fungal music - jacques & fran soddell
HOW WE CONVERTED L-SYSTEMS TO MUSIC
We chose a sonic equivalent of turtle graphics to represent changes in the movement of the fungal mycelium, with MIDI notes and duration representing the growing colony (we called this turtle sonics).
lsys : Jonathan Leech's (leech@cs.unc.edu) excellent L-system software program (for unix) was used to interpret L-systems axioms and production rules into strings which could then be interpreted using turtle graphics to produce images (as postscript files). Download it from here
lsys2midi : This program produces midi files from a string input (output file from lsys). This was originally written in 1998 as a a student project by Leigh Goodall and Matthew Watson using Jacques Soddell as a client and supervised by Fran Soddell and Lorraine Staehr. The program was rewritten by Fran Soddell in January 2000 to alter the mapping of lsys strings to midi events to more closely represent the growth of filamentous microbes.
How we mapped to midi and why we did it that way
We related changes in direction of growth of microbes (as determined by branching angles) to changes in pitch, and distances between branches to note duration. Like Mason & Saffle (1994) we found that the pitch went out of range - MIDI, hearing and instrument range. Unlike them, we could not restrict our interpretation to images within audible range because we wished to explore the usefulness of sonifying them. Therefore we adopted the idea of a circular keyboard as describd below, by modifying a software program lsys2midi, previously written by students under our supervision.
The modified lsys2midi interprets parametric L-system symbols as shown in the table below. For MIDI files, available pitches range from 0 to 127, where the interval between each pitch is a semitone. At first, like McCormack (1996) we interpreted + and - as instructions to increment and decrement pitch by one semitone. However, when the pitch reaches 0, decrementing sets it to 127. So we can consider a pitch of 0 equivalent to that of 128 and picture this in terms of a circular keyboard. This resembles the turtle interpretation of size of a branching angle, where 360 degrees coincides with 0 degrees.
We found two problems with this interpretation. First, MIDI note 127 corresponds to a note of G and note 0 to a note of C. Although this can be interesting, it seems more appropriate to move from B to C ie to specify a pitch range of 0 to 119 (the B before the C of the 10th octave) and regard a pitch of 120 (C) equivalent to to that of 0 (C). Second, the range from 0 to 119 may not always be appropriate since it is too big a range for most instruments. So we enhanced lsys2midi to allow users to specify the lowest pitch, the highest pitch, and the starting pitch. This means that the same string can be interpreted over different ranges with starting notes of different pitches. In the future we plan to extend the software to include the mapping of other MIDI parmeters.
The methods used have been described and discussed in the following publication:
Soddell, Fran & Soddell, Jacques (2000). Microbes and Music. 767-777. PRICAI 2000. Lecture Notes in Artificial Intelligence 1886. (eds R. Mizoguchi and J. Slaney). Springer-Verlag: Berlin
Other approaches
There is no "correct" way of mapping l-systems strings to music. A number of different approaches have been investigated by others. Swome of these can be found in the following papers, books or sites.
Mason S & Saffle M (1994). L-systems, melodies and musical structure. Leonardo Music Journal, 4, 31-38.
McCormack J (1996). Grammar-based music composition. Complexity International, 3
Nelson G (1996). Real Time transformation of musical material with fractal algorithms. Computers Math. Applic, 32, 1 109-116.
Prusinkiewicz P & Hanan (1989) Lindenmayer systems, plants and fractals. Lecture Notes in Biomathematics. Springer-Verlag: Berlin.
Prusinkiewicz P & Lindenmayer A (1990). The Algorithmic Beauty of Plants. Springer-Verlag: Berlin.
Sharp D (1998). LMUSe software