In music theory, tertian (Latin: tertianus, "of or concerning thirds") describes any piece, chord, counterpoint etc. constructed from the intervals of (major and minor) thirds. An interval such as that between the notes A and C encompasses 3 semitone intervals (A-B♭-B♮-C) and is termed a minor third while one such as that between C and E encompasses 4 semitones (C-D♭-D♮-E♭-E♮) and is called a major third. Tertian harmony (also called tertiary harmony) principally uses chords based on thirds; the term is typically used to contrast with quartal and quintal harmony which uses chords based on fourths or fifths.
Quartal chord on A equals thirteenth chord on B♭, distinguished by the arrangement of chord factors.
A common triad chord can be regarded as consisting of a "stack" of two thirds. There are four permutations: A major third stacked on a major third creates an augmented triad. A minor third on top of a major third manifests a major triad. A major third on top of a minor third produces a minor triad. Finally, a minor third stacked on a minor third constitutes a diminished triad.
A musical scale may also be analysed as a succession of thirds.
The meantone temperament, a system of tuning that emphasises pure thirds, may be called "tertian".
Chords built from sixths may also be referred to as tertian because sixths are equivalent to thirds when inverted, and vice versa: any sixth can be taken as the inversion of a third. For instance the interval C-A is a major sixth that, when inverted, gives the interval A-C, which is a minor third.
Tertian root movements have been used innovatively in chord progressions as an alternative to root motion in fifths, as for example in the "thirds cycle" used in John Coltrane's Coltrane changes, as influenced by Nicolas Slonimsky's Thesaurus of Scales and Melodic Patterns. Wikipedia, Tertian