How to compose Mandelbrot Music : Fractal music

How to compose Mandelbrot Music

This page is HTML converted from the help file of Mandelbrot music program. So I recommend you to read the help file directly if you understand Japanese and have Windows environment. Otherwise try this page.
Red letters are sentences originally in the popup-window of the help file.

There are many Mandelbrot display programs on the Internet (refer to Links page). My recommendation is WNFRA182.ZIP - "Fractint for Windows". It displays the coordinates of a point in real-time operation. This function is very handy to see the exact location which is used in the automatic composition.

Books about Mandelbrot Set.

Mr.Yamamoto's choice : "Computer Recreation" by A. K. Dewdney
My choice : "Chaos - to create new world of science" by James Grick

Rules to create MIDI data

Starting from Mr.Yamamoto's initial proposal,

"Take a point in x-y space near to the Mandelbrot Set. Then, fix the x axis and continually take points with constant y-axis distance. Calculate iteration values for each point. Apply the values in sequence to pitches of 16th notes. For example, if you want to use piano, you can spread such values to 88 different keys from the bottom to the top. In this way, you will obtain a series of 16th notes from the Mandelbrot Set." By Mr.Yamamoto
coordinates of the point to start(x, y), ticking length(xi, yi), direction and length of the axis(decided by xi, yi and ticking times "w") and these parameters can be set freely.

This means, when you plot iteration value vertically, the horizontal axis shows time transition and vertical axis shows tone pitch, (additionally tone length and tone strength) on cross sections of Mandelbrot *mountain* plotted by iteration values.
Transition on time

The length of a tune will be decided by "step" (time length of minimum note) * number of "step" ("w"). The transition on the x-y plane with one "step" will be determined by the constant distance (xi, yi).

The shortest note decided by ticking value of one "step". If you set step=30, the shortest note is sixteenth because the timebase of Masndelbrot music program is fixed to 120 per quarter note.
So this means that w * step is the music length which is shown as the length of the axis (=route((w*xi)^2+(w*yi)^2)).

If you set w=1000 and step=30, the music time is 16th-note * 1000.

If you set xi=0.004, yi=-0.003 and w=100, your music will go from the starting point down to east-southeast direction with the length of 0.5.
Tone Pitch

In the Mandelbrot music program I use some words in a different meaning from ordinary usage. In the explanation below, "scale" means the scale which you select in the pop-up list and "scale's-note-number" means the value which you fill out in the form of "scale=" in the dialog box. Hence the value in "scale=" is the total number of notes which you use in your composition rule.

Pitch on a specified scale is decided by the remainder in dividing iteration by scale's-note-number or by the value as a result to enlarge/compress iteration to scale's-note-number.
The latter way of using the value by enlarging/compressing iteration reflects directly Mandelbrot mountain range to up and down in the generated melody but if the upper limit of iteration is too small to scale's-note-number, iteration compressed excesively causes repetition of same note. Use them appropriately according to the iteration values of the axis you choose.

Also you can select starting pitch from top or bottom. To start from top, visual image and note pitch correspond to each other and to start from bottom, they turn upside down. Make your choice.

The lowest pitch is specified by "note=". Scale's-note-number is allocated upwards from "note=" according to the specified scale. Be careful about that the number of note is different from a scale to scale. Default setting is the piano's register.

A point where iteration value is more than the upper limit("i")

the point of which iteration value is over the limit in Mandelbrot set
becomes a rest.
Tone length

Tone length is decided by adding the timebase("step=") when same iteration value repeats.

To sum up, same iteration's continuation means longer note.
Visually, the flatness of surface decides note length.

Mandelbrot set has a character that there are broad flat plane surfaces here and there. In this case a very long note will be generated. You can avoid this by specifying "maxstep=". If you specify "step=30" and "maxstep=4", the longest note length will be 120. As the program set TimeBase=120, quarter notes repeat in a long plane surface. Fill out "maxstep=" value according to your specified tune and taste.
Tone volume

Visually speaking, a uphill slope becomes a crescendo, a downhill slope becomes a decrescendo and a flat surface becomes no crescendo. The rate of a crescendo/decrescendo depends on the steepness of the slope. The steeper is a slope, the more crescendo/decrescendo of a generated music results. The program uses key velocity to control tone strength and not generate volume change within the tune.

Middle point of velocity(tone volume) can be specified by "vel=". The range of Velocity is from vel(127 - vel) to 127.
The default volume to a composition is specified by "vol=". It is inserted in the top of a track.
Polyphony

You can compose a piece polyphonically by specifying "part=". Generated MIDI data are format 1.

If "part=0", the generated music is monophonic.
The channel number of each track is decided by channel(specified in "ch=") + part-number(from zero to "part="). The range of track you can use is zero to 15. Therefore you can not set a parameter that results in a track number over 15, such as "part=5" and "ch=14".

The way to compose polyphonically is shift of the time-axes by "xpi=" and "ypi=" which specify the distance between parts.

It means that if "xpi=0" and ypi=a (certain number), axes are moved to the upper or lower sides vertically and if "ypi=0" and xpi=a (certain number), axes are moved to the right and left horizontally. In other cases axes are moved slantwise.
Again as visually speaking, you could see paralleled cross sections overlaped each others.

It's very interesting to compose poliphnically in a suitable location. The music sounds like a Minimal.
Others

Scale
Micro tone specification
Calculation Precision
Iteration value

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