Fourth

(Fr. quarte; Ger. Quarte; It. quarta; Gk. diatessarōn).

The Interval between any two notes that are three Diatonic scale degrees apart (e.g. C–F, E–A). Unless specified, the term usually implies ‘perfect 4th’, which is the sum of two whole tones and a diatonic semitone. The augmented 4th, the sum of three whole tones (i.e. the sum of a perfect 4th and a chromatic semitone), can occur diatonically (e.g. C–F in G major or E minor); the diminished 4th, which is equal to a perfect 4th less a chromatic semitone (e.g. C–F, F–B), is never diatonic. The ratio of the perfect 4th in Just intonation is 4:3.

The 4th has a unique position in Western music because it has been regarded as a Perfect interval (like the unison, 5th and octave) and a dissonance at the same time. In ancient Greek music the basis of melody was the Tetrachord, a set of four pitches encompassed by a 4th. The earliest forms of medieval parallel Organum favoured it as the interval between the vox organalis and vox principalis. With the further development of polyphonic music in the 12th and 13th centuries, the 5th replaced the 4th as the most important Consonance after the octave and the unison. By the 15th century the 4th appeared as a consonance only between the upper parts of a vertical sonority, for example in 6-3 chords of the fauxbourdon style and at 8-5-1 cadences (e.g. D–A–D); composers of the later 15th century, including Du Fay, sometimes deliberately avoided the 4th in three-part writing (see Non-quartal harmony), and Tinctoris deemed it a dissonance in his Terminorum musicae diffinitorium (c1473).

Since the Renaissance the 4th has been considered a consonance only when it is understood as the inversion of the 5th. By itself it is considered not so much dissonant as ‘unstable’; reckoning from the lower note, it lies halfway between the 3rd and the 5th that make up a triad and must therefore resolve to one of these (usually the 3rd). With the avoidance of triadic harmony in the 20th century, in both rigorously non-tonal and ‘neo-modal’ music, the 4th has come back into use as an important vertical interval. Moreover, chords built of perfect 4ths have come to be regarded as stable harmonic structures (particularly in the music of Hindemith; their use in Schoenberg's Chamber Symphony no.1 and Bartók's Concerto for Orchestra is well known), and the tonic ‘triad’ in which the 4th has been substituted for the 3rd (in C major, C–F–G–C instead of C–E–G–C) has been used effectively by composers like Stravinsky as the final sonority of a tonal work.

WILLIAM DRABKIN