Tertium major

In harmony, the tertium major is the ratio 5:4 between a pair of frequencies or, equivalently, the ratio 4:5 between a pair of wavelengths. It is the arithmetic mean of unison and diapente.

It is 1.01 in binary, and it is the inversion of the minor sixth (8:5), which means that it is equal to diapason divided by the minor sixth:

The minor sixth is the sum of the first four reciprocals of triangular numbers:

The tertium major is approximately equal to 4 semitones of equal temperament:

Four semitones is equal to 400 cents in equal temperament, but the tertium major in just intonation is 386.31 cents, which makes a error of -13.68 cents with respect 4 semitones of equal temperament.

Three tertium majors are slightly less (-41.05 cents) than a diapason. A tertium major is also called a major third, but notice that here it has been defined as a simple ratio, such as is used in just intonation.

See also: diatessaron, tertium minor.