Hertz Google Doodle, correctly done

wave_doodle.py

import numpy
import pylab

points = [
  (3, 3.0),
  (3, 3.0),
  (3, 3.0),
  (2, 2.0),
  (2, 2.0),
  (2, 2.0),
  (2, 2.0),
  (2, 3.0),
  (2, 3.0),
  (1, 3.0),
  (2, 2.0),
  (2, 2.0),
]

points = points * 3

N = 50
frequency = []
amplitude_modulation = []
for pitch, amplitude in points:
  frequency += [1.0 / pitch / (2 * N)] * N
  amplitude_modulation += [amplitude] * N

smoothing = numpy.hanning(N)
smoothing /= smoothing.sum()

frequency = numpy.convolve(smoothing, frequency, 'same')
amplitude_modulation = numpy.convolve(smoothing, amplitude_modulation, 'same')

phase = numpy.cumsum(frequency)

y = numpy.sin(2 * numpy.pi * phase) * amplitude_modulation
y = y[len(y) / 3 + 4:-len(y) / 3 + 5]
pylab.figure(figsize=(20, 6))

colors = 'brybgr'
zeros_crossings = numpy.where(numpy.abs(numpy.diff(numpy.sign(y))))[0]
zeros_crossings = [0] + list(zeros_crossings)

for c, x_from, x_to in zip(colors, zeros_crossings[:-1], zeros_crossings[1:]):
  x = range(x_from, x_to + 1)
  pylab.plot(x, y[x], c)

pylab.savefig('doodle.png')