A Composer's Guide to Sound Production with Mathematica

Arun Chandra

Wolfram Research, Inc.
(Draft)

Basic Sound Operations with Mathematica

Playing a Function

Playing Lists of Integers

Playing Sequences of Sounds

Stereo Output

Changing the SampleRate

Changing the SampleDepth (Quantization)

Setting the PlayRange

Apparent Loudness and the PlayRange

Clipping and the PlayRange

Efficient Computation with Mathematica

Nesting

Using the Evaluate Command

Problems with Output Distortion

Standard Defaults

SampleRate

SampleDepth

Standard Wave Forms

Efficient Generation of Standard Waveforms with Mathematica

Sawtooth Waves

Square Waves

Triangle Waves

Fourier Synthesis of Sawtooth Waves

Plotting Sawtooth Waves

Playing a Sawtooth Wave

Fourier Synthesis of Square Waves

Plotting Square Waves

Playing Square Waves

Fourier Synthesis of Triangle Waves

Plotting Triangle Waves

Playing Triangle Waves

Envelopes

Amplitude Change

Decay Envelopes

Decay Envelopes for a Single Tone

Decay Envelopes for a Fundamental with Overtones

Growth Envelopes

Interference

Interference due to Phase Relationships

Interference due to Beating

Amplitude Modulation

Simple Amplitude Modulation (tremolo)

Complex Amplitude Modulation

``Ring'' Modulation (Suppressed Carrier Modulation)

Complex Ring Modulation

Frequency Modulation

The Modulation Index

The Modulation Ratio (Harmonic and Inharmonic Partials)

Simple Frequency Modulation (Vibrato)

Complex Frequency Modulation

Serial Frequency Modulation ("Cascade" FM)

Parallel Frequency Modulation

Double Modulator FM

Double Carrier FM

Scales and Tunings

Pythagorean Tuning

Just Intonation

Mean-Tone Temperment

Equal Temperment

Quarter-Tone and Sixth-Tone Scales

References