Notes to 31 fractals: 31 SMALL FRACTAL PIECES is music created by a computer and played by a computer. The role of me, the “composer”, was to program the computer to perform the task of creating a melody with orchestration, with sufficiently many parameters to change and play with to make each piece sound unique. The software has two steps: first, a melody is created by a prescription telling the average frequency distance between adjacent notes. Parameters are the primary key to be used (with notes from various 4-tone to 12-tone scales), a secondary key and the average frequency of using it rather than the primary key, and finally a parameter describing the distribution of pauses (and thereby creating rhythm). The average distance between notes is for the majority of my pieces taken from the 1/f rule, where the stochastic probability of a frequency jump f is inversely proportional with the size of the jump. This rule is obeyed by nearly all music is western civilizations, from classical to jazz and rock music, with one exception being Gregorian chant, where the music is less “eventful” by using a 1/f^2 distribution.
The second step is to add a fractal flavour, inspired by the fractal pictures receiving much attention during the 1980ies. Fractal means that a given pattern is repeated on smaller and smaller scales, whether patterns in a picture or as here the pattern of the melody created in step one. The fractal picture is viewed “at once” but the fractal music develops in time. The time sequence of a chunk of the melodic material is repeated on smaller and smaller time scales, meaning that the notes are played (usually by other instruments) faster and faster. To make it more interesting the copies are not exact but have stochastic variations from the previous fractal level. Parameters to play with are the degree of deviations allowed and the average length of the melody chunks used for fractal accompaniment. Most of the pieces use three fractal layers below the melody line, but other choices are possible, including layers slower than the melody.
An analysis of western music shows that a certain amount of fractal patterns is present in the works of nearly all composers. One exception I have found is K-H Stockhausen: I have not been able to detect any fractal traits in his music. For this reason I thought it would be fun to try to add fractal accompaniment to a piece of his. More precisely, what I did was to take his opera cycle “Woche” (the performance duration of which is a week, as it uses extended sounds in the same way as the late-romantic composer R. Wagner but even more extreme) and make a version of the seven day-themes condensed to a few minutes, skipping the large note extensions. I then added fractal voices by using my computer program. The result can be heard in the middle part of the last track on the CD. I you agree with me, adding a fractal accompaniment does not improve Stockhausen’s work!
The CD opens with 8 of the 31 fractal examples created during the period from late 1986 to early 1988. They illustrate the variability possible with my computer program, starting with a charming bird song, joined by a whistler and a marimba. Then there is jazz-like syncopation in the second song for sitar and synthesizer, accompanied by human heartbeat, and choir song with 12-tone piano accompaniment in melody #3. Did you know that the beat of nearly all music is about 100 per minute, or very similar to our heartbeat. A reasonable conclusion is that our heartbeat was essential in forming human preferences in musical expression. The string piece #4, using vibes, electric bass and percussion, is based on a pop melody, while the blues #5 uses a saloon piano. A snare drum, a percussion set, claves, vibes and a beep-emitter perform piece #6. The following drum piece uses many kinds of drums plus a synthetic bass, and #8 is a rapid march theme for xylophone, tom drum, vibes and electric piano. The following 23 small pieces explores the algorithm further, using different tone scales (5, 6, 7 and 12 tone scales, with major and minor variants when applicable) and different instrument choices. Some sound like compositions known from various time periods in history, others like advanced experimental music and some are just plainly awful. The last three pieces #28-30 on the track are plain wanderings with four fingers across a Mandelbrot fractal picture, playing a certain note when a change is detected, rather than displaying a certain color as in the picture.
Surrounding the Stockhausen experiment are a pentatonic fanfare for strings and percussion, and a dodecaphonic (12-tone) fadeout for flute, a hollow tube and percussion, both with fractal ornamentation.