Ripples Through Pitch Space

Hello,

I've been lurking silently on this list in digest mode for some time.
Finally, I'm posting to inform you that I've 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

From: "Carl McTague" <box-0cccbec56b@storrs.net>

> I've been lurking silently on this list in digest mode for some time.
> Finally, I'm posting to inform you that I've made an experimental
> piece titled "Ripples Through Pitch Space" available online at:
>
> http://www.mctague.org/carl/music/computer/pieces/ripples

I liked it! It sounded like static electricity released upon a many-stringed
santur. And it does have a relaxing effect as everything resolves to a
simple consonance, very windchime-like. Good luck with the performance!

Reminds me, I need to get busy writing some music... of course the stuff I
write is more traditional. I keep getting a C-to-E-sesquiflat (septimal
minor third) motif stuck in my head.

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

> I've been lurking silently on this list in digest mode for some time.
> Finally, I'm posting to inform you that I've made an experimental
> piece titled "Ripples Through Pitch Space" available online at:
>
> http://www.mctague.org/carl/music/computer/pieces/ripples
>

This is brilliant!!!!

The sustained sounds behind the plucked sounds remind me of Harry
Partch's harmonium.

Gabor

[Sorry I'm so slow to respond. I'm in Digest mode, and don't remember
my yahoogroups password, or the birth date I chose when I registered.]

Thanks! I like your electrified santur image.

Most of my music is somewhat more traditional, too. If you're
interested, see:

http://www.mctague.org/carl#algorithmus

There are only two other pieces there, but I'll be making a few more
available in the coming weeks, ahead of my graduation this spring.

Carl [McTague, not Lumma]

From: "Danny Wier" <dawiertx@s...>
> From: "Carl McTague" <box-0cccbec56b@s...>
> > I've been lurking silently on this list in digest mode for some
> > time. Finally, I'm posting to inform you that I've made an
> > experimental piece titled "Ripples Through Pitch Space" available
> > online at:
> >
> > http://www.mctague.org/carl/music/computer/pieces/ripples
>
> I liked it! It sounded like static electricity released upon a
> many-stringed santur. And it does have a relaxing effect as
> everything resolves to a simple consonance, very
> windchime-like. Good luck with the performance!
>
> Reminds me, I need to get busy writing some music... of course the
> stuff I write is more traditional. I keep getting a
> C-to-E-sesquiflat (septimal minor third) motif stuck in my head.

Thanks! The background sounds are due to Paul Lansky's Reverbit
filter in Cmix. It "reverberates the input signal using a variation
on a typical Schroeder network of comb and allpass filters". I'm
obsessed with its effect.

Carl (McTague)

In tuning@yahoogroups.com, "alternativetuning" <alternativetuning@y...> wrote:
>--- In tuning@yahoogroups.com, Carl McTague <box-0cccbec56b@s...> wrote:
>
>> I've been lurking silently on this list in digest mode for some time.
>> Finally, I'm posting to inform you that I've made an experimental
>> piece titled "Ripples Through Pitch Space" available online at:
>>
>> http://www.mctague.org/carl/music/computer/pieces/ripples
>
> This is brilliant!!!!
>
> The sustained sounds behind the plucked sounds remind me of Harry
> Partch's harmonium.
>
> Gabor

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

Hi Carl,

Thanks for posting! I don't have any specific comments yet, but
I did download your Xi and helix papers. Studied with Jim
Crutchfield, did you? Coincidentally, he and I exchanged e-mail
last week.

-Carl L. (I've been waiting to have to do that!)

Hi Carl,

Believe it or not, this is actually the first email I've ever
addressed to a Carl.

Thanks for taking a look at my papers. I don't know how interested
you are in computational music composition, but do let me know what
you think of my Xi paper.

From your perspective, the helix paper is really just about 3-limit
tuning. But it's true emphasis is traditional notation, and is mainly
a summary of a small part of Eric Regener's 1973 thesis. However, I
found the technique very useful for generating my piece (ii-V-I)^7,
especially its score:

http://www.mctague.org/carl/music/computer/pieces/ii-V-I7

The recording there is in 3-limit tuning. In fact, my favoriate part
of the piece is about 4:09 into it, when there is a sudden
discontinuity in the tuning.

So how do you know Jim Crutchfield? I've been studying with him for
almost four years now, and in fact was just out at SFI working with
him for a couple of weeks during my spring break, and will be out
there again this summer.

Carl M.

> Hi Carl,
>
> Thanks for posting! I don't have any specific comments yet, but I
> did download your Xi and helix papers. Studied with Jim
> Crutchfield, did you? Coincidentally, he and I exchanged e-mail
> last week.
>
> -Carl L. (I've been waiting to have to do that!)

>Believe it or not, this is actually the first email I've ever
>addressed to a Carl.

A quick search of my outbox shows the same is true for me!

>Thanks for taking a look at my papers. I don't know how interested
>you are in computational music composition,

Always slightly interested. By the way, there is a list on yahoo
called SpecMus, moderated by our very own Gabor Bernath, which is
not tuning-centric. You may find more interest in algocomp there.

>but do let me know what you think of my Xi paper.

I don't quite get it, I'm afraid, probably because of my
unfamiliarity with the set theory lingo in your brief. Does Xi
have any application outside of music? I have your scheme
code running here, if I knew what to do with it...

>From your perspective, the helix paper is really just about 3-limit
>tuning. But it's true emphasis is traditional notation, and is mainly
>a summary of a small part of Eric Regener's 1973 thesis. However, I
>found the technique very useful for generating my piece (ii-V-I)^7,
>especially its score:
>
> http://www.mctague.org/carl/music/computer/pieces/ii-V-I7
>
>The recording there is in 3-limit tuning. In fact, my favoriate part
>of the piece is about 4:09 into it, when there is a sudden
>discontinuity in the tuning.

Neat. The reverb really gets some wild sounds in it once this
gets going. I wonder what happens to the tuning at 4:09... are
you hitting the edge of your chain of fifths?

>So how do you know Jim Crutchfield? I've been studying with him for
>almost four years now, and in fact was just out at SFI working with
>him for a couple of weeks during my spring break, and will be out
>there again this summer.

I don't know him, other than as a name at SFI. I was trying to read
one of his papers last week, which was broken across three files. I
made a single-file version for my own use, and sent it to him.

-Carl

Hi Carl,

sorry I'm so slow to respond.

At 4:09 of (ii-V-I)^7, the progressions jump from the tonic of the
home key, I, all the way up into the neighborhood of
ii/ii/ii/ii/ii/ii/ii (in an abuse of the conventional notation for
secondary embellishment in functional harmony), which seems to be a
nice leap within 3-limit tuning (a distance of ca. 3^14 mod 8ve).
However, because the chords have begun to blur together by that point,
it might not be precisely 3^14 that sounds good: it might be 3^13 or
3^12, or somehow the amalgam of several of these intervals, and
others, as the progression flies by, winding its way back down to I.

Carl M.

PS: If you have any questions about notation in the Xi paper, please
feel more than free to email me privately. Some of it is a bit
idiosyncratic.

Message: 5
Date: Sat, 01 May 2004 19:21:48 -0700
From: Carl Lumma <ekin@lumma.org>
Subject: Re: Re: Ripples Through Pitch Space

Neat. The reverb really gets some wild sounds in it once this gets
going. I wonder what happens to the tuning at 4:09... are you hitting
the edge of your chain of fifths?

>So how do you know Jim Crutchfield? I've been studying with him for
>almost four years now, and in fact was just out at SFI working with
>him for a couple of weeks during my spring break, and will be out
>there again this summer.

I don't know him, other than as a name at SFI. I was trying to read
one of his papers last week, which was broken across three files. I
made a single-file version for my own use, and sent it to him.

-Carl