Thursday, September 30, 2010

My new musical instrument: Python

It's still very young, but here is the library I've been working on for generating music in (nothing but) Python. "" is an example of what you can do. The real purpose isn't to code your music out this way, it's intended as a backend for generating / manipulating music. My end goal is a tab-based editor that plays back with this, but I'm going to keep working on this backend and hope some brave snake wrestler comes along and has the itch to write a proper interface (and if that doesn't happen, I'll start on the interface when I feel satisfied with the backend).

The Timeline and Hit classes are just ideas right now. I'm not sure they'll stay in the form they are (I'm thinking a guitar-oriented timeline, holding fret/string/amplitude per hit, is more along the lines of what I need).

I'm also on the hunt for efficient numpy/scipy implemented effects and sound sources. I've been playing around some with generating Karplus-Strong pluck sounds and delay/chorus/flanger effects, but I'm not exactly satisfied with the sound and runtime efficiency of what I have.

Be sure to check out the "minor" scale version of this "major" progression.

Also be sure to let me know if you have any advice on optimizing (without jumping into the C just yet) or creating a better code interface / representation of these concepts.

Tuesday, September 21, 2010

Procedural music with PyAudio and NumPy

Combining two of my favorite pastimes, programming and music... This is the hacky "reduced to it's basic components" version of a library I've been working on for generating music and dealing with music theory.

Tweaking the harmonics by changing the shape of the harmonic components and ratios can produce some interesting sounds. This one only uses sine waveforms, but a square / saw generator is trivial with numpy.

It takes a second to generate, so don't turn your volume up too loud in anticipation (it may be loud).

import math
import numpy
import pyaudio
import itertools
from scipy import interpolate
from operator import itemgetter

class Note:

NOTES = ['c','c#','d','d#','e','f','f#','g','g#','a','a#','b']

def __init__(self, note, octave=4):
self.octave = octave
if isinstance(note, int):
self.index = note
self.note = Note.NOTES[note]
elif isinstance(note, str):
self.note = note.strip().lower()
self.index = Note.NOTES.index(self.note)

def transpose(self, halfsteps):
octave_delta, note = divmod(self.index + halfsteps, 12)
return Note(note, self.octave + octave_delta)

def frequency(self):
base_frequency = 16.35159783128741 * 2.0 ** (float(self.index) / 12.0)
return base_frequency * (2.0 ** self.octave)

def __float__(self):
return self.frequency()

class Scale:

def __init__(self, root, intervals):
self.root = Note(root.index, 0)
self.intervals = intervals

def get(self, index):
intervals = self.intervals
if index < 0:
index = abs(index)
intervals = reversed(self.intervals)
intervals = itertools.cycle(self.intervals)
note = self.root
for i in xrange(index):
note = note.transpose(
return note

def index(self, note):
intervals = itertools.cycle(self.intervals)
index = 0
x = self.root
while x.octave != note.octave or x.note != note.note:
x = x.transpose(
index += 1
return index

def transpose(self, note, interval):
return self.get(self.index(note) + interval)

def sine(frequency, length, rate):
length = int(length * rate)
factor = float(frequency) * (math.pi * 2) / rate
return numpy.sin(numpy.arange(length) * factor)

def shape(data, points, kind='slinear'):
items = points.items()
keys = map(itemgetter(0), items)
vals = map(itemgetter(1), items)
interp = interpolate.interp1d(keys, vals, kind=kind)
factor = 1.0 / len(data)
shape = interp(numpy.arange(len(data)) * factor)
return data * shape

def harmonics1(freq, length):
a = sine(freq * 1.00, length, 44100)
b = sine(freq * 2.00, length, 44100) * 0.5
c = sine(freq * 4.00, length, 44100) * 0.125
return (a + b + c) * 0.2

def harmonics2(freq, length):
a = sine(freq * 1.00, length, 44100)
b = sine(freq * 2.00, length, 44100) * 0.5
return (a + b) * 0.2

def pluck1(note):
chunk = harmonics1(note.frequency(), 2)
return shape(chunk, {0.0: 0.0, 0.005: 1.0, 0.25: 0.5, 0.9: 0.1, 1.0:0.0})

def pluck2(note):
chunk = harmonics2(note.frequency(), 2)
return shape(chunk, {0.0: 0.0, 0.5:0.75, 0.8:0.4, 1.0:0.1})

def chord(n, scale):
root = scale.get(n)
third = scale.transpose(root, 2)
fifth = scale.transpose(root, 4)
return pluck1(root) + pluck1(third) + pluck1(fifth)

root = Note('A', 3)
scale = Scale(root, [2, 1, 2, 2, 1, 3, 1])

chunks = []
chunks.append(chord(21, scale))
chunks.append(chord(19, scale))
chunks.append(chord(18, scale))
chunks.append(chord(20, scale))
chunks.append(chord(21, scale))
chunks.append(chord(22, scale))
chunks.append(chord(20, scale))
chunks.append(chord(21, scale))

chunks.append(chord(21, scale) + pluck2(scale.get(38)))
chunks.append(chord(19, scale) + pluck2(scale.get(37)))
chunks.append(chord(18, scale) + pluck2(scale.get(33)))
chunks.append(chord(20, scale) + pluck2(scale.get(32)))
chunks.append(chord(21, scale) + pluck2(scale.get(31)))
chunks.append(chord(22, scale) + pluck2(scale.get(32)))
chunks.append(chord(20, scale) + pluck2(scale.get(29)))
chunks.append(chord(21, scale) + pluck2(scale.get(28)))

chunk = numpy.concatenate(chunks) * 0.25

p = pyaudio.PyAudio()
stream =, channels=1, rate=44100, output=1)

The scale in use is Harmonic Minor.
It's encoded via halfsteps as: "[2, 1, 2, 2, 1, 3, 1]"
Try changing it to natural minor: "[2, 1, 2, 2, 1, 2, 2]"

I'd be interested in teaming up with anyone willing to write some actual input methods (matrix sequencer, tab reader, however else it could be done) as well as an interface for tweaking synthesized sounds. My present code base is a bit much for a blog post, so contact me if interested.

Thursday, September 9, 2010

Javascript insort function

I recently had the need for some sorted insertion in Javascript arrays, thought I'd share this tiny bit of code:

Array.prototype.bisect = function(x, lo, hi) {
var mid;
if(typeof(lo) == 'undefined') lo = 0;
if(typeof(hi) == 'undefined') hi = this.length;
while(lo < hi) {
mid = Math.floor((lo + hi) / 2);
if(x < this[mid]) hi = mid;
else lo = mid + 1;
return lo

Array.prototype.insort = function(x) {
this.splice(this.bisect(x), 0, x);

Of course, these methods only work on an already sorted (or empty) array, so if you're using them on an array that came from elsewhere, sort it first. But once sorted, these insertions will maintain the sortedness, no need to 'push' and 'sort' every time you need to insert something into a sorted array.

(lo and hi parameters are optionally possible for the bisection method to allow restricted searches)