Tritone
From Wikipedia, the free encyclopedia
| Inverse | tritone | |
|---|---|---|
| Name | ||
| Other names | augmented fourth, diminished fifth | |
| Abbreviation | TT | |
| Size | ||
| Semitones | 6 | |
| Interval class | 6 | |
| Just interval | 7:5, 10:7, 45:32... | |
| Cents | ||
| Equal temperament | 600 | |
| Just intonation | 583, 617, 590... | |
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. It is often used as the main interval of dissonance in Western harmony, and is important in the study of musical harmony.
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[edit] Definition and Nomenclature
Only the augmented fourth consists of three whole tones in meantone temperament. This is where the term is derived. Calling the diminished fifth a "tritone" is parlance. Writers often use the term tritone to mean specifically half of an octave from a given tone, 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.
[edit] Occurrences
The tritone occurs naturally between the 4th and 7th scale degrees of the major scale (for example, from F to B in the key of C major). It is also present in the natural minor scale as the interval formed between the second and sixth scale degrees (for example, from D to Ab in the key of C minor). The melodic minor scale, having two forms, presents a tritone in different locations when ascending and descending (when the scale ascends, the tritone appears between the third and sixth scale degrees and the fourth and seventh scale degrees, and when the scale descends, the tritone appears between the second and sixth scale degrees). Supertonic chords using the notes from the natural minor mode will thus contain a tritone, regardless of inversion.
The major-minor seventh chord contains a tritone within its tone construction. Thus, the tritone will occur between the third and seventh of the dominant seventh chord (for example, G7 in the key of C major) or of any secondary dominant seventh chord (for example, D7 in the key of C major), because both of these chords are forms of the major-minor seventh sonority. Furthermore, the Italian augmented sixth chord (Ab, C, and F# in C major) and German augmented sixth chord (Ab, C, Eb, and F#) are enharmonic equivalents of the major-minor seventh sonority and also contain tritones.
Unlike the similar German and Italian augmented chords, the French augmented sixth chord (Ab, C, D, and F# in C major) is unique in that it can be viewed as being constructed by a superimposition of two intervals of a tritone a whole step apart: a tritone between C and F#, and then a tritone between D and Ab.
The diminished triad (for instance, B, D, and F) also contains a tritone in its construction, and from this fact is derived its name, for it contains a diminished fifth interval (i.e. a tritone). Furthermore, the fully diminished seventh sonority (for instance, B, D, F, and Ab) is made up of the superimposition two tritone intervals a minor third apart (from B to F, and then from D to Ab).
In all of the sonorities mentioned above, the restless sound of the tritone serves as an important push towards resolution.
- In jazz tertian harmony, where triads and seventh chords are often expanded to become 9th, 11th, or 13th chords, the tritone often occurs as a substitute for the the naturally ocurring interval of the perfect 11th. Since the perfect 11th (i.e. an octave plus perfect fourth, or C to F') is typically perceived as a dissonance requiring a resolution to a major or minor 10th, chords that expand to the 11th or beyond typically raise the 11th a half step (thus giving us an augmented 11th, or an octave plus a tritone from the root of the chord) and present it in conjunction with the perfect 5th of the chord. In other words, a typical jazz 11th chord contains the following notes: C, E, G, Bb, D, F#.
- Again, 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.
- The tritone interval is used in the musical/auditory illusion known as the tritone paradox.
The tritone is also one of the defining features of the often neglected Locrian mode.
Compared to other commonly ocurring intervals like the major second or the minor third, the augmented fourth and the diminished fifth (both two valid enharmonic interpretations of the tritone) are awkward intervals to sing. Western composers have traditionally avoided using it explicitly in their melody lines, often preferring to use passing tones or extra note skipping instead of using a direct leap of an augmented fourth or diminished fifth in their melodies. However, as time went by, composers have gradually used the tritone more and more in their music, disregarding its awkwardness and exploiting its expressiveness. (See Musical examples below).
[edit] Historical uses
The tritone is a restless interval, classed as a dissonance in Western music from the early Middle Ages through the end of the common practice period. The name diabolus in musica ("the Devil in music") has been applied to the interval from at least the early eighteenth century. Telemann in 1733 notes that "mi contra fa...welches die alten den satan in der music nenneten," ("Mi against Fa, which the ancients called 'Satan in music'") while Mattheson in 1739 writes that the "alten Solmisatores dieses angenehme Intervall mi contra fa oder den Teufel in der Music genannt haben." ("Older singers with solmization called this pleasant interval 'mi contra fa' or 'the devil in music'.") [1] Although both of these authors cite the association with the devil as from the past, there are no known citations of this term from the Middle Ages, as is commonly asserted.[2] (Suggestions that singers were excommunicated or otherwise punished by the church for invoking this interval are likewise fanciful). However, avoidance of the interval for musical reasons has a long history, stretching back to the parallel organum of the Musica Enchiriadis. In all these expressions, including the commonly cited "mi contra fa est diablous in musica," the "mi" and "fa" refer to notes from two adjacent hexachords. For instance, in the tritone B-F, B would be "mi," that is the third scale degree in the "hard" hexachord beginning on G, while F would be "fa," that is the fourth scale degree in the "natural" hexachord beginning on C.
In Baroque and Classical music, the tritone is one of the defining intervals of the dominant-seventh chord and two tritones separated by a minor third give the fully-diminished seventh chord its characteristic sound. In minor, the diminished triad (comprising two minor thirds which together add up to a tritone) appears on the second scale degree, and thus features prominently in the progression iio-V-i. Often, the inversion iio6 is used to move the tritone to the inner voices as this allows for stepwise motion in the bass to the dominant root. In three-part counterpoint, free use of the diminished triad in first inversion is permitted, as this eliminates the tritone relation to the bass.[3]
The tritone was exploited heavily in the Romantic period as an interval of modulation for its ability to evoke a strong reaction by moving quickly to distantly related keys. Later on, in twelve-tone music, serialism, and other 20th century compositional idioms it came to be considered as a neutral interval.[4]
The equal-tempered tritone (a ratio of 
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.
[edit] Musical examples
- 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. The entire opening riff of Rush's instrumental song "YYZ" is made up of two notes in a tritone interval. Other metal songs with prominent tritones in their main riffs are Diamond Head's "Am I Evil?", Dream Theater's "As I Am", and Metallica's "For Whom the Bell Tolls" and "Enter Sandman". Thrash metal band Slayer, known for their occult references and themes, released an album entitled Diabolus in Musica.
- The two note introduction to Jimi Hendrix's "Purple Haze" is a bare tritone interval.
- Franz Liszt outlines a diminished triad in the opening bars of his symphonic poem Haláltánc, and tritones pop up very frequently throughout the piece to convey a restless fear of death.
- 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.
- 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 augmented fourth 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.
- The tritone is used very extensively throughout Beethoven's Piano Sonata No. 8 in C minor, "Pathétique". It is particularly evident in the opening bars of the piece.
- An episode of Charmed entitled "We All Scream for Ice Cream" has an ice cream truck playing a tritone to attract demons so that the ice cream man can kill them.
| Diatonic intervals | edit |
| Perfect : unison (0) | fourth (5) | fifth (7) | octave (12) | |
| Major : second (2) | third (4) | sixth (9) | seventh (11) | |
| Minor : second (1) | third (3)| sixth (8) | seventh (10) | |
| Augmented : unison (1) | second (3) | third (5) | fourth (6) | fifth (8) | sixth (10) | seventh (12) | |
| Diminished : second (0) | third (2) | fourth (4) | fifth (6) | sixth (7) | seventh (9) | octave (11) | |
| semitones of equal temperament are given in brackets | |
[edit] References
- ^ Reinhold Hammerstein, Diabolus in Musica: Studien zur Ikonographie der Musik im Mittelalter, Bern: Francke Verlag, 1974. p. 7.
- ^ F. J. Smith, "Some aspects of the tritone and the semitritone in the Speculum Musicae: the non-emergence of the diabolus in music," Journal of Musicological Research 3 (1979), pp. 63-74, at 70.
- ^ Jeppesen, Knud: "The Polyphonic Style of the Sixteenth Century", Dover, 1992, ISBN 0-486-27036-X (pbk)
- ^ Persichetti, V., "Twentieth-Century Harmony: Creative Aspects and Practice", W. W. Norton & Company, 1961, ISBN 0-393-09539-8
[edit] External links
- Tritone paradox and Shepherd Tones
- Tonalsoft Encyclopaedia of Tuning
- BBC News Magazine article about the tritone
