Re: [LAD] Music, Undecidability, and the tiling problem (was Re: update: OT-ish: realtime 2d placement algorithms :-/)

2010-05-28 Thread Jens M Andreasen

On Thu, 2010-05-27 at 13:54 -0500, Charles Henry wrote:
 I would like a computer to be able to say, This would sound good, if
 I were a human.  Better yet, I'd like the computer to describe it to
 me in numbers that I myself could not calculate.

The question then becomes: Do androids really dream of electric sheep,
and if so, why would we care?

   - Computer, explain: Like tears in rain ?!


Ravi Shankar in one his masterclasses (televised here recently) talked
about hitting an inner melancholic string. If you can find that and get
it to resonate so you can feel it, then others will feel it too. This is
to a certain degree bound to be dependent on the cultural background of
the involved parties, what kind of musical vocabulary they possess - not
all elements of music can easily be explained by heartbeats or simple
Pythagorean relationships, and just like with any other language you may
hit an initial language barrier where it doesn't matter how beautiful a
poem or well written a scientific article you present; if the audience
do not recognize the words it will be in vain.

As an aside, this is not in any way to say that you need to understand
the /lyrics/ of a song to get the underlying musical structure -
certainly not if the structure is very direct and efficiently exposed. 

I believe that just about anybody on this planet would be able to
understand that these tongue wrestling Karelian chicks easily could eat
up Pythagoras in a heartbeat:

Värttinä - Käppee [*]
 http://www.youtube.com/watch?v=t4YRT-MZR_U



Keith Emerson, while working on the Trilogy album, also talked about
searching for a kind of resonance with inner emotions - doing it by
actually living them out on the piano - and then how he would use formal
composition only at a later stage, as a touch-up to make ends meet. So
here again we have an expert in the field in favor of using your own
mind and mental abilities as the primary tool. It makes perfect sense to
me - because, hopefully, the intended audience will be a lot more like
people like yourself rather than, say, people from Mars.

Emerson - Composing The Endless Enigma
 http://www.youtube.com/watch?v=abVhSCzByw8

Judging by the number of ambitious ELP covers on YouTube - not all of
them equally interesting - he did manage to hit a note within quite a
few, and still do. As an example, here a really cool French acoustic
jazz rendering with strings. No Hammond organs was stabbed to death
during this performance:

Jad  Den - Trilogy
  http://www.youtube.com/watch?v=xNxoIDPoURY


So there you have it, at the end of the day, when the last note has been
written down and  gone to print, as a composer - human or inhuman - you
would still end up being at the complete mercy of the musicians who are
eventually going to play your music. It is their sound judgment while
being in the process of making what was yours into their own, that
decides whether the music will finally reach out to a real human
audience.

If they then in that process are not listening for that inner resonance
Shankar talked about, then that just won't happen. You will instead end
up with something only a refrigerator could enjoy. And even if computers
one day, somehow, might be programmed to elegantly dream of electric
sheep, it will still be a poor substitute for us.

Because we are not.

/j


* For an alternative rendering of Käppee, try: Бони НЕМ :)
  http://www.youtube.com/watch?v=to12RY_p2Rs


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Re: [LAD] Music, Undecidability, and the tiling problem (was Re: update: OT-ish: realtime 2d placement algorithms :-/)

2010-05-27 Thread Charles Henry
On Wed, May 26, 2010 at 5:14 PM, Paul Davis p...@linuxaudiosystems.com wrote:


 On Wed, May 26, 2010 at 5:35 PM, Charles Henry czhe...@gmail.com wrote:

  The degree to which computers can
 compose music depends on the success of modeling musical experience in
 humans.

 I'm willing to grant you the benefit of the doubt with regards this claim,
 because I suspect you mean it in a different way than you wrote it. I don't
 think that having a model of human musical experience is at all a necessary
 component of computer composition, just as it isn't for human composition. I
 feel that this can be said with some confidence given the fact that
 *different* humans have wildly different musical experiences when presented
 with the same material. There is no comprehensive model of human musical
 experience, because there is no comprehensive human musical experience.

True, there's a lot going on and a lot of factors to consider.  I
should have said, at some level of musical experience, because we
all have a lot in common.  Barring amusia or any other major hearing
difficulty, people's sensory experience is much the same.  Up to the
primary auditory cortex, the auditory system is highly specialized.
It's a neural architecture driven by evolution in pursuit of specific
auditory functions, that precedes learning and exposure to music.

For example, pitch perception is no longer considered a learned,
template-matched response (as it has been debated since the 60s/70s),
but is intrinsic to neurons themselves (see works by Julyan (JHE)
Carwright and Dante Chialvo, for reference).

At some level of conscious experience, we all hear the same things.
However a powerful model should also be able to explain why people
hear things differently.

  As musicians and composers, we approach the tiling problem
 with a set of techniques, instruments, and vocabulary.  We are able to
 get direct, immediate feedback on the effectiveness of a giving
 tiling, which computers, at present, cannot.

 Not sure about this either. Its only been in the very recent past that human
 composers could compose anything for an ensemble and get direct immediate
 feedback on the effectiveness. In fact, a lot of the skill of the composers
 of western classical music from the baroque era on seem to hinge on their
 ability to *imagine* what the composition would sound like rather than have
 any direct, immediate feedback on their ideas.

I perhaps should have used the term capable rather than able, b/c
what I was really getting at was the complete lack of a computer's
ability to say, this sounds good :)

I would like a computer to be able to say, This would sound good, if
I were a human.  Better yet, I'd like the computer to describe it to
me in numbers that I myself could not calculate.

There's certainly no point in having a computer tell me what I already
know, because I was there, I heard it, and I know what I like.  But I
also can't listen to all the possibilities of music, though a
sufficiently powerful computer could do so.
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Re: [LAD] Music, Undecidability, and the tiling problem (was Re: update: OT-ish: realtime 2d placement algorithms :-/)

2010-05-26 Thread Lorenzo



Paul Davisp...@linuxaudiosystems.com:
 

this might be how users of ableton live think about making music, and more 
generally, users of computer software aimed at pattern-based music 
composition/creation.

but i would submit that if you offered this description of making music to 
musicians who play instruments or sing, they would find it unrecognizable.
   
Well... I guess one important element in the tiling/sequencing issue 
(forgive me for my lack of the exact mathematical knowledge) is 
time-domain. Much of Music and it's drama, versus for instance painting, 
is time: suspense, arousal/relaxation etc. have to do with time. So if 
you take a piece which are the 'tiles'? Measures? themes of the 'sonata' 
form? Simply recurring elements?
So if on the one hand many academics disregard 'quality' composition as 
a mere juxtaposition of cool sounding melodies or progressions, on the 
other hand it's true that the time-domain calls for some sort of tiling 
in the sense that something comes after something

Mathematics is fundamental to music -- everything from the
relationship of notes to frequency, to what people consider musical,
or rhythmic... has to do with math, group theory, etc.
 


This is putting the cart before the horse. People were making music
long before there was any remotest concept of mathematics. Many of us
still work on the basis of just noodling about and 'ooo, that sounds
nice' without the slightest thought of relationships etc.
   
Ok but the fact that people used mathematical relationships without 
being fully aware of them (e.g. I IV V I progression) doesn't mean the 
relationships don't exist or aren't important. The whole 'western' tonal 
system is heavily dependent on this 'maths' we like it or not :)

The only time I ever think about chords, progressions, is when I've
more-or-less finished a composition and/or want to collaborate with
someone else.

When I was a child, I put together a construction of timber and waxed
string. To this day I don't have the faintest idea what the string
tunings were. I just know it produced some lovely sound combinations.

Group/orchestral instrument  synth makers are no doubt deeply involved
in the mathematics of their designs, but the players don't necessarily
have any concept of this.

A friend of mine is a member of a local choral group. He can't read
music, just uses the dots as a vague reminder of when bits go up, down
speed up or slow down. He seems quite happy like that.

There may be incredible mathematical 'truths' in music, but I think it
will be a very sad day when people concentrate on these rather than
just having fun.
   
Being (as I said) a musician and not a mathematician I have to say that 
I don't like much this kind of maths=boring=kills the fun etc. When I 
started studying electronic music and also some of the physics and maths 
behind it I was clearly fascinated to learn some of the things behind 
music, and I still have great fun making it.. but of course that's me :)


Lorenzo
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Re: [LAD] Music, Undecidability, and the tiling problem (was Re: update: OT-ish: realtime 2d placement algorithms :-/)

2010-05-26 Thread Charles Henry
On Tue, May 25, 2010 at 3:33 PM, Chris Cannam
can...@all-day-breakfast.com wrote:

 I think the point Neils has is just that the outcome of your noodling
 is somewhat independent of your explicit intention.  Notes that sound
 satisfying together are probably going to sound satisfying largely
 because of some intrinsic mathematical relationship, or at least
 something that is probably open to analysis to some extent but that
 you don't yourself understand or plan.  Quite an interesting
 philosophical avenue here, and one that's fairly well trodden in other
 fields (ask an English theory student about Wimsatt and Beardsley).

I've been reluctant to weigh in, because I just know I'm going to blah
blah about math, waste time, and no one will care :)  I'm good at it.

When we consider the analysis of what sounds good, we are probing a
psychological question.  The mind, being completely un-observable and
distinct in study from the brain itself, is impossible to measure
directly.  We can model the mind, and analyze whether or not our model
fits with observed behavior.  The actual intrinsic math that goes on
in the brain and its counterpart, the mind, cannot be exactly known.
So, what we do is model the various interacting processes that make up
our direct experience of music and sound.  This approach is, in fact,
objective despite the fact that we may not be able to explain all of
the significant interpersonal and moment-to-moment sources of
variation that affect our experience.

It's really an exciting time for the study of music psychology (and
I've been saying so for 10 years).  The degree to which computers can
compose music depends on the success of modeling musical experience in
humans.  As musicians and composers, we approach the tiling problem
with a set of techniques, instruments, and vocabulary.  We are able to
get direct, immediate feedback on the effectiveness of a giving
tiling, which computers, at present, cannot.  Currently, computers
have expanded our techniques and instruments while people have
expanded their vocabulary to compose new and novel music with them.

The point I'm getting at:  the structure isn't in the music itself,
it's in the mind of the listener.

I've been toying around with the idea of modeling high-dimensional
psychoacoustic spaces as non-linear manifolds (I'll skip the subject
for now, b/c I'm not sure I can describe it).  Because I intend to
work on it, I do think that successive approximations through modeling
are possible that will push the outer boundary of musical vocabulary
and instruments further than musicians and composers alone could.

Chuck
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Re: [LAD] Music, Undecidability, and the tiling problem (was Re: update: OT-ish: realtime 2d placement algorithms :-/)

2010-05-26 Thread Paul Davis
On Wed, May 26, 2010 at 5:35 PM, Charles Henry czhe...@gmail.com wrote:

  The degree to which computers can
 compose music depends on the success of modeling musical experience in
 humans.


I'm willing to grant you the benefit of the doubt with regards this claim,
because I suspect you mean it in a different way than you wrote it. I don't
think that having a model of human musical experience is at all a necessary
component of computer composition, just as it isn't for human composition. I
feel that this can be said with some confidence given the fact that
*different* humans have wildly different musical experiences when presented
with the same material. There is no comprehensive model of human musical
experience, because there is no comprehensive human musical experience.


 As musicians and composers, we approach the tiling problem
 with a set of techniques, instruments, and vocabulary.  We are able to
 get direct, immediate feedback on the effectiveness of a giving
 tiling, which computers, at present, cannot.


Not sure about this either. Its only been in the very recent past that human
composers could compose anything for an ensemble and get direct immediate
feedback on the effectiveness. In fact, a lot of the skill of the composers
of western classical music from the baroque era on seem to hinge on their
ability to *imagine* what the composition would sound like rather than have
any direct, immediate feedback on their ideas.



 The point I'm getting at:  the structure isn't in the music itself,
 it's in the mind of the listener.


I'm with you 100% here. For years I've been trying to figure out what the
music I like all has in common. There must be something, some common
experience i told myself. I *must* be able to find it. Its only been in the
last couple of years that I've realized I had this ass backwards. All the
music I like has one and only one thing in common: me. I, the humble
listener, am the thing that unites the bach cello suites with steve roach
with touamani diabate with shawn lane with steve reich with the cinematic
orchestra with interpol (to name just a few). not the music, not the
structure. the listener is at the center of it all, and each listener is a
different locus where some kind of rorschach-like experience takes places
uniting musical experiences in unpredictable and, I suspect, utterly
un-musical ways.
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[LAD] Music, Undecidability, and the tiling problem (was Re: update: OT-ish: realtime 2d placement algorithms :-/)

2010-05-25 Thread Niels Mayer
Related to my last reply to your question about the tiling problem
vs undecidability...

Ever since they started putting out relevant articles for computer
scientists (in the last year), the American Math Society monthly
Notices has gone from dull to fascinating; in the spirit of
open-source, all the articles are available free and online.

The latest ( http://www.ams.org/notices/201003/ ), focusing on
Cryptography issues, has an excellent article that goes into the
tiling problem in great detail -- and yet is a very clear explanation
(IMHO) that isn't predicated on incomprehensible (to the general
public) mathematical formalisms.

http://www.ams.org/notices/201003/rtx100300343p.pdf
Can't Decide? Undecide! by Chaim Goodman-Strauss
See also: http://www.srcf.ucam.org/~jsm28/tiling/

I've posted previously about other excellent articles in a previous
issue Mathematics and the Arts ( http://www.ams.org/notices/201001/
) with a though-provoking introductory essay by Sir Michael Atiyah :

 In the broad light of day mathemati-
 cians check their equations and their
 proofs, leaving no stone unturned in
 their search for rigour. But, at night,
 under the full moon, they dream, they
 float among the stars and wonder at
 the miracle of the heavens. They are
 inspired. Without dreams there is no
 art, no mathematics, no life.

Niels
http://nielsmayer.com

PS: I think the tiling problem is actually a direct analogy to music
making... which involves fitting together tiles (musical passages,
patterns, etc) that are highly constrained in terms of geometry
(pitch, key, time-signature, BPM, starting and ending pitches or
chords). Music making is clearly an undecidable problem, which is
where human creativity comes in. Can computers help us tile music
more easily and therefore augment our musical creativity??
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Re: [LAD] Music, Undecidability, and the tiling problem (was Re: update: OT-ish: realtime 2d placement algorithms :-/)

2010-05-25 Thread Paul Davis
On Tue, May 25, 2010 at 11:48 AM, Niels Mayer nielsma...@gmail.com wrote:


 PS: I think the tiling problem is actually a direct analogy to music
 making... which involves fitting together tiles (musical passages,
 patterns, etc) that are highly constrained in terms of geometry
 (pitch, key, time-signature, BPM, starting and ending pitches or
 chords). Music making is clearly an undecidable problem, which is
 where human creativity comes in. Can computers help us tile music
 more easily and therefore augment our musical creativity??


this might be how users of ableton live think about making music, and more
generally, users of computer software aimed at pattern-based music
composition/creation.

but i would submit that if you offered this description of making music to
musicians who play instruments or sing, they would find it unrecognizable.
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Re: [LAD] Music, Undecidability, and the tiling problem (was Re: update: OT-ish: realtime 2d placement algorithms :-/)

2010-05-25 Thread Arnout Engelen
On Tue, May 25, 2010 at 11:59:45AM -0400, Paul Davis wrote:
 On Tue, May 25, 2010 at 11:48 AM, Niels Mayer nielsma...@gmail.com wrote:
  music making involves fitting together tiles (musical passages,
  patterns, etc) that are highly constrained in terms of geometry
  (pitch, key, time-signature, BPM, starting and ending pitches or
  chords). 
 
 but i would submit that if you offered this description of making music to
 musicians who play instruments or sing, they would find it unrecognizable.

Actually, I think most musicians would recognise this concept (though perhaps
not when explained with too technical nomenclature), especially those who ever
dabbled in composition, improvisation or even just playing together with 
someone else. Generally, a 'pleasing' piece contains enough 'structure' (chord
progressions, chorus/verse/chorus, melody line vs counter-melody, even 'genre'
in a way, etc) for the structure to be recognisable (instead of dissonant and 
random), yet not so much that it'd get predictable/boring.

It doesn't seem far-fetched to use a computer to recognise (impro-visor) and/or
apply (sibelius/finale plugins etc) those structures - at least to some extent.
How far this envelope can be pushed and integrated into a composers' workflow -
well - that's just interesting :).


Arnout
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Re: [LAD] Music, Undecidability, and the tiling problem (was Re: update: OT-ish: realtime 2d placement algorithms :-/)

2010-05-25 Thread Niels Mayer
Paul Davis p...@linuxaudiosystems.com:
 this might be how users of ableton live think about making music, and more 
 generally, users of computer software aimed at pattern-based music 
 composition/creation.

 but i would submit that if you offered this description of making music to 
 musicians who play instruments or sing, they would find it unrecognizable.


Mathematics is fundamental to music -- everything from the
relationship of notes to frequency, to what people consider musical,
or rhythmic... has to do with math, group theory, etc.

Ultimately, it doesn't matter what musicians recognize... what
matters is what music *is* -- and when that *is* causes an audience to
cheer, be moved emotionally, get up and dance, etc. Chances are,
anybody too close to their own subject will be unable to actually
recognize it's true shape and meaning -- due to can't see the forest
for the trees syndrome Computer tools, pattern-based or not, are
there to  help us see that forest, (but usually lead us down the
garden path instead).

Sources:

Book: David Wright's Mathematics and Music

Book: J. Fauvel, R. Flood, and R. Wilson (eds.), Music and
Mathematics: From Pythagoras to Fractals, Oxford,
New York, 2003.

http://www.sciencemag.org/cgi/content/full/313/5783/72/DC1
http://www.sciencemag.org/cgi/data/313/5783/72/DC1/1
The Geometry of Musical Chords by Dmitri Tymoczko

http://www.ams.org/notices/201001/rtx100100030p.pdf
Music: Broken Symmetry, Geometry, and Complexity
( http://www.uwec.edu/walkerjs/MBSGC/ )
 excerpt .
Example 15 (Melody and rhythm in “Unsquare
Dance”). In the 1961 Dave Brubeck Quartet’s
recording of “Unsquare Dance” [94], there is an
amazing performance involving hand claps, piano
notes, and bass notes all played in the unusual
time signature of 7 . In Figure 16 we show our
analysis of the melody and rhythm in a passage
from “Unsquare Dance”. We used three different
frequency ranges from the spectrogram to isolate
the different instruments from the passage. The
passage begins with a transition from rapid drum-
stick strikings to hand clappings when the piano
enters. The rhythm of the hand clappings plus
piano notes has a 7 time signature. Notice that the
bass notes are playing with a simple repetition
of 4 beats that helps the other musicians play
within this unusual time signature. In sum, the
analysis shown in Figure 16 provides quantitative
evidence for the “tightness” (rhythmic coherence)
with which these musicians are performing.


Niels
http://nielsmayer.com
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Re: [LAD] Music, Undecidability, and the tiling problem (was Re: update: OT-ish: realtime 2d placement algorithms :-/)

2010-05-25 Thread Folderol
On Tue, 25 May 2010 12:31:57 -0700
Niels Mayer nielsma...@gmail.com wrote:

 Paul Davis p...@linuxaudiosystems.com:
  this might be how users of ableton live think about making music, and more 
  generally, users of computer software aimed at pattern-based music 
  composition/creation.
 
  but i would submit that if you offered this description of making music to 
  musicians who play instruments or sing, they would find it unrecognizable.
 
 
 Mathematics is fundamental to music -- everything from the
 relationship of notes to frequency, to what people consider musical,
 or rhythmic... has to do with math, group theory, etc.


This is putting the cart before the horse. People were making music
long before there was any remotest concept of mathematics. Many of us
still work on the basis of just noodling about and 'ooo, that sounds
nice' without the slightest thought of relationships etc.

The only time I ever think about chords, progressions, is when I've
more-or-less finished a composition and/or want to collaborate with
someone else.

When I was a child, I put together a construction of timber and waxed
string. To this day I don't have the faintest idea what the string
tunings were. I just know it produced some lovely sound combinations.

Group/orchestral instrument  synth makers are no doubt deeply involved
in the mathematics of their designs, but the players don't necessarily
have any concept of this.

A friend of mine is a member of a local choral group. He can't read
music, just uses the dots as a vague reminder of when bits go up, down
speed up or slow down. He seems quite happy like that.

There may be incredible mathematical 'truths' in music, but I think it
will be a very sad day when people concentrate on these rather than
just having fun.

-- 
Will J Godfrey
http://www.musically.me.uk
Say you have a poem and I have a tune.
Exchange them and we can both have a poem, a tune, and a song.
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Re: [LAD] Music, Undecidability, and the tiling problem (was Re: update: OT-ish: realtime 2d placement algorithms :-/)

2010-05-25 Thread Chris Cannam
On Tue, May 25, 2010 at 9:07 PM, Folderol folde...@ukfsn.org wrote:
 On Tue, 25 May 2010 12:31:57 -0700
 Niels Mayer nielsma...@gmail.com wrote:
 Mathematics is fundamental to music -- everything from the
 relationship of notes to frequency, to what people consider musical,
 or rhythmic... has to do with math, group theory, etc.

 This is putting the cart before the horse. People were making music
 long before there was any remotest concept of mathematics. Many of us
 still work on the basis of just noodling about and 'ooo, that sounds
 nice' without the slightest thought of relationships etc.

I think the point Neils has is just that the outcome of your noodling
is somewhat independent of your explicit intention.  Notes that sound
satisfying together are probably going to sound satisfying largely
because of some intrinsic mathematical relationship, or at least
something that is probably open to analysis to some extent but that
you don't yourself understand or plan.  Quite an interesting
philosophical avenue here, and one that's fairly well trodden in other
fields (ask an English theory student about Wimsatt and Beardsley).

As an angle for compositional software, this suggests that if you can
begin to model what actually happens, you may be able to help to
short-circuit your limited understanding of your own work.  The
problem with that (as I think Paul was saying?) is that as long as the
model can be comprehended, the departures from it will continue to be
more interesting than the model itself.

Excuse me, I've probably had a glass of interesting Croatian red too many.


Chris
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Re: [LAD] Music, Undecidability, and the tiling problem (was Re: update: OT-ish: realtime 2d placement algorithms :-/)

2010-05-25 Thread fons
On Tue, May 25, 2010 at 03:46:23PM -0400, Paul Davis wrote:

 On Tue, May 25, 2010 at 3:31 PM, Niels Mayer nielsma...@gmail.com wrote:
 
 
  Ultimately, it doesn't matter what musicians recognize... what
  matters is what music *is*
 
 
 i believe it was lord kelvin who once said don't mistake your models for
 reality.
 
 anyone who thinks that there is a single way to adequately describe music
 clearly hasn't listened to enough of it yet.

True. After probably more than half of the time I'll have to 
understand how music works and why we are so sensitive to it,
I'm nowhere at all. It's way too complicated. 

The 'math' relation can't be ignored. Clearly our brain loves
to discover and decode patterns, and see expectations based on
them either first contrasted and then confirmed.

I'm not a big Arvo Part fan, but I do like some his works. One
of the best known ones, 'Fratres' [*] is very 'mathematical',
you can describe it by 3 or 4 nested for() loops with very
little code inside. But it has this haunting beauty that 
works even if you don't consciously discover the structure.

Ciao,

[*] http://www.youtube.com/watch?v=r4UecUwdalI

-- 
FA

O tu, che porte, correndo si ?
E guerra e morte !
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Re: [LAD] Music, Undecidability, and the tiling problem (was Re: update: OT-ish: realtime 2d placement algorithms :-/)

2010-05-25 Thread Niels Mayer
On Tue, May 25, 2010 at 1:33 PM, Chris Cannam
can...@all-day-breakfast.com wrote:
 I think the point Neils has is just that the outcome of your noodling
 is somewhat independent of your explicit intention.  Notes that sound
 satisfying together are probably going to sound satisfying largely
 because of some intrinsic mathematical relationship, or at least
 something that is probably open to analysis to some extent but that
 you don't yourself understand or plan.

testify(wordUp); /*Chris, thanks for clarifying my point!*/

Consider how the snowflake, the mountain, coastlines, leaves and
trees, whose shapes put the cart before the horse of the mathematics
of  fractals: http://www.ams.org/notices/201001/rtx100100010p.pdf (the
most mind-blowing AMS paper i've read so far: is DNA and life itself
shaped fractally in the same way time and erosion sculpts a
mountain?).

nature put the cart before the horse of analog
synthesizers/computers when it made the sounds in the link below,
without ever conceiving of operational-amplifiers:
http://boingboing.net/2010/01/17/cracking-ice-sheets.html

Last time I was thinking about this in public, I said:

 The other thing that would be interesting is to explore the
 intersection between fractal self-similarities and rhythm/melody. Is
 music, and that which sounds musical fractal in nature, much like
 when we see something and instantly identify tree or mountain or
 coastline because of their fractal nature? Do we appreciate when
 music is more fractal, versus being a kind of latticework, infinite
 pattern, or just a random potpourri of sounds strung together for no
 purpose?

Niels
http://nielsmayer.com
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