07_synth.md

This is one of the 100+ free recipes of the IPython Cookbook, Second Edition, by Cyrille Rossant, a guide to numerical computing and data science in the Jupyter Notebook. The ebook and printed book are available for purchase at Packt Publishing.

▶ Text on GitHub with a CC-BY-NC-ND license
▶ Code on GitHub with a MIT license

Chapter 11 : Image and Audio Processing

11.7. Creating a sound synthesizer in the Notebook

In this recipe, we will create a small electronic piano in the Notebook. We will synthesize sinusoidal sounds with NumPy instead of using recorded tones.

How to do it...

1. We import the modules:

import numpy as np
import matplotlib.pyplot as plt
from IPython.display import (
    Audio, display, clear_output)
from ipywidgets import widgets
from functools import partial
%matplotlib inline

2. We define the sampling rate and the duration of the notes:

rate = 16000.
duration = .25
t = np.linspace(
    0., duration, int(rate * duration))

3. We create a function that generates and plays the sound of a note (sine function) at a given frequency, using NumPy and IPython's Audio class:

def synth(f):
    x = np.sin(f * 2. * np.pi * t)
    display(Audio(x, rate=rate, autoplay=True))

4. Here is the fundamental 440 Hz note:

synth(440)

5. Now, we generate the note frequencies of our piano. The chromatic scale is obtained by a geometric progression with the common ratio $2^{1/12}$:

notes = 'C,C#,D,D#,E,F,F#,G,G#,A,A#,B,C'.split(',')
freqs = 440. * 2**(np.arange(3, 3 + len(notes)) / 12.)
notes = list(zip(notes, freqs))

6. Finally, we create the piano with the Notebook widgets. Each note is a button, and all buttons are contained in a horizontal box container. Clicking on one note plays a sound at the corresponding frequency.

layout = widgets.Layout(
    width='30px', height='60px',
    border='1px solid black')

buttons = []
for note, f in notes:
    button = widgets.Button(
        description=note, layout=layout)

    def on_button_clicked(f, b):
        # When a button is clicked, we play the sound
        # in a dedicated Output widget.
        with widgets.Output():
            synth(f)

    button.on_click(partial(on_button_clicked, f))
    buttons.append(button)

# We place all buttons horizontally.
widgets.Box(children=buttons)

How it works...

A pure tone is a tone with a sinusoidal waveform. It is the simplest way of representing a musical note. A note generated by a musical instrument is typically much more complex. Although the sound contains many frequencies, we generally perceive a musical tone (fundamental frequency).

By generating another periodic function instead of a sinusoidal waveform, we would hear the same tone, but a different timbre. Electronic music synthesizers are based on this idea.

There's more...

Here are a few references:

• Synthesizer on Wikipedia, available at https://en.wikipedia.org/wiki/Synthesizer
• Equal temperament on Wikipedia, available at https://en.wikipedia.org/wiki/Equal_temperament
• Chromatic scale on Wikipedia, available at https://en.wikipedia.org/wiki/Chromatic_scale

See also

• Applying digital filters to speech sounds