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.
creates a pitch sequence from a predefined interval list or an arbitrary list of numbers interpreted as intervals measured in cents.
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
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.
Here is a list consisting of the frequencies in a one-octave, equal-tempered chromatic scale starting at 440 hertz.
This confirms that the distance between adjacent pairs of frequencies in
is 100 cents.
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.
Here is a list of all the frequencies of equal-tempered half-steps between 880 and 1760 hertz.
Here are the frequencies of a 36-tone octave, starting at 660 hertz.
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
is 700 cents in equal temperament.
This plays a perfect fifth.