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the fish must jump out

🔗jpehrson@rcn.com

6/10/2001 10:12:08 AM

"The fish must jump out... the fish must jump out...."

Listening AGAIN to McLaren's "Introduction to Microtonality" which, I
erroneously assumed would be too "elementary" for me... ahem...

His quote is "the fish must jump out, in order to appreciate the
value of the water in which it swims..." meaning, of course, that one
must experience a WIDE VARIETY of tuning systems in order to
appreciate ANY GIVEN one. This is a good and valid point, and made a
BIG impression on me...

However, there is another assertion from the "Introduction to
Microtonality" CD that seems somewhat more "controversial..."

McLaren states (I paraphrase), "Just Intonation is no particular
stopping point in the infinite continuum of pitches of any
significance..."

Now is this true or untrue?? Admittedly it flys in the face of
Helmholtz, Erlich and, apparently, Daniel Wolf.

Is it possible to TEST the significance of Just Intonation in some
way without invoking the CULTURE of the particpants, as McLaren
suggests? Helmholtz, of course, TRIED, but then again, he was a
scientist, not a musician. Also, he never discussed the possibilties
of cultural influence on the results.

Even more, is it even POSSIBLE to discuss this subject so that *I*
personally understand it in such a way as to not invoke a flame war??

We've have "fried fish" in that respect... something certainly to
avoid.

The fish must jump out...

_________ _______ _________
Joseph Pehrson

🔗X. J. Scott <xjscott@earthlink.net>

6/10/2001 10:33:34 AM

Joe,

> McLaren states (I paraphrase), "Just Intonation is no particular
> stopping point in the infinite continuum of pitches of any
> significance..."

I may be overinterpreting Brian here, but what I myself
find to be true, and possibly what he means (though I
am sure he will jump in and clarify this) is that:

1) just intervals are not usually detectable (unless one
has damaged their hearing enough that nonlinear effects
became significant; or when played loud enough that
nonlinear effects aro also significant) when played as a
dyadic harmony using sine wave timbres. The Plomp/Levelt
experiment bears this out -- the only area of interest in
sinewave dyadic harmonies is the area near the unison.

Because of this, the specialness of just harmonies using
more complex or real world harmonic timbres is not because
of the just intervals between partials but because of the
unison and near-unison hits among the partials present in
the dyad.

I suppose it is also possible that Brian means:

2) as a matter of taste (and thus probably not stateable
in absolutes), just intervals are not intrinsically better
sounding than other intervals, but merely part of a
continuum. This is more true if you consider the general
case where most real world timbres are highly inharmonic,
and thus just intervals are not as easiy identifyable by
ear.

- Jeff

🔗JSZANTO@ADNC.COM

6/10/2001 10:41:02 AM

Joe,

Get a hold of yourself! Really!

--- In tuning@y..., jpehrson@r... wrote:
> His quote is "the fish must jump out, in order to appreciate the
> value of the water in which it swims..." meaning, of course, that
> one must experience a WIDE VARIETY of tuning systems in order to
> appreciate ANY GIVEN one.

I don't agree entirely. It is only one person's way of discovering
variety or personal significance of an item, and while experience and
exposure are invaluable, one should have enough common sense to be
able to extrapolate at some point and bring a slowing to the endless
parade of intonations (experiences). I didn't have to go to every
single peak in the California Sierra range to appreciate (very much)
the view from the one I was standing on.

> McLaren states (I paraphrase), "Just Intonation is no particular
> stopping point in the infinite continuum of pitches of any
> significance..."
>
> Now is this true or untrue?? Admittedly it flys in the face of
> Helmholtz, Erlich and, apparently, Daniel Wolf.

Come on! If he is speaking of JI as an intonational tool (and not
simply the raw calculations of JI) then it isn't true or untrue, it
is just AN OPINION!!! Why are you looking for one true, provable
way???

McLaren has interesting opinions, and so do a lot of other people on
this list, and out in the world. If you keep pitting all these
opinions against each other, you continue to muddy your own waters,
and will make whatever this curious quest you are on endless and
confusing.

Joe, just think for yourself on these matters, and take a look at
what is fact, what is historical, and what is simply one person's
take on the subject. There are an infinite number of ways to tune
music, and each person simply finds the resources needed to express
what they desire to express. For some, multiple tunings are the best
way to go; others will work in one or a few tunings, maybe JI
exclusively.

Instead of just reading someone writing about it, why don't you put
down the paper and listen to a lot of music; in this case, listen to
McLaren's. You've certainly heard music that really strikes you; if
that is the case, then that particular tuning system may be worthy of
investigation. Beyond the music, it is almost entirely subjective.

I offer one example:

During McLaren's presentation at MicroFest, I started perusing the
paper. On page 4 he says

"...truly interesting JI music only begins at the 23 limit..."

So when the opportunity arose I asked him if he found nothing of
interest in the works of Partch, which is only 11 limit. It may have
been the only time he stammered during that entire weekend, and he
had to publicly admit that, yes, it *was* possible, and that the
statement wasn't really applicable in all cases.

Duh.

Just pick something, or some things, and start using it/them.
Thankfully, in a world of many absolutes, there aren't any rights or
wrongs in the *creation* of art.

Cheers,
Jon

🔗JSZANTO@ADNC.COM

6/10/2001 10:43:06 AM

Joe,

I mistakenly attibuted your 'reading' of McLaren. Of course, you are
*listening* to him on the CD, unless it is a booklet that comes with
it. In any event, I refer to what he says, be it in print or
verbally, in my last post...

Cheers,
Jon

🔗Kraig Grady <kraiggrady@anaphoria.com>

6/10/2001 11:04:46 AM

Cousin Jeff!
No 1 without elaborating, contradicts 25 year experience with just these intervals. If this
was true how could Partch have tuned his instruments so easily, on instruments with fast decay and
high inharmonic timbres. That he did not tune his marimba complicates this assertion in that each
bar will and does have different harmonics. Something he chose to keep. One of the easiest ways to
tune a just interval is the drop in volume (a possible reason why many cultures don't use them in
music that must carry over distance.

With No.2 I'll place the music of Terry Riley , La Monte Young, Lou Harrison for there sure
beauty of intervals against any ET composition i have ever heard. It is not without good reason
that just has attracted these talents. I'm Completely subjective. :)

"X. J. Scott" wrote:

> J
>
> 1) just intervals are not usually detectable (unless one
> has damaged their hearing enough that nonlinear effects
> became significant; or when played loud enough that
> nonlinear effects aro also significant) when played as a
> dyadic harmony using sine wave timbres. The Plomp/Levelt
> experiment bears this out -- the only area of interest in
> sinewave dyadic harmonies is the area near the unison.
>
> Because of this, the specialness of just harmonies using
> more complex or real world harmonic timbres is not because
> of the just intervals between partials but because of the
> unison and near-unison hits among the partials present in
> the dyad.
>
> I suppose it is also possible that Brian means:
>
> 2) as a matter of taste (and thus probably not stateable
> in absolutes), just intervals are not intrinsically better
> sounding than other intervals, but merely part of a
> continuum. This is more true if you consider the general
> case where most real world timbres are highly inharmonic,
> and thus just intervals are not as easiy identifyable by
> ear.

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

🔗Alison Monteith <alison.monteith3@which.net>

6/10/2001 12:00:49 PM

Kraig Grady wrote:

> Cousin Jeff!
> No 1 without elaborating, contradicts 25 year experience with just
> these intervals. If this was true how could Partch have tuned his
> instruments so easily, on instruments with fast decay and high
> inharmonic timbres. That he did not tune his marimba complicates this
> assertion in that each bar will and does have different harmonics.
> Something he chose to keep. One of the easiest ways to tune a just
> interval is the drop in volume (a possible reason why many cultures
> don't use them in music that must carry over distance.
>
> With No.2 I'll place the music of Terry Riley , La Monte Young,
> Lou Harrison for there sure beauty of intervals against any ET
> composition i have ever heard. It is not without good reason that just
> has attracted these talents. I'm Completely subjective. :)
>
> I'd like to jump in the deep end and say that despite what my head and
> maybe ( heaven forbid ) even my ears tell me about the
> indistinguishability of some just versus tempered systems, my heart
> yearns for Just Intonation. There's a scent of purity that attracted
> my imagination and my emotions in the first instance and there's a
> poetry about Just Intonation that appeals to my sense of music as ART.
> I find it easier to find the inspiration to strive for excellence if I
> meditate on Just Intonation. Again - very subjective.

Best Wishes.

🔗X. J. Scott <xjscott@earthlink.net>

6/10/2001 12:04:21 PM

Cousin Kraig!

> If this was true how could Partch have tuned his instruments so
easily, on instruments with fast decay and high inharmonic
timbres.

Wow! I did not know how exactly Partch tuned his
instruments. But let me make sure I understand this
completely: are you suggesting that Partch was
able to tune the fundamentals of completely inharmonic
acoustic instruments to perfectly true just intervals,
by ear only, and without the aid of any tools such
as strobes, tuning forks, electronic devices, monochords,
or other instruments?

> One of the easiest ways to tune a just interval is the drop in
volume (a possible reason why many cultures don't use them
in music that must carry over distance.

Hm, OK, well if there is a drop in volume at a certain
point that would be because two or more partials have
cancelled each other out, right? Meaning that the tuning
is being done by aligning partials to unisons and not by
aligning fundamentals to just intervals directly by ear
which I say is not possible excepting nonlinear effects in
the ear (which of course can cause sum and difference
tones which can be used to tune unisons between phantom
pitches.)

> With No.2 I'll place the music of Terry Riley , La Monte Young,
Lou Harrison for there sure beauty of intervals against
any ET composition i have ever heard. It is not without
good reason that just has attracted these talents. I'm
Completely subjective. :)

OK, so for you music in JI sounds markedly BETTER than
other tunings, right? That's OK by me! And I am glad
you identified that as a possibly subjective choice
and not a universal truth that applies to all. In my
own subjective evaluation, all just intervals in a piece
(particularly a piece constructed with perfectly harmonic
digital wavetable sounds) makes me cringe. I like beats.

- Jeff

🔗Kraig Grady <kraiggrady@anaphoria.com>

6/10/2001 1:26:24 PM

Cousin Jeff!

"X. J. Scott" wrote:

> Cousin Kraig!
>
> > If this was true how could Partch have tuned his instruments so
> easily, on instruments with fast decay and high inharmonic
> timbres.
>
> Wow! I did not know how exactly Partch tuned his
> instruments. But let me make sure I understand this
> completely: are you suggesting that Partch was
> able to tune the fundamentals of completely inharmonic
> acoustic instruments to perfectly true just intervals,
> by ear only, and without the aid of any tools such
> as strobes, tuning forks, electronic devices, monochords,
> or other instruments?

i believe he tuned his organ first being the instrument of long decay.

> > One of the easiest ways to tune a just interval is the drop in
> volume (a possible reason why many cultures don't use them
> in music that must carry over distance.
>
> Hm, OK, well if there is a drop in volume at a certain
> point that would be because two or more partials have
> cancelled each other out, right?

you got me there

> Meaning that the tuning
> is being done by aligning partials to unisons and not by
> aligning fundamentals to just intervals directly by ear
> which I say is not possible excepting nonlinear effects in
> the ear (which of course can cause sum and difference
> tones which can be used to tune unisons between phantom
> pitches.)

I believe there is quite a bit of data on Sum and Difference tones as a basis of allot of our
perception. research where isolated pitches in different ears will produce difference tones .
Roederer
The fact is that Just intonation is more wide spread in melodic music than harmonic. There is
the research of Boomsliter and Creel which BMcL leaves out even mentioning showing a natural
disposition for people to play melodies in Just intonation with constant adaptation by extended
reference. (temporary tonics).

> OK, so for you music in JI sounds markedly BETTER than
> other tunings, right? That's OK by me! And I am glad
> you identified that as a possibly subjective choice
> and not a universal truth that applies to all. In my
> own subjective evaluation, all just intervals in a piece
> (particularly a piece constructed with perfectly harmonic
> digital wavetable sounds) makes me cringe.

What you find this music intolerable in intonation, along with Persian and North Indian. Sorry to
hear that

> I like beats.

I imagine that my music beats more than yours :)
let us trade!

>
>
> - Jeff

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

🔗jpehrson@rcn.com

6/10/2001 2:12:17 PM

--- In tuning@y..., JSZANTO@A... wrote:

/tuning/topicId_24755.html#24759

> Joe,
>
> Get a hold of yourself! Really!

I have *no idea* what you mean. I was just commenting on a rather
humorous and, I feel, rather pertinent comment that McLaren made,
with a fun analogy.

>
> I don't agree entirely. It is only one person's way of discovering
> variety or personal significance of an item, and while experience
and exposure are invaluable, one should have enough common sense to
be able to extrapolate at some point and bring a slowing to the
endless parade of intonations (experiences). I didn't have to go to
every single peak in the California Sierra range to appreciate (very
much) the view from the one I was standing on.

OK... well at last we finally get an opinion from you, rather than
commentary on the commentary...

>
> > McLaren states (I paraphrase), "Just Intonation is no particular
> > stopping point in the infinite continuum of pitches of any
> > significance..."
> >
> > Now is this true or untrue?? Admittedly it flys in the face of
> > Helmholtz, Erlich and, apparently, Daniel Wolf.
>
> Come on! If he is speaking of JI as an intonational tool (and not
> simply the raw calculations of JI) then it isn't true or untrue, it
> is just AN OPINION!!! Why are you looking for one true, provable
> way???
>

Do Just Intonation sonorities have any particular "resonance" with
you and, if so, do you feel it is endemic or cultural? I never
really heard your *own* opinion on that topic.

> McLaren has interesting opinions, and so do a lot of other people
on this list, and out in the world. If you keep pitting all these
> opinions against each other, you continue to muddy your own waters,
> and will make whatever this curious quest you are on endless and
> confusing.
>

I disagree. Listening to many opinions and evaluating them is how
people LEARN things... Especially people more acquainted with this
field than *I* am...

There are an infinite number of ways to tune
> music, and each person simply finds the resources needed to express
> what they desire to express. For some, multiple tunings are the
best way to go; others will work in one or a few tunings, maybe JI
> exclusively.
>

OK... so I am just looking for different people's opinion on this
topic.

> Instead of just reading someone writing about it, why don't you put
> down the paper and listen to a lot of music; in this case, listen
to McLaren's.

Sorry... but that's EXACTLY what I *have* been doing. I listened to
his "Introduction to Microtonality" CD and also his "Microtonal Music
Volume 6." I haven't been READING ANYTHING!

________ _______ ________
Joseph Pehrson

🔗Paul Erlich <paul@stretch-music.com>

6/10/2001 3:39:32 PM

--- In tuning@y..., jpehrson@r... wrote:
>
> McLaren states (I paraphrase), "Just Intonation is no particular
> stopping point in the infinite continuum of pitches of any
> significance..."
>
> Now is this true or untrue?? Admittedly it flys in the face of
> Helmholtz, Erlich and, apparently, Daniel Wolf.

I believe it's patently untrue. The best way to demonstrate this is with two variable-pitch
tone generators (don't use sine waves, though), preferably controlled continuously, as
with knobs. Now you can easily sweep through the entire range of intervals. As you do
this, you'll notice stretches of confused, "rough", "turbulent" intervals, punctuated with
points of "focus", of "blending", of "stability". If you stop at one of these points, and
measure the frequencies, you'll see that the ratio of the frequencies is a simple-integer
ratio -- and I mean simple -- there probably won't be any higher numbers than 8 in
these ratios unless you're dealing with ideal conditions of pitch, timbre, etc. Try this if
you can. I tried this when I was very young, and it's overwhelmingly clear -- as clear as
day.

Now whether these qualities have anything to do with music is another issue. I believe
that some styles of music have, and even today (in the case of barbershop, for example),
continue to function by seeking to obtain minimum "roughness" and "turbulence" in
many vertical intervals and chords, while a few structurally important chords may be
dissonant by contrast. Some styles, on the other hand, thrive on the "turbulence" and
"stability" becomes a rare feature, to be exploited carefully. Many styles may use
timbres and envelopes where only the very simplest of these ratios are of any
perceptual relevance, while in other cases (such as, say, LaMonte Young's music), even
rather complex ratios can be perceived. In all cases there is some degree of latitude,
ranging from perhaps a fraction of a cent to about 20 cents depending on factors such as
these, as to how precisely the ratios need to be tuned. But under no circumstances can I
completely agree with the paraphrase of McLaren that you've provided.

🔗George Zelenz <ploo@mindspring.com>

6/10/2001 3:38:35 PM

Kraig wrote:

>
>
> With No.2 I'll place the music of Terry Riley , La Monte Young,
> Lou Harrison for there sure beauty of intervals against any ET
> composition i have ever heard. It is not without good reason that just
> has attracted these talents. I'm Completely subjective. :)
>

I second this, and offer a toast.

TO SUBJECTIVITY!

GZ

🔗Paul Erlich <paul@stretch-music.com>

6/10/2001 3:48:58 PM

--- In tuning@y..., "X. J. Scott" <xjscott@e...> wrote:
> Joe,
>
> > McLaren states (I paraphrase), "Just Intonation is no particular
> > stopping point in the infinite continuum of pitches of any
> > significance..."
>
> I may be overinterpreting Brian here, but what I myself
> find to be true, and possibly what he means (though I
> am sure he will jump in and clarify this) is that:
>
> 1) just intervals are not usually detectable (unless one
> has damaged their hearing enough that nonlinear effects
> became significant; or when played loud enough that
> nonlinear effects aro also significant) when played as a
> dyadic harmony using sine wave timbres.

That's why I said not to use sine waves.

> The Plomp/Levelt
> experiment bears this out -- the only area of interest in
> sinewave dyadic harmonies is the area near the unison.
>
> Because of this, the specialness of just harmonies using
> more complex or real world harmonic timbres is not because
> of the just intervals between partials but because of the
> unison and near-unison hits among the partials present in
> the dyad.

This is largely correct and given that many composers write for bowed strings, winds,
brass, and voices, which have exactly harmonic partials, JI intervals clearly are "special"
for such composers.

There's more to it, though. What is a pitch? It's our brain's best estimate as to the
fundamental of a best-fit harmonic series to the frequencies present. So even with sine
waves, particularly three or more, there is a difference in the perception when the chord
is a harmonic one compared to when it isn't. For example, if three sine waves are tuned
5:6:7 or 6:7:8, one hears a virtual pitch corresponding to the 1, and the sine waves
"disappear" into the sensation of the timbre. However, if the three sine waves are tuned
11:13:15, which is too high in the harmonic series to be understood as such, one hears a
confused sensation, with _two_ equally convincing candidates for what the pitch is --
one corresponding to a best-fit based on a 5:6:7 interpretation, and one corresponding
to a best-fit based on a 6:7:8 interpretation. You can read more about this in the last few
chapters of _Musical Acoustics_ by Donald E. Hall, and the various academic articles
referenced therein.

🔗Paul Erlich <paul@stretch-music.com>

6/10/2001 3:59:44 PM

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> Cousin Jeff!
> No 1 without elaborating, contradicts 25 year experience with just these intervals. If this
> was true how could Partch have tuned his instruments so easily, on instruments with fast decay and
> high inharmonic timbres.

Isn't it true that, to tune his instruments, Partch first tuned his Chromelodeon, long-
sustaining and rich in exactly harmonic partials, and only then tuned the other
instruments' fundamentals to those of the Chromelodeon?

🔗jpehrson@rcn.com

6/10/2001 5:38:33 PM

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_24755.html#24800

> --- In tuning@y..., jpehrson@r... wrote:
> >
> > McLaren states (I paraphrase), "Just Intonation is no particular
> > stopping point in the infinite continuum of pitches of any
> > significance..."
> >
> > Now is this true or untrue?? Admittedly it flys in the face of
> > Helmholtz, Erlich and, apparently, Daniel Wolf.
>

> I believe it's patently untrue. The best way to demonstrate this is
with two variable-pitch tone generators (don't use sine waves,
though), preferably controlled continuously, as with knobs. Now you
can easily sweep through the entire range of intervals. As you do
> this, you'll notice stretches of confused, "rough", "turbulent"
intervals, punctuated with points of "focus", of "blending",
of "stability". If you stop at one of these points, and
> measure the frequencies, you'll see that the ratio of the
frequencies is a simple-integer ratio -- and I mean simple -- there
probably won't be any higher numbers than 8 in
> these ratios unless you're dealing with ideal conditions of pitch,
timbre, etc. Try this if you can. I tried this when I was very young,
and it's overwhelmingly clear -- as clear as day.
>

Hi Paul...

Thanks for responding to this. In absolutely *no* way am I trying to
start any kind of "flame war" or anything of the kind. I was just
interested in a discussion concerning the paraphrase from Brian
McLaren's "Introduction to Microtonality" CD. I believe the
paraphrase is pretty accurate. I was trying to find the exact quote
from the CD, but I couldn't right off... and I've have to play the
entire thing again to find it... (I already played it twice!) In any
case, I found the comment a little surprising. For me, personally, I
remember experiments that I did in my early 20's with "knob"
oscillators and I remember finding these different effects you
mention, although I had no way of measuring the tones at that time...

> Now whether these qualities have anything to do with music is
another issue.

It seems to me that perhaps McLaren's COMPOSITIONAL focus may be
determining his position on this issue. Most probably, as you
YOURSELF state, Just Intonation intervals have no particular
significance in the COMPOSITIONAL process, other than that determined
by overall culture and the particular composer. Most probably, that
is why McLaren is de-emphasizing the significance of the Just
chords.... he wants people to see them as only part of the
compositional process, essentially equal to everything else from that
viewpoint...

Well, I still wish I had the exact quote, but it will have to wait
until my THIRD listen to the CD... certainly not today...

Thanks for the commentary!

_______ _______ _____
Joseph Pehrson

🔗Kraig Grady <kraiggrady@anaphoria.com>

6/10/2001 6:21:42 PM

Paul!
I think this has more to do where the difference tone is. if the 2 of the 11/13/15 chord is in
the middle of our hearing range, it will sounds as a consonant. Like wise if the 1 is too low in
the 6/7/8 it will sound confused.

Paul Erlich wrote:

> For example, if three sine waves are tuned
> 5:6:7 or 6:7:8, one hears a virtual pitch corresponding to the 1, and the sine waves
> "disappear" into the sensation of the timbre. However, if the three sine waves are tuned
> 11:13:15, which is too high in the harmonic series to be understood as such, one hears a
> confused sensation, with _two_ equally convincing candidates for what the pitch is --
> one corresponding to a best-fit based on a 5:6:7 interpretation, and one corresponding
> to a best-fit based on a 6:7:8 interpretation. You can read more about this in the last few
> chapters of _Musical Acoustics_ by Donald E. Hall, and the various academic articles
> referenced therein.
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

🔗Kraig Grady <kraiggrady@anaphoria.com>

6/10/2001 6:24:55 PM

Paul!
I think i said this afterwards. Still the harmonic of the organ would not match the harmonics of
the instrument being tuned.

Paul Erlich wrote:

> --- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> > Cousin Jeff!
> > No 1 without elaborating, contradicts 25 year experience with just these intervals. If this
> > was true how could Partch have tuned his instruments so easily, on instruments with fast decay and
> > high inharmonic timbres.
>
> Isn't it true that, to tune his instruments, Partch first tuned his Chromelodeon, long-
> sustaining and rich in exactly harmonic partials, and only then tuned the other
> instruments' fundamentals to those of the Chromelodeon?

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

🔗Paul Erlich <paul@stretch-music.com>

6/10/2001 7:01:20 PM

--- In tuning@y..., Kraig Grady <kraiggrady@a...> wrote:
> Paul!
> I think this has more to do where the difference tone is. if the 2 of the 11/13/15 chord is in
> the middle of our hearing range, it will sounds as a consonant. Like wise if the 1 is too low in
> the 6/7/8 it will sound confused.

I agree that this experiment is predicated on a specific register. You can look in Hall to see what
the register actually was. I also agree than 6:7:8 too low will sound confused, and that 11:13:15
might sound clear if voiced in the optimal range, around 3000 Hz.

However, I don't agree that this has anything to do with difference tones. We've gone over this
many times before. The virtual fundamental, in general, is _not_ a difference tone or any other
kind of combinational tone. For example, we've talked about the case where a
harmonic-series-plus-20-Hz-segment is played in sine waves. All the differences between
these sine wave frequencies were exact multiples of 200 Hz. Yet the perceived pitch is not
200 but something like 207 Hz. Not a difference tone, but rather a best-fit fundamental. If the
stimulus is made loud enough, difference tones _will_ be heard -- and they will not agree with
the virtual fundamental. Another reason why JI is special -- only if the sine waves are in JI will the
virtual fundamental agree with a combinational tone.

🔗Kraig Grady <kraiggrady@anaphoria.com>

6/10/2001 7:06:18 PM

J!
His style is more themmatic/counterpuntal in nature, less interested in sonic sounds per se.
JI in the hands of Kyle Gann can be quite counterpuntal but often those inclined away from harmony
would not be interested in JI. This style or approach does not change from tuning to tuning.

jpehrson@rcn.com wrote:

> It seems to me that perhaps McLaren's COMPOSITIONAL focus may be
> determining his position on this issue. Most probably, as you
> YOURSELF state, Just Intonation intervals have no particular
> significance in the COMPOSITIONAL process, other than that determined
> by overall culture and the particular composer. Most probably, that
> is why McLaren is de-emphasizing the significance of the Just
> chords.... he wants people to see them as only part of the
> compositional process, essentially equal to everything else from that
> viewpoint...
>
> Well, I still wish I had the exact quote, but it will have to wait
> until my THIRD listen to the CD... certainly not today...
>
> Thanks for the commentary!
>

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

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