Sound Synthesis with Numpy

Physically, sound is an oscillation of a mechanical medium that makes the surrounding air also oscillate and transport the sound as a compression wave. Mathematically, the oscillations can be described as



where t is the time, and f the frequency of the oscillation. Each musical note vibrates at a particular frequency and to generate a tone we have to generate an oscillation with the appropriate frequency. The following table shows the complete musical scale between middle A and A-880, in the first column we have the tone and in the second the frequency that we have to use to generate the tone:

Tone	Freq
A	440
B flat	466
B	494
C	523
C sharp	554
D	587
D sharp	622
E	659
F	698
F sharp	740
G	784
A flat	831
A	880

Sound on a computer is a sequence of numbers and we are going to see how to generate an array that represents a musical tone with numpy. The following function is able to generate a note using the formula above:

from numpy import linspace,sin,pi,int16

# tone synthesis
def note(freq, len, amp=1, rate=44100):
 t = linspace(0,len,len*rate)
 data = sin(2*pi*freq*t)*amp
 return data.astype(int16) # two byte integers

And we can use this function to generate an A tone of 2 seconds with 44100 samples per second in this way:

from scipy.io.wavfile import write
from pylab import plot,show,axis

# A tone, 2 seconds, 44100 samples per second
tone = note(440,2,amp=10000)

write('440hzAtone.wav',44100,tone) # writing the sound to a file

plot(linspace(0,2,2*44100),tone)
axis([0,0.4,15000,-15000])
show()

The script put the sound into a wav file and we can play it with an external player. This plot shows a part of the signal generated by the script:

Blog Source: http://glowingpython.blogspot.com/2011/09/sound-synthesis.html
Article Type:
How-to