Editing Tritone (section)

== Historical uses ==
{{Image frame|content=<score sound="1"> {
#(set-global-staff-size 14)
\relative c' {
  \clef treble \time 9/8 \key e \major
  \set Score.tempoHideNote = ##t \tempo "Très modéré" 4. = 36
   \override Score.SpacingSpanner #'common-shortest-duration = #(ly:make-moment 1 8)
  \set Staff.midiInstrument = "flute"
  \stemDown cis'4.~(^"Flute"\p cis8~_\markup \italic "doux et expressif" cis16 \set stemRightBeamCount = #1 b \times 2/3 { \set stemLeftBeamCount = #1 ais16 a gis } g8. a16 b bis)
  cis4.~( cis8~ cis16 \set stemRightBeamCount = #1 b \times 2/3 { \set stemLeftBeamCount = #1 ais16 a gis } g8. a16 b bis) \override DynamicLineSpanner.staff-padding = #3
  cis8(\< dis gis e4 gis,8 b4.~\! 
  b8\> b cis ais4)\!
}
}
</score>|width=530|caption=The theme that opens [[Claude Debussy]]'s {{lang|fr|[[Prélude à l'après-midi d'un faune]]}} outlines the tritone between C{{music|#}} and G.}}

The tritone is a restless interval, classed as a [[consonance and dissonance|dissonance]] in Western music from the early [[Middle Ages]] through to the end of the [[common practice]] period. 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 [[hexachord]]al system, who suggested that rather than make B{{music|flat}} a diatonic note, the hexachord be moved and based on C to avoid the F–B tritone altogether. Later theorists such as [[Ugolino of Forlì|Ugolino d'Orvieto]] and [[Johannes Tinctoris|Tinctoris]] advocated the inclusion of B{{music|flat}}.<ref>{{citation | author =Guido d'Arezzo | title = Epistola de ignoto cantu|pages=lines 309–322|no-pp=y}}{{Full citation needed|date=October 2015}}<!--If a particular manuscript copy is being cited, the location, library name, and shelf number are needed; if a modern edition, then the editor, location, and publisher are needed at a minimum.-->{{Failed verification|date=October 2015}}<!--Guido does not mention Ugolino or Tinctoris, nor how could he? Unless this incomplete citation is to a modern annotated edition, it cannot possibly verify this claim.--></ref>

From then until the end of the [[Renaissance]] the tritone was regarded as an unstable interval and rejected as a consonance by most theorists.<ref>{{cite web | last = Drabkin | first = William | title = Tritone | work = [[Grove Music Online]] (subscription access) | publisher = [[Grove Music Online#Oxford Music Online|Oxford Music Online]] | url = http://www.oxfordmusiconline.com/subscriber/article/grove/music/28403 | access-date = 2008-07-21}}</ref>

The name {{Language with name/for|la|diabolus in musica|the [[Devil]] in music}} has been applied to the interval from at least the early 18th century, or the late Middle Ages,<ref>[https://books.google.com/books?id=02rFSecPhEsC&q=tritone Randel (2003), p.239].</ref> though its use is not restricted to the tritone, being that the original found example of the term {{lang|la|"diabolus en musica"}} is {{lang|la|"Mi Contra Fa est diabolus en musica"}} (Mi against Fa is the devil in music), referring to the [[minor second]]. [[Andreas Werckmeister]] cites this term in [[1702 in music|1702]] as being used by "the old authorities" for both the tritone and for the clash between chromatically related tones such as F{{Music|natural}} and F{{Music|sharp}},<ref>[[Andreas Werckmeister]]. [https://www.digitale-sammlungen.de/de/view/bsb10527826?page=5 {{lang|de|Harmonologia musica, oder kurze Anleitung zur musicalischen Composition}}] (Frankfurt and Leipzig: Theodor Philipp Calvisius 1702): 6.</ref> and five years later likewise calls {{lang|la|"diabolus in musica"}} the opposition of "square" and "round" B (B{{Music|natural}} and B{{Music|flat}}, respectively) because these notes represent the juxtaposition of {{lang|la|"mi contra fa"}}.<ref>[[Andreas Werckmeister]], [https://www.digitale-sammlungen.de/de/view/bsb10527832?page=5 {{lang|de|Musicalische Paradoxal-Discourse, oder allgemeine Vorstellungen}}] (Quedlinburg: Theodor Philipp Calvisius, 1707): 75–76.</ref> [[Johann Joseph Fux]] cites the phrase in his seminal [[1725 in music|1725]] work {{lang|la|[[Gradus ad Parnassum]]}}, [[Georg Philipp Telemann]] in [[1733 in music|1733]] describes, "mi against fa", which the ancients called "Satan in music"—and [[Johann Mattheson]], in [[1739 in music|1739]], writes that the "older singers with solmization called this pleasant interval {{lang|la|italic=no|'mi contra fa'}} or 'the devil in music'."<ref>{{cite book |last=Reinhold |first=Hammerstein |author-link = Reinhold Hammerstein| title=Diabolus in musica: Studien zur Ikonographie der Musik im Mittelalter|series=Neue Heidelberger Studien zur Musikwissenschaft |volume=6 |year=1974 |publisher=Francke |location=Bern |language=de |oclc=1390982 |pages=7 |quote=...&nbsp;mi contra fa&nbsp;... welches die alten den Satan in der Music nenneten&nbsp;... alten Solmisatores dieses angenehme Intervall mi contra fa oder den Teufel in der Music genannt haben.}}</ref> Although the latter two 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.<ref>{{cite journal |last1=Smith |first1=F. J. |title=Some aspects of the tritone and the semitritone in the ''Speculum Musicae'': the non-emergence of the ''diabolus in musica'' |journal=Journal of Musicological Research |date=1979 |volume=3 |issue=1–2 |pages=63–74 [70] |doi=10.1080/01411897908574507}}</ref> However [[Denis Arnold]], in the ''[[Oxford Companion to Music#The New Oxford Companion to Music|New Oxford Companion to Music]]'', suggests that the nickname was already applied early in the medieval music itself:

{{blockquote|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 {{lang|la|italic=no|"Diabolus in Musica"}} ("the devil in music").<ref>[[Denis Arnold|Arnold, Denis]] (1983). "Tritone". in ''The New Oxford Companion to Music'', Volume 1: A–J, Oxford University Press. {{ISBN|0-19-311316-3}}</ref>}}

That original symbolic association with the devil and its avoidance led to Western cultural convention seeing the tritone as suggesting "evil" in music. However, stories that singers were [[excommunication|excommunicated]] or otherwise punished by the Church for invoking this interval are likely fanciful. At any rate, avoidance of the interval for musical reasons has a long history, stretching back to the parallel [[organum]] of the {{lang|la|[[Musica Enchiriadis]]}}. In all these expressions, including the commonly cited {{lang|la|"mi contra fa est diabolus in musica"}}, the "mi" and "fa" refer to notes from two adjacent [[hexachord]]s. 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, with the rise of the Baroque and Classical music era, composers accepted the tritone, but used it in a specific, controlled way—notably through the principle of the tension-release mechanism of the [[Tonality|tonal system]]. 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 ii<sup>o</sup>–V–i. Often, the [[Inverted chord|inversion]] ii<sup>o6</sup> 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.<ref>{{cite book |last=Jeppesen |first=Knud |author-link=Knud Jeppesen |translator-first=Glen |translator-last=Haydon |translator-link=Glen Haydon |others=foreword by Alfred Mann |title=Counterpoint: the polyphonic vocal style of the sixteenth century |orig-year=1939 |url=https://archive.org/details/counterpointpoly0000jepp |url-access=registration |year=1992 |publisher=Dover |location=New York |isbn=0-486-27036-X }}</ref>

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 culturally associated with it, such as [[Franz Liszt]]'s use of the tritone to suggest Hell in his ''[[Dante Sonata]]'':

{{thumb|align=center|caption=Liszt, {{lang|fr|italic=no|"Après une lecture du Dante"}} from {{lang|la|Années de Pèlerinage}}.|content=
<score override_ogg="Liszt, apres une lecture de Dante from Annees de Pelerinage.wav"> {
\relative c' { \new PianoStaff << \set PianoStaff.connectArpeggios = ##t
\new Staff { \key f \major \tempo "Andante maestoso"
  R1 R r2 \clef F << { <a, c fis>2\(
  \stemDown <bes des g> <ces ees aes> \stemUp <ees ees'>2..\) q16 s1 } \\
  { \stemNeutral s2*3 <aes bes>2\<_\markup\italic{poco rit.} <g bes>\>
  <ees aes ces ees>1\arpeggio\!^\fermata } >>
}
\new Staff { \clef F \key f \major
  \slashedGrace { <a a'>8 } <a a'>2^^ \slashedGrace { <ees ees'>8 } <ees ees'>2^^
  \slashedGrace { <a, a'>8 } <a a'>4^^ \slashedGrace { <ees ees'>8 } <ees ees'>4^^
  \slashedGrace { <a, a'>8 } <a a'>4^^ \slashedGrace { <ees ees'>8 } <ees ees'>4^^~q1~q~
  q4 <fes fes'>8. ( <ges ges'>16 <fes fes'>4 <ees ees'> )
  <aes ees' aes>1\arpeggio_\fermata %<!-- can't get fermata on the barline to work here -->
}
>> } }</score>}}

{{clear}}

{{thumb|content=[[File:Siegfried Act 2 prelude.png|400px]][[File:Wagner, Prelude to Act 2 of Siegfried.wav]]
|caption=Wagner, Prelude to Act 2 of ''Siegfried''.}}

—or [[Wagner]]'s use of timpani tuned to C and F{{music|sharp}} to convey a brooding atmosphere at the start of the second act of the opera ''[[Siegfried (opera)|Siegfried]]''.

{{thumb|content=[[File:Debussy la Damoiselle Fig 30.png|400px]][[File:Debussy, la Damoiselle Elue, Fig 30.wav]]
|caption=Debussy, {{lang|fr|La Damoiselle élue}}, Figure 30.}}

In his early cantata {{lang|fr|[[La Damoiselle élue]]}}, [[Debussy]] uses a tritone to convey the words of the poem by [[Dante Gabriel Rossetti]].

{{thumb|content=[[File:Debussy Quartet 2nd movement, bars 140-7.png|400px]][[File:Debussy Quartet 2nd movement, bars 140-7.wav]]
|caption=Debussy, String Quartet, 2nd movement,<br />bars 140&ndash;147.}}

[[Roger Nichols (musical scholar)|Roger Nichols]] (1972, p19) says that "the bare fourths, the wide spacing, the tremolos, all depict the words—'the light thrilled towards her'—with sudden, overwhelming power."<ref>Nichols, R. (1972). ''Debussy''. Oxford University Press.</ref> Debussy's String Quartet also features passages that emphasize the tritone.

The tritone was also exploited heavily in that period as an interval of [[modulation (music)|modulation]] for its ability to evoke a strong reaction by moving quickly to [[distantly related key]]s. For example, the climax of [[Hector Berlioz]]'s {{lang|fr|[[La damnation de Faust]]}} (1846) consists of a transition between "huge B and F chords" as Faust arrives in [[Pandæmonium (Paradise Lost)|Pandaemonium]], the capital of Hell.<ref>{{cite book |first=Julian |last=Rushton |title=The Musical Language of Berlioz |page=254 |publisher= Cambridge University Press |year=1983}}</ref> Musicologist [[Julian Rushton]] calls this "a tonal wrench by a tritone".<ref>{{cite book |first=Julian |last=Rushton |title=The Music of Berlioz | publisher=Oxford University Press |year=2001}}</ref>

Later, in [[twelve-tone music]], [[serial music|serialism]], and other 20th century compositional idioms, composers considered it a neutral interval.<ref>{{cite book |last=Persichetti |first=Vincent |author-link=Vincent Persichetti |title=Twentieth-century Harmony: Creative Aspects and Practice |url=https://archive.org/details/isbn_9780393095395 |url-access=registration |year=1961 |publisher=W. W. Norton |location=New York |isbn=0-393-09539-8 |oclc=398434}}</ref> In some analyses of the works of 20th century composers, the tritone plays an important structural role; perhaps the most cited is the [[axis system]], proposed by [[Ernő Lendvai]], in his analysis of the use of tonality in the music of [[Béla Bartók]].<ref>{{cite book |last=Lendvai |first=Ernő |author-link=Ernő Lendvai |title=Béla Bartók: An Analysis of his Music |others=introd. by [[Alan Bush]] |year=1971 |publisher=Kahn & Averill |location=London |isbn=0-900707-04-6 |oclc=240301 |pages=1–16}}</ref> Tritone relations are also important in the music of [[George Crumb]]{{Citation needed|date=March 2016}}<!--The cited source mentions only Britten, not Crumb.--> and [[Benjamin Britten]], whose ''[[War Requiem]]'' features a tritone between C and F♯ as a recurring motif.<ref>{{Cite web |url=http://www.cco.caltech.edu/~tan/Britten/req1.html |title=Musical Analysis of the War Requiem |access-date=16 March 2016}}</ref> John Bridcut (2010, p.&nbsp;271) describes the power of the interval in creating the sombre and ambiguous opening of the ''War Requiem'':<ref>{{cite web|url=https://www.youtube.com/watch?v=rsSMCq7pl_k|title=Britten: War Requiem|date=29 August 2014 |via=YouTube}}</ref> "The idea that the chorus and orchestra are confident in their wrong-headed piety is repeatedly disputed by the music. From the instability of the opening tritone—that unsettling interval between C and F sharp—accompanied by the tolling of warning bells&nbsp;... eventually resolves into a major chord for the arrival of the boys singing 'Te decet hymnus'."<ref>Bridcut, J. (2010), ''Essential Britten, a pocket guide for the Britten Centenary''. London, Faber.</ref> [[Leonard Bernstein]] uses the tritone harmony as a basis for much of ''[[West Side Story]]''.<ref name=":0">{{Cite news|last=Kogan|first=Judith|date=2017-10-31|title=The Unsettling Sound Of Tritones, The Devil's Interval|language=en|work=NPR|url=https://www.npr.org/2017/10/31/560843189/the-unsettling-sound-of-tritones-the-devils-interval|access-date=2021-11-11}}</ref><ref>{{Cite web|last=Rizzi|first=Sofia|date=2019-03-04|title=Why did Bernstein build West Side Story around 'The Devil's Interval'?|url=https://www.classicfm.com/composers/bernstein-l/bernstein-west-side-story-tritone/|access-date=2021-11-11|website=Classic FM|language=en}}</ref> [[George Harrison]] uses tritones on the downbeats of the opening phrases of [[the Beatles]] songs "[[The Inner Light (song)|The Inner Light]]", "[[Blue Jay Way]]", and "[[Within You Without You]]", creating a prolonged sense of suspended resolution.<ref>Dominic Pedler. ''The Songwriting Secrets of the Beatles''. Music Sales Ltd. [[Omnibus Press]]. London, 2010 pp. 522–523</ref> Perhaps the most striking use of the interval in rock music of the late 1960s can be found in [[Jimi Hendrix]]'s song "[[Purple Haze]]". According to Dave Moskowitz (2010, p.&nbsp;12), Hendrix "ripped into 'Purple Haze' by beginning the song with the sinister sounding tritone interval creating an opening dissonance, long described as 'The Devil in Music'."<ref>Moskowitz, D. (2010). ''The Words and Music of Jimi Hendrix''. Praeger.</ref> The opening riff of "[[Black Sabbath (song)|Black Sabbath]]", the first song on [[Black Sabbath]]'s eponymous debut album, is an inversion of a tritone;<ref>{{cite web|url=http://abclocal.go.com/wjrt/story?section=news/entertainment/listening_room&id=7274202|archive-url=https://web.archive.org/web/20110629021833/http://abclocal.go.com/wjrt/story?section=news%2Fentertainment%2Flistening_room&id=7274202|url-status=dead|archive-date=29 June 2011|title='Sleeping (In the Fire)': Listening Room fearless leader faces down fear|last=Chesna|first=James|date=26 February 2010|publisher=[[WJRT-TV|WJRT-TV/DT]]|access-date=28 February 2010}}</ref> the album, and this song in particular, are considered to mark the birth of [[heavy metal music]].<ref>William Irwin, ''Black Sabbath and Philosophy: Mastering Reality'' (Hoboken: Wiley-Blackwell, 2012), {{ISBN|978-1118397596}}</ref>

[[File:Tritone substitution.png|thumb|upright=1.4|right|[[Tritone substitution]]: F{{music|#}}<sup>7</sup> may substitute for C<sup>7</sup>, and vice versa, because they both share E{{music|natural}} and B{{music|flat}}/A{{music|sharp}} and due to [[voice leading]] considerations.[[File:Tritone substitution.mid]]]]

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. 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 semitone (thus giving us an augmented or sharp 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 a [[tritone substitution]]. The tritone substitution is one of the most common chord and improvisation devices in jazz.

{{blockquote|
In the theory of harmony it is known that a diminished interval needs to be resolved inwards, and an augmented interval outwards. ... and with the correct resolution of the ''true'' tritones this desire is totally satisfied. However, if one plays a ''just'' diminished fifth that is perfectly in tune, for example, there is no wish to resolve it to a major third. Just the opposite—aurally one wants to enlarge it to a minor sixth. The opposite holds true for the ''just'' augmented fourth. ...

These apparently contradictory aural experiences become understandable when the cents of both types of just tritones are compared with those of the true tritones and then read 'crossed-over'. One then notices that the just augmented fourth of 590.224 cents is only 2 cents bigger than the true diminished fifth of 588.270 cents, and that both intervals lie below the middle of the octave of 600.000 cents. It is no wonder that, following the ear, we want to resolve both downwards. The ear only desires the tritone to be resolved upwards when it is bigger than the middle of the octave. Therefore the opposite is the case with the just diminished fifth of 609.776 cents.<ref name="Renold" />}}