Ripples Through Pitch Space

Hello,

I just posted this announcement to the Alternate Tunings mailing list,
but it was suggested that I also post it to this list.

I have made an experimental piece titled "Ripples Through Pitch Space"
available online at:

http://www.mctague.org/carl/music/computer/pieces/ripples

To compose "Ripples", I released particles into a one-dimensional
potential field. Actually, I simulated this within a computer by
means of a discrete numerical integrator. I interpreted the
particles' positions as pitch, and their velocities as rhythm; roughly
speaking, the faster a particle moves, the more frequently its pitch
is heard. Since the simulated space is continuous, or at least nearly
so, many wonderful microtones emerge. Perhaps a warning is in order:
this piece contains dissonance, but exotic dissonance which ultimately
relaxes onto consonance, for I derived my potential fields from the
so-called dissonance curves first introduced by Kameoka and Kuriyagawa
in 1969, and which I first studied through William Sethares's 1998
book. Thus, the particles "swirl" into locally consonant attractors.
For additional details, please follow the link above.

Additionally, for those of you near Cincinnati (USA), "Ripples" will
be performed at the "Pi: Chaos vs. Control" event at the Mockbee on 28
May 2004. For more information, please visit:

http://home.cinci.rr.com/chrisherrick/Pi.htm

Sincerely,
Carl McTague

Hi Carl,

{you wrote...}
>I just posted this announcement to the Alternate Tunings mailing list, but >it was suggested that I also post it to this list.

Glad you joined up (glad I happened to be online when you needed admission!). I saw the piece this afternoon, and have enjoyed (just yet) the 4th movement. Welcome to MMM, especially when you've brought music with you!

Cheers,
Jon (ListMom)

If I understand correctly, you've taken those Sethares dissonance
curves, and essentially dropped some balls into them and we're
hearing them bouncing around. . . . yes?

>st studied through William Sethares's 1998
> book. Thus, the particles "swirl" into locally consonant >
>attractors.

One question: when you described this piece to me a while
ago, it sounded like the "consonant" balls stopped bouncing
around much sooner that the dissonant ones.

In which case, you've actually got a piece which shows off the
dissonant areas of the Sethares curves.

But perhaps I'm way off.

Anyway, it sounds wicked.

C Bailey

--- In MakeMicroMusic@yahoogroups.com, Carl McTague <box-

/makemicromusic/topicId_6386.html#6386

0cccbec56b@s...> wrote:
> Hello,
>
> I just posted this announcement to the Alternate Tunings mailing
list,
> but it was suggested that I also post it to this list.
>
> I have made an experimental piece titled "Ripples Through Pitch
Space"
> available online at:
>
> http://www.mctague.org/carl/music/computer/pieces/ripples
>
> To compose "Ripples", I released particles into a one-dimensional
> potential field. Actually, I simulated this within a computer by
> means of a discrete numerical integrator. I interpreted the
> particles' positions as pitch, and their velocities as rhythm;
roughly
> speaking, the faster a particle moves, the more frequently its pitch
> is heard. Since the simulated space is continuous, or at least
nearly
> so, many wonderful microtones emerge. Perhaps a warning is in
order:
> this piece contains dissonance, but exotic dissonance which
ultimately
> relaxes onto consonance, for I derived my potential fields from the
> so-called dissonance curves first introduced by Kameoka and
Kuriyagawa
> in 1969, and which I first studied through William Sethares's 1998
> book. Thus, the particles "swirl" into locally consonant
attractors.
> For additional details, please follow the link above.
>
> Additionally, for those of you near Cincinnati (USA), "Ripples" will
> be performed at the "Pi: Chaos vs. Control" event at the Mockbee on
28
> May 2004. For more information, please visit:
>
> http://home.cinci.rr.com/chrisherrick/Pi.htm
>
> Sincerely,
> Carl McTague

***I find this quite interesting and it's reminiscent somewhat of
Xenakis' electronic works, which is not surprising, since his
statistical methods seem somewhat related to yours.... I think
possibly the timbre is a bit better defined in this than in the
Xenakis works, but he likes a very "wet" post-production it seems...

Joseph Pehrson

Hi Chris,

Thanks. That's basically correct. I simulated twenty equally-spaced
point masses beginning at rest, and rolling along each of four
Sethares-like dissonance curves. The integrator has a velocity term,
as well as a first-order friction term. But there are no collisions:
all the particles' paths are computed independently. (It might be
very interesting to do something more sophisticated.) To be as
concrete as possible, here is the very naive integrator code, written
in the programming language Haskell:

g p m dx dt fc v x = (v',x')
where dp = (p x - p (x+dx))/dx -- approx. change in potential
f = dp - fc * v -- the force exerted by the field and friction
a = f / m -- Newton's law (f=ma)
v' = v + a * dt -- approx. velocity in dt seconds
x' = x + v * dt + (v'-v)*dt/2 -- approx. position in dt seconds

As is typical for such integrators, the simulation thus relies on
constants dt and dx, as well as the mass m of the particle, and the
friction constant fc. The function p is the potential field, in this
case the dissonance curve. The constant dt determines the time
resolution of the simulation. Think of the simulation's output as
still frames obtained from a strobe light that flashes every dt
seconds, except that at each frame, the simulation also provides the
particles' velocities.

For each movement, I ran the system for two-hundred frames, and
interpreted the particles' positions as pitch. But rather than using
the literal time of the frames to determine rhythm---this would be
boring, just twenty simultaneous notes every dt seconds---I used the
particles' velocities: I set the duration of each note to k/(c+|v|),
where k and c are positive constants which I chose by ear. This is
not an altogether artificial approach, for in this way, the faster a
particle moves, the more rapid are its notes. However, an additional
consequence of this scheme is that, since I sampled only two-hundred
frames, the quickly moving particles exhaust their frames sooner, and
drop out of the piece.

It is perhaps natural to wonder to what extent this rhythmic scheme
affects the perceived dynamics of the system. After some
investigation, I discovered that it is, in fact, very significant.
The particles which dominate the opening of the piece are those with
the greatest initial acceleration, and these are the particles whose
initial positions lie along the dissonance curve's sharpest slopes.
Conversely, the particles which become dominant only toward the end of
the piece are those which initially accelerate slowly, for instance
those close to the minima corresponding to Just intervals, but also
those close to maxima, where dissonance is greatest! The latter tend
to begin slowly, but then accelerate dramatically and vanish, while
the former remain relatively slow, and are active until the end of the
piece.

I hope this response was not unnecessarily technical. I've also
copied this message to the Alternative Tuning list, in case it is a
more appropriate forum, and in case any of its subscribers would find
this interesting.

Carl

> If I understand correctly, you've taken those Sethares dissonance
> curves, and essentially dropped some balls into them and we're
> hearing them bouncing around. . . . yes?
>
>> http://www.mctague.org/carl/music/computer/pieces/ripples
>
>> studied through William Sethares's 1998 book. Thus, the particles
>> "swirl" into locally consonant attractors.
>
> One question: when you described this piece to me a while ago, it
> sounded like the "consonant" balls stopped bouncing around much
> sooner that the dissonant ones.
>
> In which case, you've actually got a piece which shows off the
> dissonant areas of the Sethares curves.
>
> But perhaps I'm way off.
>
> Anyway, it sounds wicked.
>
> C Bailey

Hello Mr Pehrson,

Really? Thanks. I'm actually not using any statistics or explicit
random number generation. The simulation is completely deterministic
(although error certainly creeps in). But on the other hand, most
random number generators are in fact deterministic dynamical systems,
so the psychological perception of randomness is really, as you're
suggesting, the more important concern. I've read some of Xenakis's
writings, and have heard some of his orchestral works, but am somewhat
ashamed to admit that I have yet to investigate most of his electronic
output. Can you recommend any recordings?

Thanks,
Carl

On Fri, Apr 30, 2004 at 03:04:42AM -0000, Joseph Pehrson wrote:
> ***I find this quite interesting and it's reminiscent somewhat of
> Xenakis' electronic works, which is not surprising, since his
> statistical methods seem somewhat related to yours.... I think
> possibly the timbre is a bit better defined in this than in the
> Xenakis works, but he likes a very "wet" post-production it seems...
>
> Joseph Pehrson
>
> --- In MakeMicroMusic@yahoogroups.com, Carl McTague <box-
>
> /makemicromusic/topicId_6386.html#6386
> >
> > http://www.mctague.org/carl/music/computer/pieces/ripples

On Friday 30 April 2004 09:46 am, Carl McTague wrote:
> Hello Mr Pehrson,
>
> Really? Thanks. I'm actually not using any statistics or explicit
> random number generation. The simulation is completely deterministic
> (although error certainly creeps in). But on the other hand, most
> random number generators are in fact deterministic dynamical systems,
> so the psychological perception of randomness is really, as you're
> suggesting, the more important concern. I've read some of Xenakis's
> writings, and have heard some of his orchestral works, but am somewhat
> ashamed to admit that I have yet to investigate most of his electronic
> output. Can you recommend any recordings?

Carl,

I found your piece quite interesting and strangely beautiful to listen to.
And, Joseph beat me to it: I was thinking of posting the same impression--in
technique and sonic texture it was *very* Xenakis to me!!!

My favorite piece of electronic music of Xenakis, and one of my favorite
electronic works, period, is the 'Legend D'er'. It is almost frightening at
times, but always gorgeous with an incredibly, almost painfully rich level of
detail at its climax, wonderful on a great stereo with a rich stereo image,
but never falling into complete chaos--as if Xenakis stretches our ability to
digest his sonic landscape without ever letting us be lost into concluding it
is too complex as to be white noise.

Best,
Aaron.

> Thanks,
> Carl
>
> On Fri, Apr 30, 2004 at 03:04:42AM -0000, Joseph Pehrson wrote:
> > ***I find this quite interesting and it's reminiscent somewhat of
> > Xenakis' electronic works, which is not surprising, since his
> > statistical methods seem somewhat related to yours.... I think
> > possibly the timbre is a bit better defined in this than in the
> > Xenakis works, but he likes a very "wet" post-production it seems...

Aaron Krister Johnson
http://www.dividebypi.com
http://www.akjmusic.com

--- In MakeMicroMusic@yahoogroups.com, Carl McTague <box-
0cccbec56b@s...> wrote:

/makemicromusic/topicId_6386.html#6409

> Hello Mr Pehrson,

***Joseph or Joe is fine..

>
> Really? Thanks. I'm actually not using any statistics or explicit
> random number generation. The simulation is completely
deterministic
> (although error certainly creeps in). But on the other hand, most
> random number generators are in fact deterministic dynamical
systems,
> so the psychological perception of randomness is really, as you're
> suggesting, the more important concern. I've read some of
Xenakis's
> writings, and have heard some of his orchestral works, but am
somewhat
> ashamed to admit that I have yet to investigate most of his
electronic
> output. Can you recommend any recordings?
>
> Thanks,
> Carl
>

***I see that Amazon.com has a CD entitled _Xenakis:Electronic
Music_ put out by EMF. I'm assuming that's the "Electronic Music
Foundation."

In fact, that's true; I see it on their website:

http://www.emfmedia.org/catalog/em102/index.html

JP