#### Overview of this book

Today's world of science and technology is all about speed and flexibility. When it comes to scientific computing, NumPy is on the top of the list. NumPy will give you both speed and high productivity. "NumPy Cookbook" will teach you all about NumPy, a leading scientific computing library. NumPy replaces a lot of the functionality of Matlab and Mathematica, but in contrast to those products, it is free and open source. "Numpy Cookbook" will teach you to write readable, efficient, and fast code that is as close to the language of Mathematics as much as possible with the cutting edge open source NumPy software library. You will learn about installing and using NumPy and related concepts. At the end of the book, we will explore related scientific computing projects. This book will give you a solid foundation in NumPy arrays and universal functions. You will also learn about plotting with Matplotlib and the related SciPy project through examples. "NumPy Cookbook" will help you to be productive with NumPy and write clean and fast code.
NumPy Cookbook
Credits
www.PacktPub.com
Preface
Free Chapter
Winding Along with IPython
Get to Grips with Commonly Used Functions
Connecting NumPy with the Rest of the World
Audio and Image Processing
Special Arrays and Universal Functions
Profiling and Debugging
Quality Assurance
Speed Up Code with Cython
Index

## 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:

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...```