Synthesizes musical notes using Pulse Code Modulation, using custom waveform provided by user, using Haskell and SDL2
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stack build # Installs all dependencies
stack install # Installs the package locally
stack run # Runs the built executable
wavemaker-exe -t TEMPO_IN_BPM -i music.wmk
To play music written in music.wmk, at specified BPM
If tempo and filename is not specified, default tempo is 100, and if filename isn't
specified, all notes in an Octave are played.
Simple melodies can be specified using the following grammar
[a1a2..] implies on of (a1,a2,a3.. and so on)
a+ implies one or more of a
a* implies none or more of a
a? implies one or none of a
note := [ABCDEFGR](#?)[Integer][WHQEST]
mujik := note*
Here, [ABCDEFG] represents the Root Notes.
R is for Rest. (No Sound)
# is obvious, (Flats not supported)
[WHQEST] represents the length of the note
W -> Whole (4 Beats)
H -> Half (2 Beats)
Q -> Quarter (1 Beat)
E -> Eighth (0.5 Beat)
S -> Sixteenth (0.25 Beat)
T -> ThirtySecond (0.125 Beat)
These mappings are conventional.
any valid music reccognized by this program is nothing but a space separated list of
notes.
Refer to this sample as an example
According to wikipedia:
Pulse-code modulation (PCM) is a method used to digitally represent sampled analog signals
Consider we have an initial signal.
In order to digitally store this, we have to sample this signal at regular intervals, at some sampling rate, and store these samples.
In a sound of length t seconds, the number of samples played are t * sampleRate.
The volume can be controlled by Amplitude of the samples.
Sound S with n samples becomes a quieter sound S', which has 10 percent the volume.
S {s1, s2 .... sn } -> S' { 0.1 * s : s <- S }.
Pitch of the sound is controlled by adjusting the distance between the samples being played.
What this means is, for a sound of w hertz, the code looks like so:
S: Samples (List of Float)
N: Num Samples
W: Frequency we want to produce
wFrequencyWave = [ A * S[ i*W % N ] where i is an integer (0, UpperLim) ]
By Changing UpperLim, we change the duration of the sound wave.
By Changing A we change the volume of the sound wave.
This is the logic with which sounds are produced, and can be found here, in the function note
According to this
Any note can be generated using
freq' = freq * (2 ^ ( N / 12 ))
Simple explanation:
- 1 Octave, range of tones between any note and it's next harmonic, such that ratio is 2:1
- In an Octave, there are 12 Semitones
- If we start at freq = A = 440hz, and move N from 0 to 12, we generate the higher semitones.
- freq = A = 440, N = [0,1,2,3,4,5,6,7] -> A, A#, B, C, C#, D, D#, E
This is the logic with which pitches of notes are calculated here in the function semitone
Yes. There are.
Because of the Nyquist Rate, the highest pitch we can generate by sampling, is half of the sampling rate.
This means, if I want to generate a pitch of 10000Hz, I must have atleast 20000 samples to pick from in a single period of the signal.
When you use the default sin function given in most math libraries for this, it's a trivial point you can ignore and move on.
When you try to draw your own waveform, this becomes very relevant.
A major part of music which people forget is the timbre, or rather the voice. Two people can produce the same pitch B, but the shape of their voice has different waveforms.
We can use this project to produce any number of different voices by changing the waveform.
Below we describe how to recieve it as input and represent it efficiently
The initial idea was to simply create a simple window in SDL, and code it up draw the curve, point by point.
The Algorithm:
1. Create window of W x H
2. Create a Vector of length W, with initial value 0
3. When a point (x,y) is clicked on the window,
4. Transform (x,y) from SDL coordinate system to (x, (y-h/2) / (h/2))
this will constraint y value between -1 and 1.
5. Each X can have only single Y.
6. Window keeps taking mouse input until `Q` Pressed.
7. When Q pressed, we have W samples of some custom waveform
This gives problems because of the following reasons.
- W is constrainted to size of your display, usually 1920pixels.
- According to Nyquist Rate, highest pitch that this method can make would be 960Hz, which is lesser than the pitch a grand piano can produce.
- Also, because of the way sample is input, signal is very noisy.
- Signal can be smoothened using Discrete Time Fourier Series of input signal, but the limitation by Nyquist Rate still persists.
This logic is implemented here
Using Bezier curves, we can define a continuous line using a set of Control Points
This looks something like
The curve will necessarily pass through first and last points, and the rest of the points control the direction and sharpness of the curves.
And by using this equation, using discrete points, we can create a continuous source to sample from.
This means the sample rate can be as high as we need it do be.
We are now limited by the efficiency of the program than the quality of the algorithm.
The algorithm used to represent beziers is the De Casteljau Algorithm
This logic is implemented here