Tritone

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The augmented fourth between C and F# forms a tritone.

The tritone (tri- or three and tone) is a musical interval that spans three whole tones. The tritone is the same as an augmented fourth, which in equal temperament is enharmonic to a diminished fifth. However, only the augmented fourth consists of three whole tones in meantone temperament, from where the terminology derives, and calling the diminished fifth a tritone is incorrect in that context. Often, however, writers use the term tritone to mean specifically half of an octave, without regard to what system of tuning it may belong to. Two tritones add up to six whole tones, which in meantone temperament is a diesis less than an octave, but equal to a perfect octave in equal temperament, where the diesis is tempered out. A common symbol for tritone is TT. It is also sometimes called a tritonus, the name used in German. An equal-tempered tritone may be heard [here].

The tritone is a restless interval, classed as a dissonance in common practice music; less dissonant than the second or seventh, but given the name diabolus in musica ("the Devil's interval") by some from the early music era to the baroque period. It was exploited heavily in the Romantic period as an interval of modulation for its ability to evoke a strong reaction by entering the key least related (retaining only two common tones, the least possible) to what occurs previously.

The equal-tempered tritone (a ratio of [\sqrt:1] or 600 cents) is unique in being its own octave inversion. Note that in other meantone tunings, the augmented fourth and the diminished fifth are distinct intervals because neither is exactly half an octave. In any meantone tuning near to 2/9 comma meantone the augmented fourth will be near to the ratio 7/5 and the diminished fifth to 10/7, which is what these intervals are taken to be in septimal meantone temperament. In 31 equal temperament, for example, the diminished fourth, or tritone proper, is 580.6 cents, whereas a 7/5 is 582.5 cents.

The tritone occurs naturally between the 4th and 7th scale degrees of the major scale (for example, in C major F to B), and depending on which of the two notes occurs in the bass, it is either an augmented 4th, or a diminished 5th. Its most common occurrence is between these scale degrees, in either inversion, when played as the third and seventh of the dominant seventh chord. The sound of the tritone in this chord is arguably what gives it its strong tendency towards resolution.

• The tritone interval is used in the musical Deutsch tritone paradox.
• In jazz harmony, the tritone is both part of the dominant chord and its substitute dominant (also known as the sub V chord). Because they share the same tritone, they are possible substitutes for one another. This is known as tritone substitution.
  For example, in the key of C Major, the primary dominant G7 may be substituted with D♭7 which is its substitute dominant. Note that both have the same tritone (B and F, or enharmonically C♭ and F in reference to the D♭7 chord). In classical music Liszt uses the tritone in the same way in "Au bord d´une source" (B as dominant for B-flat) and many other places.
  This device can also be used in jazz improvisation, whereupon an improviser may use the chord tones of the D♭7 on a G7 chord to create an altered chord characteristic of jazz improvisation.
  The D♭7 chord tones spell out the ♭5, ♭7, ♭9 and maj3rd of the G7 chord, thus effectively outlining both the guide tones (maj3rd and ♭7) of the G7 as well as two altered notes (♭5 and ♭9).
• The tritone retains its "Devil in Music" character in popular music, specifically heavy metal. The opening of Black Sabbath's signature song "Black Sabbath" makes heavy use of the tritone. Other metal songs with prominent tritones in their main riffs are Diamond Head's "Am I Evil?", Metallica's "For Whom the Bell Tolls" and "Enter Sandman" and Dream Theater's "As I Am". Though not a metal band, Rush famously used the tritone to create the distinctive opening riff for the song "YYZ". Perhaps the single guitarist to have made the most extensive use of the tritone is Robert Fripp of King Crimson, who used it repeatedly in King Crimson albums like Larks' Tongues in Aspic, Starless and Bible Black, and Red. Other examples are the beginning of Liszt's Dante Sonata, Sibelius's Fourth Symphony and Jimi Hendrix's "Purple Haze". The tritone is also used throughout Benjamin Britten's War Requiem, as an ironic "point of reference" despite the tone's inherent instability, thereby offering subtle commentary on the nature of war itself. Slayer has traditionally used the tritone extensively, and their 1998 album titled Diabolus in Musica reflects that fact.
• Film composer Bernard Herrmann uses the tritone to great effect in his score for the film The Day the Earth Stood Still, where the interval functions as a motif, played by low brass, for Klaatu's robot Gort.
• Leonard Bernstein underpins almost all the music in West Side Story with persistent tritones. They feature as the opening interval to some of the songs, either melodically ("Maria" and "Cool" both begin with augmented fourths) or harmonically, when a flattened fifth is sung against a major chord ("Gee Officer Krupke"). Elsewhere, tritones figure prominently within "Something's Coming" and the "Jet Song", and the last sonority in the score is that of a high major chord with its own flattened fifth in the bass.
• Danny Elfman uses tritones in his themes for The Simpsons (the first two notes of the opening choral "The Sim-" and the first and third notes of the main instrumental theme, for example) and Dilbert.

External links

• http://www.cameron.edu/~lloydd/webdoc1.html
• [Tonalsoft Encyclopaedia of Tuning]
• [BBC News Magazine article about the tritone]

See also

• List of meantone intervals
• List of musical intervals

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