Rooted interval

From Xenharmonic Wiki
Jump to navigation Jump to search

A rooted interval is in the context of octave equivalence a rational interval over a power of 2, i.e. of the form [math]x/2^n[/math] for any positive integer x and nonnegative integer n.

Playing a rooted interval in a harmonic timbre, the virtual fundamental is of the same pitch as the bass, or whole octaves below the bass. In other words, the virtual fundamental is in the same pitch class as the bass. This gives rooted intervals the distinct characteristic of securing its own bass than suggesting other pitch classes.

Rooted intervals can be easily generalized to nonoctave equivalence such as [math]x/3^n[/math] if the tritave is used as an equivalence.

See also