Tritone

(Lat. tritonus).

The Interval equal to the sum of three whole tones. In equal temperament it is exactly half an octave and can therefore be perceived either as an augmented 4th or a diminished 5th. Since the beginnings of polyphony in the early Middle Ages theorists and composers have changed their attitudes to the tritone and its use more than to any other interval.

In the medieval system of church modes the tritone was most conspicuous as the interval between the final and the fourth degree of the modes on F, the Lydian and Hypolydian. Conjunct progressions that outline the ascending tritone or the descending diminished 5th F–B are not uncommon in Gregorian chant (although tritone leaps are rare; see Gellnick), and the introduction of B in plainsong notation seems to have been a relatively late development. The first known use of the word ‘tritonus’ occurs in the 9th- or 10th-century organum treatise Musica enchiriadis, though it was not explicitly prohibited until the development of Guido of Arezzo's hexachordal system, which made B a diatonic note, namely as the fourth degree of the hexachord on F. From then until the end of the Renaissance the tritone, nicknamed the ‘diabolus in musica’, was regarded as an unstable interval and rejected as a consonance by most theorists. In the 13th century it was classified as a discordantia perfecta, along with the minor 2nd and major 7th; and by the 15th century the Lydian mode was understood as having a flattened fourth degree (Tinctoris: Liber de natura … tonorum, 1476), that is, as being a transposed Ionian mode, as Glarean defined it in the Dodecachordon (1547).

Since the 16th century the instability of the tritone has led to developments in two directions. On the one hand, its presence in the dominant 7th chord in four-part counterpoint has made the authentic perfect cadence an even stronger affirmation of the tonality, providing an approach by semitone not only to the tonic degree but also to the 3rd (ex.1a). However, because it divides the octave into two equal parts, the tritone has also assumed the role of the tonally most ambiguous interval, as opposed to the 5th, which divides the octave into unequal parts and is (apart from the octave itself) the interval most fundamental to tonality: in particular, the tritone has come to be recognized as a basic substructure within the diminished 7th chord and the whole-tone scale (ex.1b–c). In the chorale Es ist genug (ex.2) Bach used the tritone embedded in the major scale to create an ambiguity in the relationship between tonic and dominant. Both Mozart and Beethoven used tritones thematically or motivically to divide the octave into equal parts (exx.3–4). In 19th-century Romantic opera the tritone regularly portrays that which is ominous or evil; an early instance is in the dungeon scene in Act 2 of Fidelio, for which the timpani are tuned A–E. Its importance in dramatic music led to further developments in the extension and suspension of tonality, particularly in Wagner’s Tristan und Isolde and Parsifal (see also ‘Tristan’ chord), the late piano works of Liszt and the music of Debussy (ex.5). In 12-note music, the fact that the inversion of the tritone at the interval of an octave yields another tritone (no other interval except the octave has this property) has proved fundamentally significant, both in theory and in practice.

BIBLIOGRAPHY

R. Hammerstein: Diabolus in Musica (Berne, 1974)

E. Wen: ‘A Tritone Key Relationship: the Bridge Sections of the Slow Movement of Mozart's 39th Symphony’, MAn, v (1986), 59–84

D. Deutsch, T. North and L. Ray: ‘The Tritone Paradox’, Music Perception, vii (1990), 371–84

F. Gellnick: The Disposition of the Tritone in Gregorian Chant (diss., U. of Kent, Canterbury, 1998)

WILLIAM DRABKIN