# Sound

On most computer systems,

*Mathematica* can produce not only graphics but also sound.

*Mathematica* treats graphics and sound in a closely analogous way.

For example, just as you can use

Plot[f, {x, x_{min}, x_{max}}] to plot a function, so also you can use

Play[f, {t, 0, t_{max}}] to "play" a function.

Play takes the function to define the waveform for a sound: the values of the function give the amplitude of the sound as a function of time.

Play[f,{t,0,t_{max}}] | play a sound with amplitude f as a function of time t in seconds |

Playing a function.

On a suitable computer system, this plays a pure tone with a frequency of 440 hertz for one second. |

Sounds produced by

Play can have any waveform. They do not, for example, have to consist of a collection of harmonic pieces. In general, the amplitude function you give to

Play specifies the instantaneous signal associated with the sound. This signal is typically converted to a voltage, and ultimately to a displacement. Note that

*amplitude* is sometimes defined to be the

*peak* signal associated with a sound; in

*Mathematica*, it is always the

*instantaneous* signal as a function of time.

This plays a more complex sound. |

Play is set up so that the time variable that appears in it is always measured in absolute seconds. When a sound is actually played, its amplitude is sampled a certain number of times every second. You can specify the sample rate by setting the option

SampleRate.

Play[f,{t,0,t_{max}},SampleRate->r] |

| play a sound, sampling it r times a second |

Specifying the sample rate for a sound.

In general, the higher the sample rate, the better high-frequency components in the sound will be rendered. A sample rate of

*r* typically allows frequencies up to

*r*/2 hertz. The human auditory system can typically perceive sounds in the frequency range 20 to 22000 hertz (depending somewhat on age and sex). The fundamental frequencies for the 88 notes on a piano range from 27.5 to 4096 hertz.

The standard sample rate used for compact disc players is 44100. The effective sample rate in a typical telephone system is around 8000. On most computer systems, the default sample rate used by

*Mathematica* is around 8000.

You can use

Play[{f_{1}, f_{2}, ...] to produce stereo sound. In general,

*Mathematica* supports any number of sound channels.

ListPlay[{a_{1},a_{2},...},SampleRate->r] |

| play a sound with a sequence of amplitude levels |

Playing sampled sounds.

The function

ListPlay allows you simply to give a list of values which are taken to be sound amplitudes sampled at a certain rate.

When sounds are actually rendered by

*Mathematica*, only a certain range of amplitudes is allowed. The option

PlayRange in

Play and

ListPlay specifies how the amplitudes you give should be scaled to fit in the allowed range. The settings for this option are analogous to those for the

PlotRange graphics option discussed in

"Options for Graphics".

PlayRange->Automatic | use an internal procedure to scale amplitudes |

PlayRange->All | scale so that all amplitudes fit in the allowed range |

PlayRange->{a_{min},a_{max}} | make amplitudes between a_{min} and a_{max} fit in the allowed range, and clip others |

Specifying the scaling of sound amplitudes.

While it is often convenient to use the setting

PlayRange->Automatic, you should realize that

Play may run significantly faster if you give an explicit

PlayRange specification, so it does not have to derive one.

Playing sounds programmatically.

A

Sound object in output is typically formatted as a button which contains a visualization of the sound and which plays the sound when pressed. Sounds can be played without the need for user intervention or producing output by using

EmitSound. In fact, the internal implementation of

Sound buttons uses

EmitSound when the button is pressed.

The internal structure of

Sound objects is discussed in

"The Representation of Sound".