Semiditonus

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In harmony, the semiditonus is the ratio 6:5 (sesquiquintum) between a pair of frequencies or, equivalently, the ratio 5:6 between a pair of wavelengths. It is the harmonic mean of unison and diapente:

It is equal to diapente divided by ditonus:

This means that diapente is equal to a ditonus and a semiditonus, put together.

The semiditonus is 1.00110011001100110011... in binary, and it is the inversion of the exadem maius (major sixth) (5:3), viz.

The exadem maius is the sum of the first five reciprocals of triangular numbers:

The semiditonus is also called the minor third.

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

External links

Pythagorean tuning (Contemporary text in English.)
Johannes Tinctoris Liber de arte contrapuncti, Liber secundus (The text is in Latin.)