# The Representation of Sound

"Sound" described how you can take functions and lists of data and produce sounds from them. Here we discuss how sounds are represented in

*Mathematica*.

*Mathematica* treats sounds much like graphics. In fact,

*Mathematica* allows you to combine graphics with sound to create pictures with "sound tracks".

In analogy with graphics, sounds in

*Mathematica* are represented by symbolic sound objects. The sound objects have head

Sound, and contain a list of sound primitives, which represent sounds to be played in sequence.

Sound[{s_{1},s_{2},...}] | a sound object containing a list of sound primitives |

The structure of a sound object.

The functions

Play and

ListPlay discussed in

"Sound" return

Sound objects.

Play returns a Sound object. On appropriate computer systems, it also produces sound. |

SampledSoundList[{a_{1},a_{2},...},r] | a sound with a sequence of amplitude levels, sampled at rate r |

SampledSoundFunction[f,n,r] | a sound whose amplitude levels sampled at rate r are found by applying the function f to n successive integers |

SoundNote[n,t,"style"] | a note-like sound with note n, time specification t, with the specified style |

*Mathematica* sound primitives.

At the lowest level, all sounds in

*Mathematica* are represented as a sequence of amplitude samples, or as a sequence of MIDI events. In

SampledSoundList, these amplitude samples are given explicitly in a list. In

SampledSoundFunction, however, they are generated when the sound is output, by applying the specified function to a sequence of integer arguments. In both cases, all amplitude values obtained must be between

-1 and 1. In

SoundNote, a note-like sound is represented as a sequence of MIDI events that represent the frequency, duration, amplitude and styling of the note.

ListPlay generates

SampledSoundList primitives, while

Play generates

SampledSoundFunction primitives. With the default option setting

Compiled->True,

Play will produce a

SampledSoundFunction object containing a

CompiledFunction.

Once you have generated a

Sound object containing various sound primitives, you must then output it as a sound. Much as with graphics, the basic scheme is to take the

*Mathematica* representation of the sound, and convert it to a lower-level form that can be handled by an external program, such as a

*Mathematica* front end.

The low-level representation of sampled sound used by

*Mathematica* consists of a sequence of hexadecimal numbers specifying amplitude levels. Within

*Mathematica*, amplitude levels are given as approximate real numbers between

-1 and 1. In producing the low-level form, the amplitude levels are "quantized". You can use the option

SampleDepth to specify how many bits should be used for each sample. The default is

SampleDepth->8, which yields 256 possible amplitude levels, sufficient for most purposes. The low-level representation of note-based sound is as a time-quantized byte stream of MIDI events, which specify various parameters about the note objects. The quantization of time is determined automatically at playback.

You can use the option

SampleDepth in

Play and

ListPlay. In sound primitives, you can specify the sample depth by replacing the sample rate argument by the list

{rate, depth}.