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For other uses, see Tritone (disambiguation).
tritone
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. In Music theory, the word inversion has several meanings There are inverted chords, inverted melodies, inverted intervals, and A semitone, also called a half step or a half tone, is the smallest Musical interval commonly used in Western tonal music and it is considered the In Musical set theory, an interval class (usual abbreviation ic) is the shortest distance in Pitch class space between two unordered Pitch classes In music just intonation is any Musical tuning in which the frequencies of Notes are related by Ratios of Whole numbers Any interval . .
Cents
Equal temperament 600
Just intonation 583, 617, 590. The cent is a logarithmic unit of measure used for musical intervals. Equal temperament is a Musical temperament, or a system of tuning in which every pair of adjacent notes has an identical Frequency ratio. In music just intonation is any Musical tuning in which the frequencies of Notes are related by Ratios of Whole numbers Any interval . .
The augmented fourth between C and F# forms a tritone.
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. Pitch represents the perceived Fundamental frequency of a sound In Music theory, the term interval describes the relationship between the pitches of two Notes Intervals may be described as vertical A major second () also called a whole step or a whole tone, is a Musical interval that occurs between the first and second degrees of a The tritone is the same as an augmented fourth, which in 12-tone equal temperament is enharmonic to a diminished fifth. Equal temperament is a Musical temperament, or a system of tuning in which every pair of adjacent notes has an identical Frequency ratio. In modern Music and notation, an enharmonic equivalent is a Note ( enharmonic tone) interval ( enharmonic interval) or It is often used as the main interval of dissonance in Western harmony, and is important in the study of musical harmony. The term Western world, the West or the Occident ( Latin: occidens -sunset -west as distinct from the Orient) can have multiple meanings In Western music, harmony is the use of different pitches simultaneously and chords actual or implied in Music. "Any tendency for a tonality to emerge may be avoided by introducing a note three whole tones distant from the key note of that tonality" [1].

Contents

Definition and nomenclature

Only the augmented fourth consists of three whole tones in meantone temperament. Meantone temperament is a Musical temperament, which is a system of Musical tuning. 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 in equal temperament, where the diesis is tempered out, it is equal to a perfect octave. A diesis is a comma type of Musical interval, usually meaning the difference between three justly tuned major thirds (tuned in the Frequency Equal temperament is a Musical temperament, or a system of tuning in which every pair of adjacent notes has an identical Frequency ratio. In Music, an octave ( is the the use of which is "common in most musical systems 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 equal-tempered tritone (a ratio of √2:1 or 600 cents) is unique in being its own octave inversion. The square root of 2, also known as Pythagoras' Constant, often denoted by \sqrt{2}   or   √2 The cent is a logarithmic unit of measure used for musical intervals. In Music theory, the word inversion has several meanings There are inverted chords, inverted melodies, inverted intervals, and Note that in other meantone tunings, the augmented fourth and the diminished fifth are distinct intervals because neither is exactly half an octave. Meantone temperament is a Musical temperament, which is a system of Musical tuning. 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 music septimal meantone temperament, also called standard septimal meantone or simply septimal meantone, refers to the tempering of 7-limit In 31 equal temperament, for example, the diminished fifth, or tritone proper, is 580. In music 31 equal temperament, which can be abbreviated 31-tET 31- EDO, 31-ET is the tempered scale derived by dividing the Octave into 31 equal-sized 6 cents, whereas a 7⁄5 is 582. 5 cents.

The tritone interval is used in the musical/auditory illusion known as the tritone paradox. The tritone paradox is an Auditory illusion in which a sequentially played pair of Shepard tones separated by an interval of a Tritone, or

Common uses

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). In Music theory, the major scale or Ionian scale is one of the diatonic scales It is made up of seven distinct Notes plus an eighth See also C minor, C-sharp minor C major (often just C or key of C) is a musical Major scale based on C 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 A♭ in the key of C minor). Also see C major, or C-sharp minor. C minor (abbreviated c or cm) is a Minor scale based 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 dominant seventh chord contains a tritone within its tone construction: it occurs between the third and seventh above the root. A seventh chord is a chord consisting of a triad plus a note forming an interval of a Seventh above the chord's root. In Music the root ( basse fouhuhuhe) of a chord is the note or pitch upon which that chord is perceived or labelled as being built In addition, augmented sixth chords, some of which are enharmonic to dominant seventh chords, contain tritones spelled as augmented fourths (for example, the German sixth, from A to D♯ in the key of A minor); the French sixth chord can be viewed as a superposition of two tritones a major second apart. An augmented sixth chord contains the interval of an Augmented sixth above its "root A minor (abbreviated Am) is a Minor scale based on A consisting of the pitches A, B, C, D, E, F,

In tonal music the tritone normally resolves inward to a major third:

Tritone resolution inward

Tritone resolution inward to a major third. Tonality is a system of Music in which specific hierarchical pitch relationships are based on a key "center" or tonic.
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The diminished triad also contains a tritone in its construction, deriving its name from the diminished fifth interval (i. Generally in Music, a diminished chord ( is a minor chord which has a Diminished fifth in it e. a tritone). The half-diminished seventh chord contains the same tritone, while the fully diminished seventh chord, like the French sixth chord, is made up of two superposed tritones, here a minor third apart. In Music theory, the half-diminished seventh chord (also known as a minor seventh flat five) is created by taking the root, Minor third In Music theory, a diminished seventh ( is an interval encompassing nine Semitones or a particular chord containing this interval Other chords built on these, such as ninth chords, often include tritones (as diminished fifths). In Music or Music theory a ninth is the Note nine Scale degrees from the root of chord (counting the root itself and also

In all of the sonorities mentioned above, used in functional harmonic analysis, the tritone pushes towards resolution, generally resolving by step in contrary motion. In Music, a step is a linear or successive interval between two pitches which are consecutive Scale degrees Any larger interval is called a In Music theory, contrary motion is the general movement of two melodic lines in opposite directions

The tritone is also one of the defining features of the Locrian mode, being featured between the first and fifth degrees. The Locrian mode is a Musical mode or Diatonic scale. It may be considered a Minor scale with the second and fifth scale degrees lowered a Semi-tone

Compared to other commonly occurring 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 considered 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.

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 common practice period, in the history of European Art music (broadly called Classical music) spanning the Baroque, Classical, and This interval was frequently avoided in medieval ecclesiastical singing because of its dissonant quality. The first explicit prohibition of it seems to occur with

"the development of Guido of Arezzo's Hexacordal system which made B flat a diatonic note, namely as the 4th degree of the hexachordal on F. Guido of Arezzo or Guido Aretinus or Guido da Arezzo or Guido Monaco or Guido D'Arezzo (991/992&ndashafter 1033 was a music theorist From then until the end of Renaissance the tritone, nicknamed the "diabolus in musicā" was regarded as an unstable interval and rejected as a consonance". [2]

The name diabolus in musica ("the Devil in music") has been applied to the interval from at least the early 18th century. The Devil is the Georg Philipp Telemann in 1733 notes that "mi contra fa . Georg Philipp Telemann (March 14 1681 &ndash June 25 1767 was a German Baroque music Composer, born in Magdeburg. Events Susannah Maria Arne makes her stage début in the first opera written by her brother Thomas . . welches die alten den Satan in der Music nenneten" ("mi against fa, which the ancients called 'Satan in music'"), while Johann 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'"). Johann Mattheson (September 28 1681 &ndash April 17 1764 was a German composer writer Lexicographer, diplomat Events September - Leopold Mozart is expelled from the Benedictine University of Salzburg for poor attendance [3] 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. [4] However Denis Arnold, in the referential The New Oxford Companion to Music, suggests that the nickname was already applied early in the medieval music itself:

"It seems first to have been designated as a 'dangerous' interval when Guido of Arezzo developed his system of hexachords and with the introduction of B flat as a diatonic note, at much the same time acquiring its nickname of 'Diabolus in Musica' ('the devil in music')". Guido of Arezzo or Guido Aretinus or Guido da Arezzo or Guido Monaco or Guido D'Arezzo (991/992&ndashafter 1033 was a music theorist [5]

Because of that original symbolic association with the devil and its avoidance, this interval came to be heard in Western cultural convention as suggesting an "evil" connotative meaning in music. Today the interval continues to suggest an "oppressive", "scary", or "evil" sound. However, suggestions that singers were excommunicated or otherwise punished by the Church for invoking this interval are likewise fanciful. Excommunication is a religious Censure used to deprive or suspend membership in a religious community At any rate, avoidance of the interval for musical reasons has a long history, stretching back to the parallel organum of the Musica Enchiriadis. Organum (ˈɔrgənəm though the stress is now sometimes incorrectly put on the second syllable from Ancient Greek ὄργανον - organon "organ instrument Musica enchiriadis is an anonymous musical Treatise from the 9th century. 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. In Music, a hexachord is a six-note segment of a scale or tone row 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.

Later in history with the rise of the Baroque and Classical music era, that interval came to be perfectly accepted, but yet was used in a specific controlled way, notably through the principle of the tension/release mechanism of the tonal system. Tonality is a system of Music in which specific hierarchical pitch relationships are based on a key "center" or tonic. In that system (which is the fundamental musical grammar of 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. [6]

It is only with the Romantic music and modern classical music that composers started to use it totally freely, without functional limitations notably in an expressive way to exploit the evil connotations which are culturally associated to it (e. Romantic Music is a Musicological term referring to a particular period theory compositional practice and canon in European music history from about 1815 to 1910 At the turn of the 20th century classical music was characteristically late Romantic in style while at the same time the Impressionist movement spearheaded by Claude Debussy g. , Liszt's use of the tritone to suggest hell in his Dante Sonata). Après une Lecture de Dante Fantasia quasi Sonata ( French for After a Reading of Dante Fantasia quasi Sonata; also Dante Sonata) The tritone was also exploited heavily in that period as an interval of modulation for its ability to evoke a strong reaction by moving quickly to distantly related keys. In Music, modulation is most commonly the act or process of changing from one key ( tonic, or tonal center) to another Later on, in twelve-tone music, serialism, and other 20th century compositional idioms it came to be considered as a neutral interval. [7] In some analyses of the works of 20th century composers, the tritone plays an important structural role; perhaps the most noted is the axis system, proposed by Ernő Lendvai, in his analysis of the use of tonality in the music of Béla Bartók. In Music the axis system, proposed by Ernő Lendvai (1971 p1-16 in his analysis of the use of Tonality in the music of Béla Bartók, is an Ernő Lendvai (1925 – 1993 was one of the first theorists to write on the appearance of the Golden section and Fibonacci series and how these are implemented in Béla Viktor János Bartók (March 25 1881&ndashSeptember 26 1945 was a Hungarian Composer and Pianist, considered to be one of the greatest [8]

Tritones also became important in the development of jazz tertian harmony, where triads and seventh chords are often expanded to become 9th, 11th, or 13th chords, and the tritone often occurs as a substitute for the naturally occurring interval of the perfect 11th. Jazz is an American Musical art form which originated in the beginning of the 20th century in African American communities in the Southern United States Since the perfect 11th (i. e. an octave plus perfect fourth) 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. Also 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. In Jazz Music, a tritone substitution is the use in a Chord progression of a dominant seventh chord (major/minor seventh chord that is three

Notable occurences of the tritone

In classical music

In popular music

In popular entertainment

The theme to the Fox Television series "The Simpsons" features a tritone prominently throughout, most notably in the bassline.

In literature

References

  1. ^ Brindle, Reginald Smith (1966). Serial Composition. Oxford University Press. ISBN 0-19-311906-4.
  2. ^ Sadie, Stanley (1980). "Tritone " in The New Grove Dictionary of Music and Musicians (1st ed. ). MacMillan, pp. 154-155, ISBN 0-333-23111-2)
  3. ^ Reinhold Hammerstein, Diabolus in Musica: Studien zur Ikonographie der Musik im Mittelalter, Bern: Francke Verlag, 1974. p. 7.
  4. ^ 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.
  5. ^ Arnold, Denis (1983) « Tritone » in The New Oxford Companion to Music, Volume 1: A-J,Oxford University Press. ISBN 0-19-311316-3
  6. ^ Jeppesen, Knud: "The Polyphonic Style of the Sixteenth Century", Dover, 1992, ISBN 0-486-27036-X (pbk)
  7. ^ Persichetti, V. , "Twentieth-Century Harmony: Creative Aspects and Practice", W. W. Norton & Company, 1961, ISBN 0-393-09539-8
  8. ^ Lendvai, Ernő. Béla Bartók: An Analysis of His Music. London: Kahn and Averill, 1971, p. 1-16)
  9. ^ See http://nl.wikipedia.org/wiki/Connie_Palmen
  10. ^ Dutch review at http://www.nrc.nl/kunst/article681634.ece

External links

See also

A Shepard tone, named after Roger Shepard, is a Sound consisting of a superposition of sine waves separated by Octaves When played with the base The following is a list of intervals of Meantone temperament. Background List See also List of meantone intervals

Dictionary

tritone

-adjective

  1. (music) Having three tones
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