# M-Relation

##### Glossary

#### Set Theory

Two set classes are **M-related** if they share the same interval content in the interval classes for whole-tone, minor third, major third, and tritone (equivalent to the FC2, FC3, FC4, FC6 components) but have semitones and fourths swapped. The “M” stands for __M__ultiplication, referring to **M _{5}**(y) and

**M**(y).

_{7}So for example the pentatonic scale and the five-note subset of the chromatic scale are M-related, since they have the same interval content for everything but semitones and fourths, which are swapped.

Many set classes are **self-M-related**, for example 6-Z12, (012467), which means replacing semitones with fourths results in the same set class. (Perhaps the set class has no semitone or fourth interval content, such as the augmented chord.)

The M-relation works on FC1 and FC5 (semitones and fourths) in 12-TET because 1 and 5 (or 11 and 7) are the generators of the cyclic group **Z**_{12}, since 5, 7, and 11 are relatively prime to 12.

The animated lines show fourths and fifths, going out from the note C to notes 5 or 7 steps away on the circle, repeatedly, until we arrive one tritone away, at F#. The fact that the same transformation converts the circle of fifths to the circle of semitones and back demonstrates that the M-relation is its own inverse.

See also Z-Relation.