Constants as Music

I've just seen the following video

and I wondered how hard it was to automatically generate this myself only with software. Turns out, it is super easy.

Python ¶

You have to install MIDIUtil:

$ sudo pip install MIDIUtil

and then you can execute the following code:

#!/usr/bin/env python

from midiutil.MidiFile import MIDIFile

# Just an example
try:
    # import version included with old SymPy
    from sympy.mpmath import mp
except ImportError:
    # import newer version
    from mpmath import mp
mp.dps = 1000  # set number of digits

# Create the MIDIFile Object with 1 track
MyMIDI = MIDIFile(1)

track = 0
channel = 0


pitch = 60
time = 0
duration = 1
volume = 100
for digit in str(mp.pi):
    if digit == ".":
        continue
    MyMIDI.addNote(track, channel, pitch + int(digit), time, duration, volume)
    time += 1
    if time == 180:
        break

# And write it to disk.
binfile = open("output.mid", "wb")
MyMIDI.writeFile(binfile)
binfile.close()

This will make the first 180 digits of $\pi$ to a MIDI file.

See MIDIUtil docs for more information.

Create MP3 ¶

I use timidity to create a .wav and then lame to convert it to mp3:

$ timidity -Ow -o output.wav output.mid
$ lame output.wav pi.mp3

For YouTube, I had to convert it to avi:

$ ffmpeg -loop 1 -r 1 -i pi.jpg -i pi.mp3 -c:a copy -shortest pi.avi

Examples ¶

$\pi$:

It sounds much more intersting if you play two versions of it simultaneously, starting at different points:

$e$:

$\sqrt{2}$

Ideas ¶

You could reserve one digit for meta-choices, e.g. making 0 a control character. If 0 is followed by...

• ... 0, all modifiers are reset
• ... 1, the pitch is doubled all the time
• ... 2, the pitch is doubled for 10 notes
• ... 3, `time = time - 5.5`
• ... 4, `tempo = tempo*2`
• ... 5, `tempo = tempo*4
• ... 6, `tempo = tempo - 10
• ... 7, volume increases in as many beats as the next two digits indicate
• ... 8, volume decreases by 10 in the next 2 seconds
• ... 9, duration is doubled

Let me know if you made something that sounds interesting 🙂