boopadoop

Mathematically sound sound synthesis.

A music theory library for just intonation and other mathematically pure ideas. Documentation and additional exposition on Hackage!

Usage

Run the provided executable, or run main using stack exec perfprof. To interact with boopadoop, run stack ghci using Haskell Stack Tool.

SolFeck guide

SolFeck is a shorthand language for quickly writing down twelve tone note sequences

SolFeck Symbol	What it does
Digit in {0,1,...,9,a,b}	Play the nearest pitch to the previous note from the corresponding pitch class
^	Go an octave up for the next note
v	Go an octave down for the next note
-	Extend the previous note
= followed by number	=5 is the same as -----
~ followed by pitch symbol	~4 modulates the key into k=4
	Plays a rest (silence)
x	Repeat previous note, e.g. 024xxxxx is 02444444
'	Go up by one scale step, e.g. 0' is 02
.	Go down by one scale step, e.g. 0. is 0b
```	Go up by two scale steps, e.g. 0\`` is 04`
,	Go down by two scale steps, e.g. 0, is 09
i	Go up by three scale steps, e.g. 0i is 05
!	Go down by three scale steps, e.g. 0! is 07

Output

Boopadoop will play your input or the generated music, and also output it to out/listen.wav as an audio file, and to out/lilyout.ly as a LilyPond music typesetting file. If you get the Lilypond program, you can double click this file and it will output a lilyout.pdf rendering of it as sheet music.

Older features (may not still work)

Pitches and Chords

We can build chords:

majorAChord :: DWave
majorAChord = balanceChord
  [sinWave concertA
  ,sinWave $ intervalOf majorThird concertA
  ,sinWave $ intervalOf perfectFifth concertA
  ]

and pretty print the resulting sound wave:

>>> show majorAChord
........................................................................................................
..xxx.......................................................xxx.........................................
.x...............................................xxx....................................................
.....x.......xxx...............xx...............x..........x...x.......xxx...............xxx............
x...........x...xx..xxxx......x..xx....xx......x....x.................x...xx..xxxx......x...xx...xx.....
......x....x......xx....xx..xx.....xxxx..xx...x...........x.....x...........xx....xx..xx......xxx..xxx..
.......x..................xx...............xxx.......x...........x...x..............xx................xx
........xxx...........................................x..x........xxx...................................
.......................................................xx...............................................

or write it to a .wav file by specifying sampling parameters with

testWave "aChord" (tickTable 32000 . discretize $ majorAChord)

The intervals can be given as ratios

perfectFifth :: PitchFactorDiagram
perfectFifth = countPFD (3/2)

or using "Pitch Factor Diagrams":

octave       = normalizePFD $ Factors [1]
perfectFifth = normalizePFD $ Factors [0,1]
majorThird   = normalizePFD $ Factors [0,0,1]
minorThird   = normalizePFD $ Factors [0,1,-1] -- Minor third is up a p5, down a M3

Also supports equal temperament semitones: (a perfect fifth is approximately seven semitones)

>>> diagramToSemi perfectFifth
7.019550008653875

>>> equalTempPerfectFifth = countPFDFuzzy $ semi ** 7
Factors {getFactors = [1,-2,0,0,1,0,0,1,0,0,-1]}

Filtering

We have a Waveform that is made of a sine wave concert A (440 Hz) and a tritone above it (D# 609 Hz), and we want to filter out the tritone and end up with just the A.

unfiltered :: Wavetable
unfiltered = modulate (+) 
  (setVolume 0.5 $ fastSin concertA                      stdtr) 
  (setVolume 0.5 $ fastSin (intervalOf tritone concertA) stdtr) 

tritone = countPFD (18/13)

The original signal looks something like this:

>>> show unfiltered
...xxxxx..............................................xxxx.................xx...........................
..x.....x............................................x....x..............xx..xx.........................
.x.......x.............xxxx..........x..............x......x............x......x.......................x
..........x..........xx....xxxx.xxxxx.xxx..........x........x..........x........x..........xxx.......xx.
x.......................................................................................................
...........x.......xx..........x.........x........x..........x........x..........xx.....xxx...xxxxxxx...
............x.....x.......................xx....xx............x......x.............xxxxx................
.............xxxxx..........................xxxx...............x....x...................................
................................................................xxxx....................................

Its (Discrete) Fourier Transform looks like this, with two peaks (one for the A, one for the D#):

>>> show (realDFT 200 stdtr unfiltered)
........................................................................................................
...........................................xxx...............xxxx.......................................
........................................xxx...xxx.........xxx....xx.....................................
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx.........xxxxxxxxx.........xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
........................................................................................................
........................................................................................................
........................................................................................................
........................................................................................................
........................................................................................................

Now, we filter it using a bandpass filter centered at concert A:

filtered :: Wavetable
filtered = tickConvolution 160 10 (sampleFrom $ const theFilter) $ unfiltered
  where
    !theFilter = optimizeFilter 160 $ tickTable stdtr $ bandpassFilter concertA 100

The filtered signal looks more like a single sine wave now:

>>> show filtered
........................................................................................................
........................................................................................................
.....xxxx...................xxxxx...................xxxxx....................xxxx...................xxxx
.xxxx....xxxx............xxx.....xxxx............xxx.....xxxx............xxxx....xxxx............xxx....
........................................................................................................
x............xxxx....xxxx............xxx.....xxxx............xxxx....xxxx............xxx.....xxxx.......
.................xxxx...................xxxxx....................xxxx...................xxxxx...........
........................................................................................................
........................................................................................................

If we take the Fourier Transform of the filtered signal, we get only one peak, at concert A:

>>> show (realDFT 200 stdtr filteredTicks)
........................................................................................................
........................................................................................................
...........................................xxxxx........................................................
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx.....xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
........................................................................................................
........................................................................................................
........................................................................................................
........................................................................................................
........................................................................................................

If you write filtered and unfiltered to .wav files using testWave, you can hear the difference!