Impossible Music is the first release on the hyperfunction label, a new label created by guitarist Michael Peters and touch-guitarist Marcus Reuter, specifically for algorithmic music.
If Impossible Music is any indication, hyperfunction is off to an auspicious start.
The compositions here were created in 1996 by Michael Peters, using his software implementation of an algorithm based on a strange attractor named after Igor Gumowski and Christian Mira, CERN physicists who discovered it during their research in nonlinear dynamic systems.
Starting out with an (x,y) value pair, the next value pair (xn,yn) is computed like this: xn = a * y + p * x + 2 * sqr(x) * (1 – p) / (1 + sqr(x)) yn = -x + p * xn + 2 * sqr(xn) * (1 – p) / (1 + sqr(xn)) with “a” typically being = 1.0 and “p” being a constant between -1 and 1.
The visual output of this strange attractor is quite beautiful, and provides the cover art for the release.
While the math may look daunting, there is nothing heavy or ponderous about the music, which is light, cheerful, and full of wit and humor.
The compositions incorporate process improvisations that use the output of the algorithm as a starting point to generate a stream of musical information. Michael and collaborator Matthias Ebbinghaus then interacted with the stream in real-time by changing various parameters in response to the output, to produce the final result.
The result is a collection of sixteen tinkling, percussive pieces that will bring a smile to your face. Most of the pieces are under two minutes in length, and would work perfectly as the soundtrack to a classic Mack Sennett comedy.
The overall recording quality of the release reflects a lot of love, care, and a meticulous attention to detail. The sounds chosen to voice the pieces perfectly complement the musical structures produced. The final recording was mastered in 2007 by Walter Bruhn, who did a wonderful job. The sonic quality is superb overall.
I had my introduction to algorithmic music in 1997, at the hands of Gary Lee Nelson, a professor of composition at Oberlin Conservatory of Music, near Cleveland, Ohio.
I’d driven out there over several days on a slow, meandering route making field recordings and staying at truck stop motels, in anticipation of attending the two-week summer workshop in electronic and computer music that the conservatory makes available every summer for a modest fee to the general public.
I had expected to use the high-end digital editing tools that would be available there to create a collage of the field recordings that I’d made on the way out.
Instead, I was introduced to Opcode MAX, a visual programming language that was used then to create, process, and manipulate MIDI data. MAX was later expanded to include msp and Jitter. Today these tools can be used to manipulate sound and video too.
MIDI data works like a player piano roll. It contains information about sound that include primary characteristics pitch, duration, and velocity as well as some or all of 128 secondary characteristics that can include things like portamento, pitch bend, etc. MIDI data doesn’t contain sound, only information to be used in creating a sound. MIDI data must then be voiced by an electronic instrument that accepts MIDI data, in the same way that a player piano roll doesn’t make sound until it serves as input to a player piano.
An algorithm is a number factory that takes a stream of input, and produces one or more streams of output. In algorithmic music, the output stream of an algorithm is mapped to a musical system of one kind or another. The process is similar to cryptography in that a transformation is performed on a body of data.
In cryptography, clear text that is readable by anyone is turned into an encrypted message that only the intended recipient can read.
Creating algorithmic music is like cryptography in reverse. The composer finds a musical message in a stream of data, and then decodes it by mapping it to an appropriate musical system so that it can be enjoyed by everyone.
For instance, to map a single stream of output to a diatonic scale in one octave, you could use modular, or clock arithmetic (Mod 7), because a diatonic scale in one octave consists of 7 notes. A quick way to do clock arithmetic is to do integer division on the number by whatever the modulus is, in this case 7, throw away the result, and keep the remainder.
So, if your algorithm produced the following values: 1177, 2018, 66, 5, 3, 22, 1, 11, 299 4, they could be mapped to C major, as follows:
1177(Mod 7) = 1
2018(Mod 7) = 2
66(Mod 7) = 3
5(Mod 7) = 5
3(Mod 7) = 3
22(Mod 7) = 1
1(Mod 7) = 1
11(Mod 7) = 4
299(Mod 7) = 5
4(Mod 7) = 4
If 1 is middle C (C3), the resulting melody would be C – D – E – G – E – C – C – F – G – F.
Then, the same stream could be reused, this time to map a duration to each of the note values. To do this, you could use (Mod 5) to map one of 5 note duration values (whole, half, quarter, eighth, or sixteenth) to each of the pitches, as follows:
1177(Mod 5) = 2
2018(Mod 5) = 3
66(Mod 5) = 1
5(Mod 5) = 1
3(Mod 5) = 3
22(Mod 5) = 2
1(Mod 5) = 1
11(Mod 5) = 1
299(Mod 5) = 4
4(Mod 5) = 4
This is the result:
I selected 4/4 time here, filling in measures with rests when the note value occurring next is too large for the bar.
This is the result of a single very simple stream mapped to a simple musical system.
Impossible Music is the result of a much more complex algorithm producing two streams mapped to a carefully chosen musical system.
The composition in algorithmic composition is in the process of selecting the method of mapping, and what kind of musical system to apply this map to.
Michael Peters and collaborators Matthias Ebbinghaus and Walter Bruhn have revealed the wonderful music hidden in this strange attractor. I highly recommend this release. Impossible Music can be purchased now from Iapedus and Burning Shed.
Impossible Music
hyperfunction, 2009
Michael Peters: programming and realtime parameter manipulation
Matthias Ebbinhaus: live mix and controllers, editing
Walter Bruhn: Final Mix
