Generating sounds

A sound can be represented mathematically by a sine wave, with a certain amplitude, frequency, and phase. We can randomly select frequencies from a list specified on Wikipedia at http://en.wikipedia.org/wiki/Piano_key_frequencies that complies with the following formula:

Generating sounds

The variable n in this formula is the number of the piano key. We will number the keys from 1 to 88. We will also select the amplitude, duration, and phase at random.

How to do it...

We will begin by initializing random values, then generate sine waves, compose a melody, and finally, plot the generated audio data with Matplotlib.

  1. Initialization.

    Initialize to random values:

    • the amplitude between 200 to 2000,
    • the duration to 0.01 to 0.2,
    • the frequencies using the formula already mentioned
    • the phase to values between 0 and 2 pi
    • NTONES = int(sys.argv[1])
      amps = 2000. * numpy.random.random((NTONES,)) + 200.
durations = 0.19 * numpy.random.random((NTONES,)) + 0.01
keys = numpy.random.random_integers(1, 88, NTONES)
freqs = 440.0 * 2 ** ((keys - 49.)/12.)
phi = 2 * numpy.pi * numpy.random.random((NTONES,))
  2. Generate sine waves.

    Write a generate function to generate sine waves:

    def generate(freq, amp, duration, phi):
  t = numpy.linspace(0, duration, duration * RATE)
  data = numpy.sin(2 * numpy.pi * freq * t + phi) * amp

  return data.astype(DTYPE)
  3. Compose.

    Once we have generated a few tones, we only need to compose a coherent melody. For now, we will just concatenate the sine waves—this does not give a nice melody, but could serve as a starting point for more experimenting:

    for i in xrange(NTONES):
  newtone = generate(freqs[i], amp=amps[i], duration=durations[i], phi=phi[i])
  tone = numpy.concatenate((tone, newtone))
  4. Plot the data.

    Plot the generated audio data with Matplotlib:

    matplotlib.pyplot.plot(numpy.linspace(0, len(tone)/RATE, len(tone)), tone)
matplotlib.pyplot.show()

    The generated audio data plot is shown as follows:

    How to do it...

The source code for this example is as follows:

import scipy.io.wavfile
import numpy
import sys
import matplotlib.pyplot

RATE = 44100
DTYPE = numpy.int16

# Generate sine wave
def generate(freq, amp, duration, phi):
  t = numpy.linspace(0, duration, duration * RATE)
  data = numpy.sin(2 * numpy.pi * freq * t + phi) * amp

  return data.astype(DTYPE)

if len(sys.argv) != 2:
    print "Please input the number of tones to generate"
    sys.exit()

# Initialization
NTONES = int(sys.argv[1])
amps = 2000. * numpy.random.random((NTONES,)) + 200.
durations = 0.19 * numpy.random.random((NTONES,)) + 0.01
keys = numpy.random.random_integers(1, 88, NTONES)
freqs = 440.0 * 2 ** ((keys - 49.)/12.)
phi = 2 * numpy.pi * numpy.random.random((NTONES,))

tone = numpy.array([], dtype=DTYPE) 

# Compose 
for i in xrange(NTONES):
    newtone = generate(freqs[i], amp=amps[i], duration=durations[i], phi=phi[i])
    tone = numpy.concatenate((tone, newtone))

scipy.io.wavfile.write('generated_tone.wav', RATE, tone)

# Plot audio data
matplotlib.pyplot.plot(numpy.linspace(0, len(tone)/RATE, len(tone)), tone)
matplotlib.pyplot.show()

How it works...

We created a WAV file with randomly generated sounds. The concatenate function was used to concatenate sine waves.

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