Mathematica Cookbook

Chapter 9. Audio and Music Processing

Deep in the back of my mind is an unrealized sound Every feeling I get from the street says it soon could be found When I hear the cold lies of the pusher, I know it exists It’s confirmed in the eyes of the kids, emphasized with their fists . . .

The music must change For we’re chewing a bone We soared like the sparrow hawk flied Then we dropped like a stone Like the tide and the waves Growing slowly in range Crushing mountains as old as the Earth So the music must change

—The Who, “Music Must Change”

9.0 Introduction

Audio and music can be approached in three different ways with Mathematica: (1) as traditional musical notes with associated pitch names and other specifications, such as duration, timbre, loudness, etc.; (2) as abstract mathematical waveforms that represent vibrating systems; and (3) as digitally represented sound—just think of .wav and .aiff files. If nothing else, this chapter should hint at the ease with which Mathematica can be put in the service of the arts. Let’s make some music!

Mathematica allows you to approach music and sound in at least three different ways. You can talk to Mathematica about musical notes such as "C" or "Fsharp". You can directly specify other traditional concepts, such as timbre and loudness, with Mathematica’s Sound, SoundNote, and PlayList functions. You can ask Mathematica to play analog waveforms. And you can ask Mathematica to interpret digital sound samples.

9.1 Creating Musical Notes

Problem

You ...