Re: [crazy_music] McLaren, Math and Music

Hey Jacky,

Well I agree with everything you've said and the way
you said it too.

- Jeff

Jacky!
OK this is still where i am having problems which lead me to my post
the other day. This appears contradictory and perhaps you can clear this
up for me. I am not saying what you should do but you can't say one
thing and do something else, am i missing something here?

1. If you are proposing not using math as a basis how do you justify
using ET's which out of all tunings is more mathematically based than
any other type of tuning.

JI is at least a very close appoximation to things in nature.You can
hear the series on harmonics on the guitar, with harmonic singing as
well as harmonic flutes.

2. If you are proposing not using math as a basis how do you justify
using
long meters?

jacky_ligon@... wrote:

> When I first got to know Brian McLaren, two things he said to me that
> will resonate with me for all my days, were:
>
> 1. His comments about the importance of Melody in microtonality,
> and music in general. Obviously this *would* carry deep resonance for
> me because my musical and scale design has melody in mind at every
> step.

I believe many others have said this

>
>
> 2. That the West is the only place in the world that invokes
> mathematics in the name of music.

this is true of music throughtout the mideast, india, china and Japan
also.
It is a more northern hemishere phenomenon

>
>
>

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

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

Jacky!
Thanks for clearing this up because i was having a hard time here
making all the pieces work.

I assume you might then agree with me that the problem with math is
not math itself but the misapplication of math in a way that is contrary
to our ear's nature of our perception of sound or our basic intuition.

jacky_ligon@... wrote:

>
> It is true that I have worked with ETs and that I have used
> mathematics to understand *some* things about tuning, but during the
> creative act all this goes into the background, or else merges into
> all the other aspects of creation. I would say that that mathematics
> is not the wellspring of what compels me create music though - only a
> facet. It is valuable as a facet, but not all it's about.

I would imagine that few of us sit around when creating with
complicated charts. And i am sure you would agree with me or i with you
that the part of use that create is different than the part of us that
analysis. And likewise the music art is more than the interaction of
formal relations, these at best being the means in which we produce
something that resonates with our emotions (upper and lower).

> > JI is at least a very close approximation to things in nature.You
> can
> > hear the series on harmonics on the guitar, with harmonic singing as
>
> > well as harmonic flutes.
>
> True - except where inharmonic timbres may dominate the sound of a
> composition. I'm finding value in many kinds of tuning, and as you
> know JI is my first love.

The whole Sethares thing is interesting in that one can tune according
to the timbre, but why then does 12 ET work so well with so many
different timbres? Personally i want a tuning where i can use many
different timbres but why certain things work and others don't is a
mystery. The use of convential instruments bother me at times because
these instruments evolved along with the tuning and the the slight
modifications in their structure were not done with certain intervals in
mind. i can listen to strings do any pythagorean out to the moon but
higher limit JI? well i could do without the Partch Viola and trade it
in for a rebab any day.

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

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

jacky_ligon@... wrote:

>
> Why do stretched and compressed octave tunings sound beautiful to me?

> Can it be explained mathematically why this is so?

there are musical objects that stretch the octaves. The piano for one,
due to the high tension. But this i am sure is only part of the equation
and see no reason not to try to understand what is going on
quantitatively, which might be mathematically decipherable or not. You
are hearing something, not a non something so we should keep looking

> Do these kinds of tunings always "set well" in a lattice way of
> thinking about tunings, and if not is there some other reason why
> they work musically?

I see no reason not a lattice can't be used with a stretch octaves. But
then again lattices are useful for only certain things, if you want to
do those things, use it, other don't.

>
> I'm finding from making music with them that my intuition can be
> rather elastic in this regard. I'm wondering if the conventional
> models of the way we would believe our ear's nature and perception of
> sound works, allows us some leeway to appreciate this kind of tuning,
> while under mathematical analysis it might not hold up. When we
> analyze things mathematically aren't we always basically using some
> kind of subjective rule of measurement and comparison? [Bringing to
> mind mclaren's statement about comparing ETs to JI]
>
> Again - Gamelan is a great example. Somehow I think we'd mutually
> agree that this music is very beautiful to the ear, yet defies much
> of what mathematics might have to say about it. Imagine if the
> tunings of the Gamelan were constructed in the laboratory of the
> microtonal theorist. Do we think they would find them worthy to go
> one set forward and commit to actually creating an ensemble of bronze
> instruments in these tunings or would the microtonal theorist discard
> the shimmering quality and beating of the new found tunings, because
> they didn't "look good" on the lattice? Don't think they are thinking
> in this manner in Bali! ; )

As someone whose main tuning used over the last few years is one version
of Erv Wilson's Meta Slendro. A tuning method he will disclose in el
paso, which can beat more than anything you can imagine. (you can see
the review from the Microfest in the times in this regard). On top of
this i have now 3 vibraphones in this tuning, a set of Meru bass bars, a
pump organ, two small marimbas, two kotos and a hammer dulcimer. I am
doing just what you are describing but not in Bronze.
So you can see that in the proper hands, one can use math and not
apply some arbitrary JI or ET somewhere it doesn't belong. It seems just
as feasible that one could misuse any approach including a non one.

>
>
> Even though I have did some experimentation/recording with matching
> tuning to timbre, and have had some interesting results with this,
> some of my reservations about this echo back to what I said in the
> beginning of this thread, about timbre [acoustic especially, and the
> better sounding electronic timbres] not being static, but
> continuously variable. Each moment it is the same - but different.
> Using FFT to analyze sound samples of Gongs being stroked in various
> places and velocities has revealed to me that depending upon where
> and how hard the gong is stricken, it will bring out totally new
> partials, while some are found in all samples. A great example of
> something that is almost living in you hands as you play it. Same
> thing with my frame drums. A tak and a dum under from the same drum
> under FFT will reveal very different partial structures, while some
> common partials remain. I think many timbres are this way -
> especially the inharmonic ones, so the point is that I feel at best
> all we can hope for is to find some best mean when we think of
> matching tuning to timbre. Perhaps when it is achieved with
> resynthesis, then a match for all timbres can be found - but I think
> generally speaking it is a very complex undertaking to think of ways
> to bring ensembles of timbres into a similar spectrum tuning, where
> resynthesis is not being used. So in a major way, I think what you
> have said in the past about the importance of tuning by the perceived
> fundamentals must be a good rule of thumb for making many kinds of
> timbres work with a given tuning - this has also been my experience
> too, because I know that the music sound good when I play inharmonic
> timbres on stretched or compressed tunings, and in this instance, the
> tuning is not matched to the timbre spectrum. All this is hugely
> interesting stuff to me - just how both of these things seem to be
> valid possibilities. Certainly Bill has did some incredible music
> with this, which I'm in total admiration and awe of.
>
> Rebab is cool!

I have constantly drawn back to Gagaku which has it's origin in
Afghanistan, of which the civilization from which it came is gone
without a trace. This is according to Chinese and Japanese sources.
(This area is also where all ceremonial magic has been traced by
anthropologist BTW)
Anyway here we have more than one tuning going on. Pythagorean in
the strings. With each of the wind groups having their own particular
intonational approaches. Notice how the flutes move almost is a very
tight little clusters.
Subharmonics like scales on the oboe. Basically we have parallel tunings
having a similar structure. To do such a thing today or in the future is
going to require much more work on all our part! And the place where
this work happens will be in the trenches and away from the calculator!

>
>
> Jacky

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

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

> Why do stretched and compressed octave tunings sound beautiful to
> me?
>
> Can it be explained mathematically why this is so?

Jacky,

It is not mathematics, but psychology that attempts to deal with
the perception of beauty. There may be something about human
physiology that makes octave stretching and compressing sound
good to us, and then it would be psychoacoustics, and still not
math, that would step up to bat.

I am not aware of anything in psychoacoustics that would explain
your observation. This definitely does not mean that nothing
exists. I am familiar with several attempts, including ones by
a fellow named Terhardt (who has his own web page), but none
that I have seen are satisfactory to me. Brian McLaren and Paul
Erlich are both more read on this topic than I.

Even if no results exist in this area, it certainly would not
mean that your observation does not warrant a new study.

> Do these kinds of tunings always "set well" in a lattice way of
> thinking about tunings, and if not is there some other reason why
> they work musically?

Usually (but not always), octaves are completely ignored (do not
appear) in lattice diagrams. In any case, I do not know of a way
that lattices could shed any light on octave compression or
expansion. A lattice is just a picture that makes it easy to
see consonances formed by a tuning or scale.

> When we analyze things mathematically aren't we always basically
> using some kind of subjective rule of measurement and comparison?

Generally, mathematical statements do not make value judgements.
It takes a human interpreter to do that!

> Again - Gamelan is a great example. Somehow I think we'd mutually
> agree that this music is very beautiful to the ear, yet defies much
> of what mathematics might have to say about it.

Does it?

> Imagine if the tunings of the Gamelan were constructed in the
> laboratory of the microtonal theorist. Do we think they would find
> them worthy to go one set forward and commit to actually creating
> an ensemble of bronze instruments in these tunings or would the
> microtonal theorist discard the shimmering quality and beating of
> the new found tunings, because they didn't "look good" on the
> lattice? Don't think they are thinking in this manner in Bali!

The only microtonal theorist I know of who has studied gamelan
music is Bill Sethares (Bill Alves, Lou Harrison, and others
have mainly studied other aspects of gamelan music, apart from
tuning). If memory serves, he was able to take a timbre of a
struck metal bar, apply a formula to it that is supposed to
describe how beating works, and wind up with a scale that is
very similar to scales actually used in Indonesia. His work
hasn't been rigorously peer-reviewed, and even if it had, such a
result does not (nor does Bill claim that it does) amount to a
proof that gamelan tunings are chosen to minimize beating. Bill's
book, if you don't already have it, is available from Amazon.com.

-Carl

> there are musical objects that stretch the octaves. The piano for
> one, due to the high tension.

Hmm. I thought that higher-tension strings actually behave more
harmonically. Maybe JdL can help us out here.

> So you can see that in the proper hands, one can use math and
> not apply some arbitrary JI or ET somewhere it doesn't belong. It
> seems just as feasible that one could misuse any approach including
> a non one.

Perfectly spoken!

>> Rebab is cool!
>
> I have constantly drawn back to Gagaku which has it's origin in
> Afghanistan, of which the civilization from which it came is gone
> without a trace.

I don't actually know what a Rebab or Gagaku is, if anyone would
like to explain it?

-Carl

Hi Carl,

--- In crazy_music@y..., carl@l... wrote:
> The only microtonal theorist I know of who has studied gamelan
> music is Bill Sethares (Bill Alves, Lou Harrison, and others
> have mainly studied other aspects of gamelan music, apart from
> tuning).

I believe Daniel Wolf has also studied gamelan in a somewhat similar
vein as Bill, maybe not in the same way, but certainly has spent time
on it.

Cheers,
Jon

carl@... wrote:

>
> I don't actually know what a Rebab

a bowed string instrument introduced into indonesia fro mthe persians. a
skin instead of a wood body as in a violin it sounds more nasal in
quality as a violin through a cheaop AM radio. I love it too although at
first hearing it might take you back.

> or Gagaku is, if anyone would
> like to explain it?

Gagaku is the court music of Japan and its members are descended from
members of the orchestra in i believe in the 16th and 17th century
although the music goes back much further. It is rthe the oldest
existing orchestra in the world. recordings are available and i don't
know anyone who doesn't like it.

>
>

-- 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 wrote:]
>>there are musical objects that stretch the octaves. The piano for
>>one, due to the high tension.

[Carl Lumma:]
>Hmm. I thought that higher-tension strings actually behave more
>harmonically. Maybe JdL can help us out here.

The inharmonicity of piano strings is due to limited bending
flexibility, so that higher harmonics have an effectively higher spring
constant to push against than they would if the string were infinitely
flexible.

This implies that any _given_ string is more harmonic at higher tension
than at low (bending flexibility is relatively less important). But,
as tensions go up, so must the thickness of the string that will take
the tension without breaking.

Since a thicker string has bending stiffness that increases faster than
string area (assuming a uniform cross-section), the statement that
higher tensions lead to greater inharmonicity is correct, I believe.

JdL

>> I don't actually know what a Rebab
>
> a bowed string instrument introduced into indonesia from the
> persians. a skin instead of a wood body as in a violin it sounds
> more nasal in quality as a violin through a cheaop AM radio. I
> love it too although at first hearing it might take you back.

Thanks!

>> or Gagaku is, if anyone would
>> like to explain it?
>
> Gagaku is the court music of Japan and its members are descended
> from members of the orchestra in i believe in the 16th and 17th
> century although the music goes back much further. It is the the
> oldest existing orchestra in the world. recordings are available
> and i don't know anyone who doesn't like it.

Cool. Can you recommend a recording?

-Carl

> [Carl Lumma:]
>>Hmm. I thought that higher-tension strings actually behave more
>>harmonically. Maybe JdL can help us out here.
>
> The inharmonicity of piano strings is due to limited bending
> flexibility, so that higher harmonics have an effectively higher
> spring constant to push against than they would if the string were
> infinitely flexible.

Right.

> This implies that any _given_ string is more harmonic at higher
> tension than at low (bending flexibility is relatively less
> important).

Ah, that's what I never understood.

> But, as tensions go up, so must the thickness of the
> string that will take the tension without breaking.

Really? Think the move from iron and brass to steel may have
helped?

> Since a thicker string has bending stiffness that increases faster
> than string area (assuming a uniform cross-section), the statement
> that higher tensions lead to greater inharmonicity is correct, I
> believe.

Why, then, did pianos evolve higher and higher string tension?
More amplitude?

-Carl

Carl!
Reading back of my post i realize that 2 in the morning is not the
best time to answer questions:)

carl@... wrote:

>
> Cool. Can you recommend a recording?

the best first

Gagaku - Japanese traditional music king record
KICH 2001

GAGAKU - COURT MUSIC OF JAPAN JVC VICG-5354-2

GAGAKU- ANCIENT JAPANESE COURT AND DANCE MUSIC. LEGACY CD402

NOTICE HOW INVENTIVE THEY ARE WITH THE TITLES:)

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

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

[Carl Lumma:]
>>>Hmm. I thought that higher-tension strings actually behave more
>>>harmonically. Maybe JdL can help us out here.

[I wrote:]
>>The inharmonicity of piano strings is due to limited bending
>>flexibility, so that higher harmonics have an effectively higher
>>spring constant to push against than they would if the string were
>>infinitely flexible.

[Carl:]
>Right.

[JdL:]
>>This implies that any _given_ string is more harmonic at higher
>>tension than at low (bending flexibility is relatively less
>>important).

[Carl:]
>Ah, that's what I never understood.

[JdL:]
>>But, as tensions go up, so must the thickness of the
>>string that will take the tension without breaking.

[Carl:]
>Really? Think the move from iron and brass to steel may have
>helped?

Helped in that iron/steel can take more stress than brass, so the
strings can be thinner.

[JdL:]
>>Since a thicker string has bending stiffness that increases faster
>>than string area (assuming a uniform cross-section), the statement
>>that higher tensions lead to greater inharmonicity is correct, I
>>believe.

[Carl:]
>Why, then, did pianos evolve higher and higher string tension?
>More amplitude?

That and longer sustain, I believe. We should get someone who's a
bigger expert in pianos to comment; I'm getting beyond my field of
knowledge here.

JdL

> [Carl:]
> >Really? Think the move from iron and brass to steel may have
> >helped?
>
> Helped in that iron/steel can take more stress than brass, so the
> strings can be thinner.

Cool (that's what I meant).

> [Carl:]
> >Why, then, did pianos evolve higher and higher string tension?
> >More amplitude?
>
> That and longer sustain, I believe. We should get someone who's a
> bigger expert in pianos to comment; I'm getting beyond my field of
> knowledge here.

You've been very helpful, and sometimes piano experts don't know
much about physics! Ed Foote is probably an exception... is he on
this list?

I'd make a small wager that you're right, John (that modern pianos
are less harmonic than fortepianos); I happened to get invited to
a private concert of historical pianos in San Francisco the other
day, and I was reminded how "nasal"/"vocal" their timbre is, when
compared to a modern piano.

-Carl