Tonus

In harmony, the tonus is the ratio 9:8 between a pair of frequencies or, equivalently, the ratio 8:9 between a pair of wavelengths. It is the arithmetic mean of unison and ditono:

It is equal to diapente divided by diatessaron:

This means that a diapente is equal to a diatessaron and a tonus, put together.

The tonus is 1.001 in binary — 1 + 2⁻³ — and it is the inversion of the eptadem minus (minor seventh) (16:9),

Notice also that the eptadem minus is a pair of diatessarons put together:

The eptadem minus is the sum of the first eight reciprocals of triangular numbers:

The tonus is also called major second.

Major and Minor

The tonus comes in two slightly different versions: the tuono maggiore (9:8) and the tuono minore (10:9).

The tuono minore is the harmonic mean of unison and ditono:

In binary, the tuono minore is equal to 1.000111000111000111000111...

See also: unison, diapason, diapente, diatessaron, ditonus, semiditonus, semitonium.