(In)discrete Music

Dr Giles R. Greenway
@augeas
http://www.slideshare.net/gilesgreenway
(In)Discrete Music
(See also: “Oblique Strategies Against Humanity”,
EMF 2016.)

Implement it on slow machines in low-level languages.
No chance of manipulating audio in real time.
“Back in the good-old days...”
Books on chaos, fractals, cellular automata and mathematical
recreations contained pseudocode.

Jeff Minter’s Trip-A-Tron, Colourspace, Psychedelia
Hinouema the Malediction
Fight Your Own War, Jenniffer Wallis, Headpress
“Back in the good-old days...”

Two choices for each configuration, represent as a byte.
28
= 256 possible automata.
Numbering scheme attributed to Stephen Wolfram.
Elementary 1D Cellular Automata
Consider a 1D array of cells with two states, “on” or “off”.
Often start with a single central seed cell initially on.
A cell’s future depends on the its past and that of its neighbours.
23
= 8 possible previous configurations for each cell.
“Periodic boundary conditions”?

Elementary 1D Cellular Automata
Rule 30 Rule 110

Making “Music” with 1D CAs
http://tinyurl.com/wolframsacrank

Making “Music” with 1D CAs
75 45 30 73 105 86
.
101 89
8 rules, 64 beats each.
5 central cell columns trigger drums: (mido Python library)
open hat, low tom, kick, high tom, closed hat
3 central cell columns with 6-bit “history” play “melody”.
Three note polyphony, 0-63, offset by 0, 31, 62.
Most significant bit represents the present.

What does a Gauss Map sound like?

What’s a Gauss Map?
For α, β create a sequence of x
values.
Each slice through the map is a
histogram of the x values.
Vary β on the horizontal axis.
x on the vertical axis, α varies
in time, scan β up and down.

Bifurcation diagrams as spectra
Inverse Short-Time Discrete
Fourier transform:
Take the inverse real discrete
Fourier transform of each
histogram. (numpy.fft.irfft)
Multiply each chunk of signal
by a window function.
Offset each chunk by
successive “hops” and
superimpose them.
Right channel is the left
channel played backwards.
http://ubu.com/historical/oram/
Pan according to the centre of
the distribution.

Back to elementary 1D CAs:
Take a 1D CA with an array of 512 cells.
Start with a single central defect.
Interpret the 6 previous states of each cell as bits.
Treat successive rows as spectra.
Left channel rule 30, right channel rule 86.
The results are “uncompromising”.

Meanwhile, in 1963:
Simplified model of convection currents.
Describes the rates of change of 3 variables, x, y and z.
There are no analytical solutions.
x(t) = ?, y(t) = ?, z(t) = ?
Simulate the system with numerical approximations.
Slight changes in the start-point cause dramatically
different behaviour.
“Deterministic Nonperiodic Flow”, Edward N Lorenz, Journal of
the Atmospheric Sciences, vol 20, pg 130 1963.

Change (almost) nothing and
continue with immaculate
inconsistency.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1

Variables modify the frequency of sinusoidal oscillators.
These frequencies are modulated by other oscillators, whose
frequencies are controlled by other variables.
x variable controls stereo panning.
Discard some axioms. Acquire some
more axioms:
As many parameters of the mathematical system as possible
should influence the sound.
Minimize arbitrary choices. Minimize your influence.
It should sound the way it looks.
Left channel, right channel,
centre channel.

“I never wanted a modular synth...”
A.C. circuits can be
modelled by differential
equations, so differential
equations can be modelled
by A.C. circuits.
For a time, both analogue
and digital computers
coexisted.
http://blog.analogmachine.org/2012/03/15/analog-computers/
http://users.physics.harvard.edu/~horowitz/misc/lorenz.htm

“It's almost too simple”

http://augeas.github.io/Chaoscillator/

“Notes from the Metalevel”
http://overtone.github.io/
Overtone: Clojure library for
controlling Supercollider. (Clojure
is a Lisp-like language that
compiles to Java. Clojurescript
compiles to JS.)
Create buffers filled with Lorenz
signals to use as LFOs.
https://github.com/augeas/chaoscillator-ii

“All right, I do want a modular synth.”
http://www.sound-machines.it/product/ns1nanosynth/
Nanosynth: One variable controls
pitch, one controls pulse width, one
controls filter cut-off. Subtract x
from 5V to control Werkstatt VCA
for panning.
Werkstatt: Variables control pitch,
LFO rate (to modulate pitch) and
filter cut-off.

Control analogue instruments via
Pygame's MIDI module.
Quantized to 128 values.
x variable plays Microbrute. (y and z
control waveshaping and filter cut-off.)
y and z variables play Volca keys
polyphonically. (x controls the filter.)
Trigger kick-drum on Volca beats when x
changes sign.
Turn up portamento, hope for the best.
Make an exhaustive list of
everything you might do and
do the last thing on the list.

“Merry Christmas, Mr Lorenz”
https://soundcloud.com/giles-richard-greenway/merry-christmas-mr-lorentz
“There's quite a nice build up of forms here that seem to
culminate and then drift apart to sort of make a flag post
around which the construction takes on a nice compositional
form! It's impressive the ways in which the saw tooth waves
are manipulated to conjure overlapping smoothness with
harsh edges here and there. Really nice outcome with this
track!” -Will Connor
https://soundcloud.com/willconnorseesar
“My God! What has sound got to do
with music?” -Charles Ives.
What has music got to do with
sound?

(In)discrete Music

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