic) harmonic
entropy yet, but I expect it to give the same
rank-order as the geometric mean (of the
otonal representaion), at least for chords
where the geometric mean is not too high.
For dyads, "too high" might mean above 8-
10; for tetrads, I'll make a wild guess that
somewhere in the range 16-30 might be
where the geometric mean rule begins to
break down due to our perceptual
limitations.

>There's
> a neutral third that seems to get implied somehow. The fiercest
clash is between the
> actual major third fundamental and the ghostly implied neutral
third.

Can you be more specific? There might be a
very good explanation for this. Where do
you hear a neutral third and what do you
mean by the "actual major third
fundamental"?

> You're absolutely right that the chord is >relatively sweet. All
36 are.

Even the stack of 442s?

--- In harmonic_entropy@egroups.com, "Paul Erlich" <PERLICH@A...>
wrote:
[I wrote]
> >There's
> > a neutral third that seems to get implied somehow. The fiercest
> clash is between the
> > actual major third fundamental and the ghostly implied neutral
> third.
>
> Can you be more specific? There might be a
> very good explanation for this. Where do
> you hear a neutral third and what do you
> mean by the "actual major third
> fundamental"?

By "actual major third fundamental" I mean the 1st partial of the
tone that is 388 cents above 0. When I listen closely to the rapid
pulsing phenomenon, whatever you want to call it, it seems to occur
between that tone and some implied tone in the neighborhood of 30-70
cents lower. When I try to identify exactly what it's pitch is, it
becomes elusive. It's like I'm hearing it with my "peripheral
hearing" and when I try to listen "right at it," it nearly disappears.

> > You're absolutely right that the chord is >relatively sweet. All
> 36 are.
>
> Even the stack of 442s?

Compared to, say, 10:11:14:15, yes. None of them is outright sour to
me, even the augmented octave chords. Only that 0 184 388 886 caused
me to react negatively at all, and that was only because I heard it
in the midst of a bunch of really concordant tetrads.

--- In harmonic_entropy@egroups.com, "David Finnamore" <daeron@b...>
wrote:
>
> By "actual major third fundamental" I mean the 1st partial of the
> tone that is 388 cents above 0. When I listen closely to the rapid
> pulsing phenomenon, whatever you want to call it, it seems to occur
> between that tone and some implied tone in the neighborhood of 30-
70
> cents lower. When I try to identify exactly what it's pitch is, it
> becomes elusive. It's like I'm hearing it with my "peripheral
> hearing" and when I try to listen "right at it," it nearly
disappears.

Aha! The simplest otonal interpretation of the chord I can think of
is 9:10:11:15, which would be 0_184_345_886. The ratio formed by the
third tone against the actual third tone is 54:55, which would beat
at six times per second in this range -- just as Carl heard!!! So, if
harmonic entropy is the result of trying to fit the notes you hear
into a harmonic series, maybe it's even creating the sensation of the
best-fit harmonic series in your "peripheral" hearing for some
reason. This is a fascinating phenomenon -- and I can't see how the
11 would be produced by any of the normally occuring difference tones.

Thanks so much to you and Carl for listening so closely.

I wrote,
>
> Aha! The simplest otonal interpretation of the chord I can think of
> is 9:10:11:15, which would be 0_184_345_886. The ratio formed by
the
> third tone against the actual third tone is 54:55, which would beat
> at six times per second in this range -- just as Carl heard!!!

Well, on these speakers (in Ara's house) I don't hear a neutral
third, but another otonal interpretation is 7:8:9:12, which could be
written -47_184_386_884. And the "phantom" lower note of that would
be different from the "real" lower note by a 35:36, and would beat
against it about 8 times per second, and I'm definitely hearing
something in the lower interval beating about 8 times per second . . .

Meanwhile . . .

The frequencies of the bottom three notes are 301.09, 334.54, and
376.36 Hz. So the difference tones are 25.53 and
41.81 Hz, and those _basso profundo_ notes beat against on another
16.28 times per second. This might lend quite a bit of audible
roughness to the chord if it is played loud enough for difference
tones to occur. (By way comparison, the difference tones of an 8:9:10
(0_204_386) triad would not beat against one another at all.)

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

http://www.egroups.com/message/harmonic_entropy/160

> It is much like Joseph Pehrson's remark on September 1st about
another utonal chord:
>
> >the utonal 1/7:1/6:1/5:1/4... which doesn't really BEAT in a
timable fashion, but which has a certain "wobble" to it that is
different from the otonal perception.
>
> What is this sensation? I might even call it a "gurgle" rather than
a "wobble" or "warble". It's definitely not a beating you can count,
that happens at a regular rate, the way beating is supposed to. It
almost seems as if different notes in the chord are fighting for
prominence, and the power shifts rapidly among them, rather than
achieving a nice equilibrium the way it does in the otonal chord.
Does this description make sense to you, David and Joseph?

ABSOLUTELY! It's a different sensation than "beating." Wow. That's
downright SPOOKY!

--- In harmonic_entropy@egroups.com, "David Finnamore" <daeron@b...>
wrote:

http://www.egroups.com/message/harmonic_entropy/172

When I listen closely to the rapid
> pulsing phenomenon, whatever you want to call it, it seems to occur
> between that tone and some implied tone in the neighborhood of
30-70
> cents lower. When I try to identify exactly what it's pitch is, it
> becomes elusive. It's like I'm hearing it with my "peripheral
> hearing" and when I try to listen "right at it," it nearly
disappears.
>

That is really wild! Sorry, I just had to comment here...

>ABSOLUTELY! It's a different sensation than "beating." Wow. That's
>downright SPOOKY!

Well, it's the subject of this list. Happy Halloween!