# Music Package

The functions defined in

allow you to make conversions between cents and hertz, and play scales in one of the common tuning systems, or in a user-specified tuning system. In addition, a set of equal-tempered pitch/frequency equivalents is defined.

When you try the examples in this documentation, your computer display may not look exactly the same, since the graphic displays accompanying

*Mathematica*'s sound generation vary from platform to platform.

MusicScale[ilist,freq,dur] | create a Sound object that is a sequence of pitches corresponding to ilist, a list of intervals measured in cents, starting at freq hertz and lasting dur seconds |

Creating a scale.

MusicScale creates a pitch sequence from a predefined interval list or an arbitrary list of numbers interpreted as intervals measured in cents.

JustMajor is an interval list. This plays a major scale in just intonation that starts at 440 Hz and lasts for 3 seconds.

The list of intervals does not have to be in ascending or descending order. Here the starting frequency is 880 Hz.

Predefined interval lists measured in cents.

HertzToCents[flist] | convert a list of frequencies measured in hertz to a list of intervals measured in cents |

CentsToHertz[ilist] | convert a list of intervals measured in cents to a list of frequencies measured in hertz, beginning at frequency 440 hertz |

CentsToHertz[ilist,f] | convert a list of intervals measured in cents to a list of frequencies measured in hertz, beginning at frequency f |

Converting between hertz and cents.

The two functions

HertzToCents and

CentsToHertz convert a list of one type to its complementary type.

This takes a list of frequencies in hertz and gives the distance from one frequency to the next in cents.

Out[4]= | |

Here is a list consisting of the frequencies in a one-octave, equal-tempered chromatic scale starting at 440 hertz.

Out[5]= | |

This confirms that the distance between adjacent pairs of frequencies in

is 100 cents.

Out[6]= | |

This gives the frequency that is 600 cents above the default frequency, 440 hertz, or in musical terminology, one-half octave above the pitch A4.

Out[7]= | |

Here is a list of all the frequencies of equal-tempered half-steps between 880 and 1760 hertz.

Out[8]= | |

Here are the frequencies of a 36-tone octave, starting at 660 hertz.

Out[9]= | |

The

package provides a list of equal-tempered pitch/frequency equivalents. Pitches are named in pitch class/octave notation, where the pitch class is given by a letter from A to G, and the octave is an integer from 0 and 7. The names of flat and sharp notes are written as

,

, and so on.

Most chromatic equivalences are available; for example, C-flat is the same as B, and E-sharp is the same as F. Double-flats and double-sharps are not defined.

The difference between

Aflat4 and

Eflat5 is 700 cents in equal temperament.

Out[10]= | |

This plays a perfect fifth.