FractMus Overview

What is FractMus

FractMus is a freeware algorithmic-music generator, that is, it creates melodies using mathematical formulas.

Screenshot of the program

Screenshot of the program.

Since the times of Ancient Greece, people have realized that music and mathematics had a very close relationship, maybe because music is the most abstract form of art. Using mathematics explicitly to create music is nevertheless something of our time. Without the help of the modern computer it would be a daunting task (if not an impossible one) to do all the necessary calculations by hand.

A word of caution: you are the composer, FractMus will create no masterpiece for you, nor it was designed for that. Think of it as a tool which gives you raw material that you can later use in your compositions. Writing a midi file and later importing it with music-editing programs such as Sibelius or Finale gives you the invaluable option of seeing your creation as a musical score, with all the correct pitches and durations, for later editing. FractMus uses only a few of the infinity of possible algorithms for note creation. Some of them exhibit fractal behavior, like the Morse-Thue sequence, Henon attractor, gingerbread man fractal, etc, while others use well-known formulas from chaotic dynamics, like the Logistic Map.

In the end, it is always your inventiveness what makes a composition better or worse, FractMus just gives you the “inspiration”.

System Requirements

FractMus is a Win32 program, so you need Windows95 or later or Windows NT 3.51 or later and a sound card to run it. Although FractMus will run in any computer that can run Windows 95, it would be of great help if you have a fast CPU, since FractMus plays and computes the music in real time. It is possible that the music will run slower than your Tempo Marking settings. This is not a bug in the program, but the result of a slower CPU.

How is the music computed?


FractMus uses two counters (see figure) as an iteration control for the algorithms. Melodies are always played from the Start counter, which counts in thirty-second notes. The End counter marks the point were the music stops. An example: Lets assume a note value of quarters (8 thirty-seconds) and the Henon algorithm. We start at counter 0, that is the first iteration of the algorithm (the first note), next, since we have chosen quarters as the note value, which corresponds to 8 thirty-seconds, we must wait until counter 8 to play the next note (iteration 2), then 16, then, 24, and so forth. Some algorithms are two dimensional maps, such as the Henon, Gingerbread man fractal, etc. As such, these equations give back (X, Y) values when iterated. In order to get a unique value from these coordinates, a modulus operation is performed, that is, the square root of the sum of the values squared [ sqrt(X*X + Y*Y) ]. From this value the final note is computed, depending on the scale chosen, the number of octaves, etc. The Reset button will set both counters to 0. The Roundbutton will set the counters to the nearest multiple (up or down) of the value of the voice of your choice (a dialog will pop up for you to choose the voice). Normally, when you play in the Current Settings mode, the End counter will start running from the value of the Start counter until you stop. If you do not want the End counter to run, press the Lock button. The music will stop automatically when the value at theEnd counter is reached. Counters can have a maximum value of 50000.



FractMus has sixteen-voice multitimbral polyphony. Each voice can be assigned to one of the sixteen midi channels (percussion channel is usually channel 9). Voices can be assigned instruments, dynamics, speaker output, algorithms, scales, note durations, etc, completely independent from each other. You can easily toggle voices on/off by pushing the voice buttons.

Midi-file support

FractMus offers complete Midi-file support (Playing and Writing). Being able to write a midi file from your composition is a great advantage, allowing you to later edit them with other MIDI software. You can also play midi files within FractMus (you need the Windows Media Player to be in your computer). FractMus will write the midi file from your composition or current settings, according which mode is selected.

NOTE: for some unknown reason, some sequencers (such as CakeWalk) have trouble loading midi files written by FractMus. If you encounter this problem, don’t panic, the solution is very easy: there are many freeware and shareware midi utilities and sequencers that read midi files generated by FractMus without any problem. Simply load the midi files in one of these programs and re-save them as either type 0 or type 1 (one track per channel). This will solve the problem in most cases.

Password protection for your files

With FractMus 2000 you can protect your files with a password. You may also write in author and copyright information. This information will be included in the generated midi files from your compositions. Protecting you files assures that only you, the legitimate author, can make changes and save compositions. If you don’t mind sharing your compositions with other users, simply leave the password option blank. Protected files will be only be available for playing. All information about the composition (algorithms, parameters, etc) as well as file saving and midi-file saving will be unavailable until the password is entered. Passwords are case-sensitive and can have 3 to 8 characters.

Graphical output from your composition

FractMus “translates” your composition into a graphical image. Basically it takes all your composition parameters (scales, durations, voices, algorithms, etc), and from them creates an interference pattern similar to the moire pattern, which has fractal structure. Every pattern is uniquely mapped to each composition. They often resemble persian rugs!. The image generated is true-color, 500×500 pixels. Unfortunately FractMus does not have a image saving routine, so you’ll need a screen capture program if you wish to save it.

Example 1

Example 1

Example 2

Example 2

Composition information

FractMus provides you with an information window about your composition. It includes general information such as approximate duration, scales used, algorithms used, file version, etc.


FractMus offers you 15 pre-defined scales to choose from and the possibility to create your own. Built in scales include.

  • Major
  • Minor Natural
  • Minor Harmonic
  • Minor melodic
  • Lydian
  • Mixolydian
  • Dorian
  • Phrygian
  • Locrian
  • Acoustic
  • Octatonic 1
  • Octatonic 2
  • Pentatonic
  • Whole tone
  • Chromatic
  • User defined

To create your own scale select “user defined ” from the scale combo box. A dialog will pop up with 12 check boxes, one for every note. User scales are pre-defined to a default Major scale when first accessed. Simply check the notes that form your scale. You can create scales with any number of pitches, from 1 to all 11 notes. Note that FractMus transposes all scales to C, thus, for example, a scale defined as E – F – Ab – Bb – B will be transposed (and shown) as C – Db – E – Gb – G.

Note Durations

FractMus provides 11 pre-defined note durations. These are (from longest to shortest):

  • Dotted Whole
  • Whole
  • Dotted Half
  • Half
  • Dotted Quarter
  • Quarter
  • Dotted Eighth
  • Eighth
  • Dotted Sixteenth
  • Sixteenth
  • Thirty-second

You can also define your own note-duration. Just select “other” from the combo box. A dialog will pop up. Enter the value of the duration (1=thirty second, 2=sixteenth, 3=dotted sixteenth, 8=quarter (8 thirty seconds), 10=quarter + sixteenth, etc).

Tempo Marking


The tempo marking controls how fast your composition goes. It is measured in quarter notes per minute. Basically works as a metronome, the higher the value the faster your music will sound. Values are between 20 and 320. Note that unless you have a really fast computer, your tempo marking may not corresponds with the playing speed (it may be noticeably slower). This happens because FractMus computes the music in real time. Nevertheless, when you save the midi-file the tempo will be correct. The Global Tempo button allows you to change the tempo globally for the whole composition (every Event’s tempo will be modified).

Time Signature


The time signature is a very useful feature if you import your midi files into a music editing program (such as Finale or Encore). The numerator is the number of values per measure. The denominator represents the base value of the measure, it must be a power of 2 (1 represents whole, 2 half, 4 quarter, etc). The Global button allows you to change the time signature globally for the whole composition (every Event’s time signature will be modified). The time signature has no effect on how the music sounds.

Voice Settings and Manipulation


instrument pic

percussion picSelect your instrument from the Instrument combo box. You can choose among the 128 instrument patches of General Midi. If your voice uses the percussion channel (usually channel 9) you can choose a percussion instrument from the Percussion combo box.


inversion pic

Inverting a melody is a compositional procedure in which the direction of intervals in the melody is reversed, for example: a fifth up becomes a fifth down, a second down becomes a second up, etc. For simplicity, FractMus inverts “from C”, that is, taking the note C as the pivot note for the inversion. For example, let’s take a simple melody (click on it to listen): Melody This melody is in A minor natural, now lets invert it: Inverted As you can see, every interval in the original melody is preserved but goes in the opposite direction. FractMus takes C as the pivot (or mirror) note for inversion. When you invert a melody, its original key will change. Nevertheless, you can force the inverted melody to remain in the same key as the original melody by checkingMatch Scale: Inverted (same scale)Note that if you force an inverted melody to remain in the key of the original melody, some intervals will not be preserved (although the direction of those will still be opposite).


Modulation pic

Modulation is a procedure were a melody changes from one key to another. In FractMus you can modulate in two different ways. First you can have the melody to modulate every N notes. To do so, simply specify N in the Every edit box (values are between 1 and 50). The other option is to let the computer choose N randomly (from 1 to 50), to do so just select Random. The actual key were the melody modulates depends on the algorithm and the value generated at the point of modulation. Melodies can modulate from a minor second to a major seventh, that is, the whole chromatic range.


Dynamics pic

You can control the dynamic volume of the voices independently for every one. Choose from PP (softest) to FF (loudest).

Panning (Stereo effect)

Pan pic

Output can be directed to the left (-64), right (63), or both speakers (0) for each voice independently. Use the scroll bar to select desired output. You can also press the 0 button to select both speakers.