RE: [tuning] Re: planets, gravity, and Darren's one dimensional t uning space

John wrote,

>The
>words energy and entropy are equivalent, depending upon the particular
>model in use.

I don't know -- energy is usual defined in terms such as the gradient of a
potential function, while entropy is defined as

-sum(p*log(p))

where the sum is over a bunch of states and p is the probability of each
state.

Jacky wrote,

>Since harmonic instruments represent a minority on the World Stage of
>music, and true harmonic timbres are very rare in nature (but can
>abound in electronics)

Disagree -- the human voice, bowed strings, brass, and reed instruments have
true harmonic timbres. These sorts of instruments are found all over the
world.

John deLaubenfels wrote,

>See, for example, my praise for his book, "Tuning, Timbre, Spectrum,
>Scale" in:

> http://www.egroups.com/message/tuning/5132

>where, in the accompanying CD, he presents an inharmonic tuning, for
>which the rules for harmony are completely different! (the sensation
>alone is worth the price of the book, howbeit we're talking 50+ bucks).

Several of his pieces (including the piece in question, I believe) have been
available on the Tuning List Tape Swap and the Tuning Punks .mp3 page, and
frankly I don't hear any new rules of harmony at work. In my personal
opinion, tonal harmony is largely a result of the virtual pitch phenomenon
acting on the fundamentals of the tones; the harmonics of the tones will
either support the fundamentals, if they're nearly integer ratios thereof;
or if not, they will sound like distinct tones of their own and "stick out"
with their own melodic and harmonic implications rather than acting merely
as elements of timbre.

John deLaubenfels wrote,

>Paul, either we're talking about completely different tracks or our
>perception is completely different. I refer to tracks 2 through 5 of
>Bill's CD accompanying his book, "Tuning, Timbre, Spectrum, Scale",
>which compare the same small piece in four ways:

> . Harmonic timbres in 12-tET
> . Harmonic timbres in stretched scale
> . Stretched timbres in stretched scale
> . Stretched timbres in 12-tET

>The first and third sound fine; the second and fourth sound awful! Yet,
>to my ear, the stretched timbres don't of their own accord sound all
>that strange. This stuff is a real ear-opener, IMHO!!

I would agree that if the amount of stretching is not too great, one
certainly should match the tuning to the timbre. That doesn't contradict
what I posted before . . .

John deLaubenfels wrote,

>Well, then I don't understand your earlier point at all. In any case,
>we agree, do we not, that integer ratios are inapplicable for reducing
>discordance in inharmonic timbres?

Don't tell Harry Partch!

Seriously, I think that they're inapplicable in the context of utonal chords
and inharmonic timbres, but otonal chords will still have a very strong
effect with inharmonic timbres, as we are wired to seek out harmonic series
in everything we hear -- and in this situation we'd hear several. Sethares
focuses on the critical band roughness component of discordance, while the
virtual pitch ambiguity (harmonic entropy) and combination tone components
are important as well.

John deLaubenfels wrote,

>What to make of these numbers? They would imply a fuzziness to any
>"virtual fundamental"

Yes, exactly my point.

>, and, as far as I can tell, don't provide much
>guidance in forming the best possible intervals between notes.

No, not much.

>If using virtual fundamentals would help in making the alignment, I'm
>not seeing it.

My point was simply that, for harmony with inharmonic timbres, the virtual
fundamental effects and the matching partial effects become incompatible. If
you play an integer otonal chord with inharmonic timbres, you'll get a nice
clear harmonic series above _each_ partial in the lowest "note", which is a
nice effect that some people on the list (I recall Darren Burgess and Carl
Lumma specifically), though the typical roles of timbre and tuning are in
effect switched here! On the other hand, if you play a stretched "otonal"
chord, you'll have a lot less roughness, though the "fuzziness" will of
course be considerable.

John, I'd strongly suggest you look at John R. Pierce's nice little book
_The Science of Musical Sound_. He recounts his own experiences with coming
up with ideas much like Sethares' (in the chapter _Helmholtz and
Consonance_) and then recounts how he had a rude awakening in certain
experiments to test these ideas (in the chapter _Rameau and Harmony_).

So to answer your question, there may be a compromise that would be most
appropriate here -- but since the "fuzziness" won't go away with any tuning,
the roughness component will dominate the compromise, since the roughness
_can_ be completely eliminated here.

Actually, as Terhardt points out, the ideal set of partials for evocation of
virtual pitch are slightly stretched -- as (perhaps relatedly) are the
melodic octaves perceived as correct when sine waves are used. However,
these would imply a theoretical octave of 2.02 or 2.01, so this is not of
much consequence for your example here, where the stretching is an order of
magnitude higher.

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:
>
> My point was simply that, for harmony with inharmonic timbres, the
virtual
> fundamental effects and the matching partial effects become
incompatible.

Paul and John,

The biggest challenge that has confronted me in my exploration of
this, are ways that it can be applied to ensembles of inharmonic
timbres. It seems very easy to bring a solo metallophone instrument
into tune with itself, by matching the its spectrum to the tuning,
and be able to play much more consonant chord simultaneities,
but what sounds good an a single instrument is one thing, and on an
ensemble another.

Any thoughts about how to do this, oh wise ones?

Jacky Ligon

P.S. I have my ways of dealing with it though - just would like to
hear yours!

: )

Jacky wrote,

>The biggest challenge that has confronted me in my exploration of
>this, are ways that it can be applied to ensembles of inharmonic
>timbres. It seems very easy to bring a solo metallophone instrument
>into tune with itself, by matching the its spectrum to the tuning,
>and be able to play much more consonant chord simultaneities,
>but what sounds good an a single instrument is one thing, and on an
>ensemble another.

Well, the tuning considerations involved in combining different instruments
with different overtone structures can be considerable. A very simplistic
beginning to this problem is attempted by, you guessed it, Sethares, who
studies the interaction of a single harmonic timbre (a voice or bowed
string) with a single inharmonic timbre (a typical gamelan instrument) and
comes up with a tuning which resembles one of the typical tunings used in
gamelan music. I wouldn't take this as any kind of explanation of gamelan
tuning (particularly as gamelan tuners seem to treasure, rather than
disdain, beating) -- but it may be interesting for a start.

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:
> Jacky wrote,
>
> >The biggest challenge that has confronted me in my exploration of
> >this, are ways that it can be applied to ensembles of inharmonic
> >timbres. It seems very easy to bring a solo metallophone
instrument
> >into tune with itself, by matching the its spectrum to the tuning,
> >and be able to play much more consonant chord simultaneities,
> >but what sounds good an a single instrument is one thing, and on
an
> >ensemble another.
>
> Well, the tuning considerations involved in combining different
instruments
> with different overtone structures can be considerable. A very
simplistic
> beginning to this problem is attempted by, you guessed it,
Sethares, who
> studies the interaction of a single harmonic timbre (a voice or
bowed
> string) with a single inharmonic timbre (a typical gamelan
instrument) and
> comes up with a tuning which resembles one of the typical tunings
used in
> gamelan music. I wouldn't take this as any kind of explanation of
gamelan
> tuning (particularly as gamelan tuners seem to treasure, rather than
> disdain, beating) -- but it may be interesting for a start.

I realize that one important aspect of his work is to resynthesize
timbres. My interest includes methods of tuning preexisting
inharmonic timbres, which I do not care to resynthesize, and just
want to use "as is".

Let me say one other thing; The overtone structure of real world
inharmonic timbres can change *radically* depending up on where and
how hard the instrument is struck (saw this with my own ears, during
a recent sampling session with gongs and such). This phenomenon can
be very difficult to nail down where ftt is involved. Also with FM
synthesis (for example); dependent upon where you play and how hard
you play, more inharmonic side-bands can be introduced into the
timbre, which in a gong or bell like timbre, would yield very
different fft results.

My point is: Timbre *IS NOT* static. This is the most difficult
obstacle which confronts timbre tuning. Where we can make use of
analysis of static timbres, and use them in our compositions, this
might not apply.

Thanks,

Jacky Ligon

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:

/tuning/message

> My point was simply that, for harmony with inharmonic timbres, the
virtual fundamental effects and the matching partial effects become
incompatible. If you play an integer otonal chord with inharmonic
timbres, you'll get a nice clear harmonic series above _each_ partial
in the lowest "note", which is a nice effect that some people on the
list (I recall Darren Burgess and Carl Lumma specifically), though the
typical roles of timbre and tuning are in effect switched here!

Hi Paul...

This is fascinating, but how, exactly, are the roles of timbre and
tuning switched, again?? I'm not quite getting this...

________ _____ ___ _
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:

> Hi Paul...
>
> This is fascinating, but how, exactly, are the roles of timbre and
> tuning switched, again?? I'm not quite getting this...

Well, if you have an inharmonic timbre whose partials are

a b c d e

and you construct an otonal chord (say, 5-limit), the full set of partials is

1a 1b 1c 1d 1e
2a 2b 2c 2d 2e
3a 3b 3c 3d 3e
4a 4b 4c 4d 4e
5a 5b 5c 5d 5e

Now, if the tones are all struck at the same time, and the envelopes are all the same,
what will you hear? Physically, you're receving the 25 frequecies listed above in
undifferented form. But your brain seeks out the harmonic series, and finds five -- not in
the rows, but in the columns! Hence you're more likely to hear the above as five
_harmonic_ timbres in an inharmonic chord, rather than as five inharmonic timbres in a
harmonic chord.

--- In tuning@y..., PERLICH@A... wrote:
>
> Now, if the tones are all struck at the same time, and the
envelopes are all the same,
> what will you hear? Physically, you're receving the 25 frequecies
listed above in
> undifferented form. But your brain seeks out the harmonic series,
and finds five -- not in
> the rows, but in the columns! Hence you're more likely to hear the
above as five
> _harmonic_ timbres in an inharmonic chord, rather than as five
inharmonic timbres in a
> harmonic chord.

Whazzzup Paul!

Likely true - but an unlikely musical scenario! I would tend to avoid
such a "full fisted" approach on an inharmonic timbre.

Jacky Ligon

--- In tuning@y..., ligonj@n... wrote:
>
> Whazzzup Paul!
>
> Likely true - but an unlikely musical scenario! I would tend to avoid
> such a "full fisted" approach on an inharmonic timbre.
>
> Jacky Ligon

I don't know if it's "unlikely" or "full-fisted", but it certainly goes to show that the integer
harmonic series still has some relevance even when using inharmonic partials -- and if
you try to say otherwise, Kraig Grady will kill you :) :) :) (seriously, would you suggest that
Grady and Partch and Darren Burgess were _completely unjustified) in using simple-
integer ratios with inharmonic timbres?)

--- In tuning@y..., PERLICH@A... wrote:
> --- In tuning@y..., ligonj@n... wrote:
> >
> > Whazzzup Paul!
> >
> > Likely true - but an unlikely musical scenario! I would tend to
avoid
> > such a "full fisted" approach on an inharmonic timbre.
> >
> > Jacky Ligon
>
> I don't know if it's "unlikely" or "full-fisted", but it certainly
goes to show that the integer
> harmonic series still has some relevance even when using inharmonic
partials -- and if
> you try to say otherwise, Kraig Grady will kill you :) :) :)
(seriously, would you suggest that
> Grady and Partch and Darren Burgess were _completely unjustified)
in using simple-
> integer ratios with inharmonic timbres?)

Actually my brother, this has always been my approach as well (for
many, many years)! But I'm leaving the doors of exploration flung
wide open to new possibilities. Can't live any other way.

One question I've always wanted to ask composers who design
instruments - either digitally or acoustic - is do they have to take
the partials into consideration when bring an instrument into tune?
How can we be sure that Partch absolutley did not do this. If he was
tuning by ear, I would allow that perhaps the partials could have
been under consideration.

I have found that it can work well for single instruments, but the
difficulty comes in when one attempts to transpose this onto
ensembles of sounds - as we've discussed. This is where a good
rational pitch set, which compliments inharmonic partials, can be
useful.

Sad to say that I don't think I've ever heard Darren Burgess' music,
and would be delighted to. As all should know, I'll be earger to hear
*any* microtonal work, and give special interest to inharmonic timbre
work - a major area of exploration here. Try writing choral parts for
inharmonic scales; ah, and the voices of angels you will hear!

Thanks,

Jacky Ligon

--- In tuning@y..., ligonj@n... wrote:
>
> One question I've always wanted to ask composers who design
> instruments - either digitally or acoustic - is do they have to take
> the partials into consideration when bring an instrument into tune?
> How can we be sure that Partch absolutley did not do this. If he was
> tuning by ear, I would allow that perhaps the partials could have
> been under consideration.

My understanding is that Partch tuned his Chromolodeon first and then tuned other
instruments to that.

> Try writing choral parts for
> inharmonic scales; ah, and the voices of angels you will hear!

I'm not sure what you have in mind here -- actual human voices singing inharmonic
chords would of course be the antithesis of JI as it is commonly known -- not to imply
that couldn't be lovely . . .

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

/tuning/topicId_17879.html#18036

>
> Well, if you have an inharmonic timbre whose partials are
>
> a b c d e
>
> and you construct an otonal chord (say, 5-limit), the full set of
partials is
>
> 1a 1b 1c 1d 1e
> 2a 2b 2c 2d 2e
> 3a 3b 3c 3d 3e
> 4a 4b 4c 4d 4e
> 5a 5b 5c 5d 5e
>
> Now, if the tones are all struck at the same time, and the envelopes
are all the same, what will you hear? Physically, you're receving the
25 frequecies listed above in undifferented form. But your brain seeks
out the harmonic series, and finds five -- not in the rows, but in the
columns! Hence you're more likely to hear the above as five _harmonic_
timbres in an inharmonic chord, rather than as five inharmonic timbres
in a harmonic chord.

Wow. This is really fascinating! So, if I'm understanding this
correctly, the nature of the TIMBRE will be the basic determinant of
what one is going to hear, and the TUNING of the fundamentals will
take a "secondary" role. I guess that, then, would be what is meant
by the "role reversal..." (??)

_________ ______ __ _
Joseph Pehrson

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

/tuning/message

> --- In tuning@y..., ligonj@n... wrote:
> >
> > Whazzzup Paul!
> >
> > Likely true - but an unlikely musical scenario! I would tend to
avoid such a "full fisted" approach on an inharmonic timbre.
> >
> > Jacky Ligon
>
> I don't know if it's "unlikely" or "full-fisted",

But wait a minute... isn't the approach of using harmonic multiples on
inharmonic timbres what Robert Walker just did to create such
interesting sounds with Fractal Tune Smithy? I believe that's what I
read...

_________ ______ ______ _
Joseph Pehrson

--- In tuning@y..., PERLICH@A... wrote:
> --- In tuning@y..., ligonj@n... wrote:
> >
> > One question I've always wanted to ask composers who design
> > instruments - either digitally or acoustic - is do they have to
take
> > the partials into consideration when bring an instrument into
tune?
> > How can we be sure that Partch absolutley did not do this. If he
was
> > tuning by ear, I would allow that perhaps the partials could have
> > been under consideration.
>
> My understanding is that Partch tuned his Chromolodeon first and
then tuned other
> instruments to that.
>
> > Try writing choral parts for
> > inharmonic scales; ah, and the voices of angels you will hear!
>
> I'm not sure what you have in mind here -- actual human voices
singing inharmonic
> chords would of course be the antithesis of JI as it is commonly
known -- not to imply
> that couldn't be lovely . . .

There's as many kinds of JI as there are Jazz and Blues. As yes, it
can be, and is very lovely to have "inharmonic" choral harmonies.

Pure magic to my ears! The partials of the human voice allow many
miraculous things to happen - the borders of JI can be stretched to
places inconceived of.

JL

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

/tuning/message

>
Try writing choral
> > inharmonic scales; ah, and the voices of angels you will hear!
> I'm not sure what you have in mind here -- actual human voices
singing inharmonic chords would of course be the antithesis of JI as
it is commonly known -- not to imply
> that couldn't be lovely . . .

Ah hoe! The plot, or is it the chord, thickens....

__________ _____ ___
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., PERLICH@A... wrote:
>
> /tuning/message
>
> >
> Try writing choral
> > > inharmonic scales; ah, and the voices of angels you will hear!
> > I'm not sure what you have in mind here -- actual human voices
> singing inharmonic chords would of course be the antithesis of JI as
> it is commonly known -- not to imply
> > that couldn't be lovely . . .
>
> Ah hoe! The plot, or is it the chord, thickens....
>
> __________ _____ ___
> Joseph Pehrson

I didn't want to frighten anyone, but I am the Antithesis.

}: )

Jacky Ligon

--- In tuning@y..., ligonj@n... wrote:

/tuning/message

>
> I didn't want to frighten anyone, but I am the Antithesis.
>
> }: )
>
> Jacky Ligon

Well, danke gott, at least that today is not der "dreizehnte!"

______ _____ _ __
Joseph

--- In tuning@y..., ligonj@n... wrote:

/tuning/topicId_17879.html#17984

> The biggest challenge that has confronted me in my exploration
> of this, are ways that it can be applied to ensembles of
> inharmonic timbres. It seems very easy to bring a solo
> metallophone instrument into tune with itself, by matching
> the its spectrum to the tuning, and be able to play much more
> consonant chord simultaneities, but what sounds good an a
> single instrument is one thing, and on an ensemble another.
>
> Any thoughts about how to do this, oh wise ones?

Hi Jacky,

If I understand correctly what you're asking, a solution I like
is a polymicrotonal one, where each instrument or ensemble of
like instruments is tuned in best accordance (pun fully intended)
to its timbre.

-monz
http://www.monz.org
"All roads lead to n^0"

Joseph wrote,

>Wow. This is really fascinating! So, if I'm understanding this
>correctly, the nature of the TIMBRE will be the basic determinant of
>what one is going to hear, and the TUNING of the fundamentals will
>take a "secondary" role. I guess that, then, would be what is meant
>by the "role reversal..." (??)

Well, what I really meant was that in this case timbre and tuning would
_literally_ switch roles, and instead of perceiving five inharmonic timbres
playing a harmonic chord, you'd perceive five harmonic timbres playing an
inharmonic chord. Each fundamental turns into an overtone of the lowest
fundamental, and each partial of the lowest note turns into a fundamental of
its own, with harmonic partials! It's a complete role-reversal!

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:

/tuning/topicId_17879.html#18080

>
> Well, what I really meant was that in this case timbre and tuning
would _literally_ switch roles, and instead of perceiving five
inharmonic timbres playing a harmonic chord, you'd perceive five
harmonic timbres playing an inharmonic chord. Each fundamental turns
into an overtone of the lowest fundamental, and each partial of the
lowest note turns into a fundamental of its own, with harmonic
partials! It's a complete role-reversal!

This continues to be really interesting.... So, basically the TIMBRE
of each of the 6 inharmonic sounds you used would be the PRIMARY
determinant of PITCH HEIGHT (??) at least insofar as the brain
intreprets it, rather than the pitch height set up in the original
harmonic "transposition.." (??)

Monz wrote,

>Hi Jacky,

>If I understand correctly what you're asking, a solution I like
>is a polymicrotonal one, where each instrument or ensemble of
>like instruments is tuned in best accordance (pun fully intended)
>to its timbre.

Monz, I think you're missing the subtlety of Jacky's point, which is that a
tuning which optimizes a particular timbre for interactions with tones of
like timbre, does not optimize that timbre for interactions with tones of a
_different_ timbre. See my responses . . .

Joseph wrote,

>This continues to be really interesting.... So, basically the TIMBRE
>of each of the 6 inharmonic sounds you used would be the PRIMARY
>determinant of PITCH HEIGHT (??) at least insofar as the brain
>intreprets it, rather than the pitch height set up in the original
>harmonic "transposition.." (??)

Yes, exactly . . . since the relationships _between_ partials from
_different_ "tones" set up by the otonal chord would be more powerful "gel"
that the inharmonic spectrum of the tones. It would be interesting if the
timbres were attacked with human timing, so sounded distinct at first, but
were sustained for a long time . . . perhaps they would then "morph" after
some period of time . . . or maybe it would be analogous to one of those
visual paradoxes where you can see two different images in the same picture
(I'm thinking of the "staircase" illusion and the "young girl/old lady"
illusion, for example).

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:

/tuning/topicId_17879.html#18100
>
> Yes, exactly . . . since the relationships _between_ partials from
> _different_ "tones" set up by the otonal chord would be more
powerful "gel" that the inharmonic spectrum of the tones. It would be
interesting if the timbres were attacked with human timing, so
sounded
distinct at first, but were sustained for a long time . . . perhaps
they would then "morph" after some period of time . . . or maybe it
would be analogous to one of those visual paradoxes where you can see
two different images in the same picture (I'm thinking of the
"staircase" illusion and the "young girl/old lady" illusion, for
example).

Wow... what incredible work for somebody to do!!... Robert Walker??
Could you possibly set this up for us?? I would try to do it myself
but, ah...er... well, I think it might be something best saved for
Robert...

_________ _____ ___ _
Joseph Pehrson

Hi Joseph,

Some time I'll have a play around with timbres and soundfonts and see what
I can do using my souncard, or with AudioCompositor, or other programs.

Meanwhile, it is getting easier and easier to make the harmonic and
inharmonic custom voices in FTS.

I'll add a custom voice consisting of the harmonic series.

You will be able to (for next upload whenever it is)
change the voice for all notes in a c.v. in one click
using Voices | Edit Custom Voices | All instr. = highlight.

So anyone who can load an inharmonic timbre into their
soundcard / synth will just need to edit the harmonic series
c.v. in that way, and select the timbre as the voice.

You can also enter volumes for all the partials in the
c.v. timbre by pasting them all as a single line of text.

(ditto for the pitches, for inharmonic seq. of partials).

Then it will be easy to do any kind of experiment with
the fractal tunes, or sustained chords.

E.g. for a long sustained chord, to set the time for one note
long.

Prob. add lots more there, e.g. inspired by some of
Christopher Bailey's ideas for gong simulation!

But I'll leave most of it to 1.10.

Playing a sustained note in harmonic series in any
timbre will be easy in next upload of FTS
(but not today, - it has still got some loose ends
and things that aren't working quite)

You can do it with the present beta by editing one
of the .ts files that uses harmonic series custom voice
that I've uploaded recently.

Look for an entry something like this:
ipatch 117
Then do a search and replace of 117 by whatever patch
you like to use instead.

That's pretty easy too - let me know if you want more details.

But you can't yet edit the volumes of the partials for the c.v.
that way, they will all be the same. Prob. to get the illusion
you want, you may need them to get quieter as they get
higher in pitch,..

For that, see next upload when I do it.

So, why not have a go yourself then!

Any questions and I'll be delighted to help,

Robert

--- In tuning@y..., "Robert Walker" <robert_walker@r...> wrote:

/tuning/topicId_17879.html#18126

> Hi Joseph,
>
> Some time I'll have a play around with timbres and soundfonts and
see what
> I can do using my souncard, or with AudioCompositor, or other
programs.
>
> Meanwhile, it is getting easier and easier to make the harmonic and
> inharmonic custom voices in FTS.
>
>
> So, why not have a go yourself then!
>
> Any questions and I'll be delighted to help,
>
> Robert

Thanks so much, Robert... this is getting more and more interesting!
I am DEFINITELY going to start working with these timbral changes
and, undoubtedly, will need a little assistance here and there...

Thanks again!!

________ _____ ___
Joseph

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:

/tuning/topicId_17879.html#18090

> Monz wrote,
>
> > Hi Jacky,
>
>
> > If I understand correctly what you're asking, a solution I like
> > is a polymicrotonal one, where each instrument or ensemble of
> > like instruments is tuned in best accordance (pun fully intended)
> > to its timbre.
>
> Monz, I think you're missing the subtlety of Jacky's point,
> which is that a tuning which optimizes a particular timbre for
> interactions with tones of like timbre, does not optimize that
> timbre for interactions with tones of a _different_ timbre. See
> my responses . . .

No, Paul, I got Jacky's point, and I agree that it's a subtle
one. I guess my idea didn't come across well. Here goes another
try...

What I'm trying to say here is that it seems to me that the
best way to integrate the tunings and timbres of an ensemble
of different-sounding instruments is to match the tunings and
timbres (for like groups) as closely as possibly.

The *overall* result, for the ensemble as a whole, would (again,
it seems to me) be the most "harmonious" sound obtainable.
That is, the best blending of all the disparate sonic elements
which concern pitch.

I could be wrong... it would be great to see and hear some
experiments of this. (Out of the question for me to create
right now, unfortunately...)

-monz
http://www.monz.org
"All roads lead to n^0"