Tritone

This article deals with the music theory term. For other meanings, see tritone (disambiguation)

Diatonic intervals
Prime second third fourth fifth sixth seventh octave none decime undezime duodecime tredezime semitone / whole tone
Special intervals
Microinterval Comma Diësis Limma Apotome Ditone Tritone Wolf fifth Natural septime
units
Cent Millioctave Octave Savart

The tritone , sometimes also called the semi-octave , is a musical interval that spans three whole tones .

The frequency ratio of the tritone is ⁴⁵ / ₃₂ ≙ 590 cents (in gleichstufiger mood 600 cents).

Example 1 : Tritone f'-b 'up and down :

Example 2 : Here in the first chord, the dominant seventh chord GHDF, the interval f 'h' is a tritone.

Example 3 Conclusion of “He who only lets God rule” . Here the sixth D ( sixth ajoutée ) is added to the subdominant chord F-A-flat-C . The first chord contains the tritone as' d '' .

The word tritone is made up of the ancient Greek words tri- ("three") and tónos ("tension", sc. The string, from it metonymically "tone"). In Latin it becomes tritone, which gives the plural tritoni .

Although the tritone is contained in diatonic scales , it is understood as an excessive fourth , i.e. as a chromatic variant of the pure fourth, and is therefore not included in the diatonic intervals. Strictly speaking, the term tritone only applies to the excessive fourth (for example F – B ), as only it can be represented by three diatonic whole-tone steps ( F – G, G – A and A – B ). However, it is common to also refer to the diminished fifth - the complementary interval to the excessive fourth, for example HCDEF (semitone + whole tone + whole tone + semitone) - as a tritone, as it also includes three whole tones in total.

The tritone was formerly also because of its related technical vocal and harmonic problems devil in music ( latin diabolus in musica ) or Devil interval called.

Dissolution of the tritone

In European music, the tritone has always been regarded as a very unstable interval, which was initially completely avoided and later felt at least as in need of resolution . This need for resolution ensures that the tritone has a strongly dominant character and that its components function as leading tones . The type of resolution depends on whether the tritone is interpreted as an excessive fourth or a diminished fifth. The latter dissolves by default "inward", the former "outward".

diminished fifth with resolution

excessive fourths with resolution

As with the diminished seventh chord , the direction of the leading tone effect is often ambiguous or easily reversible, which has been used to achieve sophisticated modulations .

The following example reinterprets the excessive fourth f′ – h ′ from C major into the diminished fifth eiz′ – h ′ from F sharp major. Here f ' enharmonic is confused with ice' (in the equal tuning: same frequency).

excessive fourth reinterpreted into a diminished fifth (with resolution to F sharp major)

useful information

• Within the equal pitch , the tritone (= 6 semitones) halves exactly one octave (= 12 semitones).
• In the circle of fifths , the fundamental tones of diametrically opposed keys always form a tritone (greatest possible harmonic distance).
• Seen harmoniously , in every dominant seventh chord there is a tritone between the third and seventh tone, e.g. B. H – F at G ⁷ .
• The tritone is used very frequently in jazz and also plays an important role in the reharmonization of pieces of music as a so-called tritone substitution .
• In the blues , a “floating” tone (see blue notes ) between a tritone and a pure fifth is a style-defining interval.
• In the Baroque period , the (unnatural) gait of a voice in a tritone is a form of the passus duriusculus (hard gait). Similarly, the jump into a mostly reduced interval (e.g. tritone) is called saltus duriusculus (hard jump). Such durezze (= hardship) are often explained by the topic. A passus duriusculus often stands for the crossing of a limit or the achievement of the impossible, as well as for unbearable and painful things.
• In the gypsy scale , a variant of the harmonic minor, the raised fourth degree (tritone) is the characteristic interval.

Different forms of the tritone

In the following table, in addition to the equal tritone, some naturally occurring tritone intervals in the overtone series are listed:

designation	Frequency ratio	Size in cents
equal tritone	${\displaystyle {\sqrt {2}}:1}$	600.00
excessive fourth, diatonic tritone (f – b)	45:32	590.22
diminished fifth (h – f)	64:45	609.78
diminished fifth (g – des)	17:12	603.00
Pythagorean augmented fourth, Pythagorean tritone	729: 512	611.73
Pythagorean diminished fifth	1024: 729	588.27
Huygens' tritone (also called BP fourth)	7: 5	582.51
Euler's tritone	10: 7	617.49

Application examples

The tritone can be used in any music that works a lot with tonal tension, as this interval demands resolution more than many others. Tritone chords are also particularly suitable for chromatic or enharmonic modulations . Often, however, the tritone has also been used in a meaning that goes beyond this everyday compositional function. Its reputation as the "devil's interval " (diabolus in musica) was often used to represent the dark, painful, uncanny or demonic in tone symbolism. This is the case with most of the following characteristic examples from music history:

• Often with Johann Sebastian Bach , e.g. B .:
  • in a recitative of the St. Matthew Passion , which addresses Jesus' encounter with a leper
  • Aria from Cantata No. 170 " I dislike living more"
  • The theme of the G sharp minor fugue from Volume 1 of the Well-Tempered Clavier
• In Vivaldi's Credo RV 591, 4th movement, on " resurrectionem "
• In Beethoven's opera Fidelio : timpani motif in the introduction to the dungeon scene of the 2nd act
• In Mendelssohn Bartholdy's Elias as a curse motif
• Chromatic tritone chains in both hands in Chopin's piano étude op.10.3 in preparation for the climax. Here the tonality is practically dissolved.
• As an introduction to Liszt's Après une lecture du Dante
• With the striking use of the solo violin in Saint-Saëns' Danse Macabre op. 40; the meaning in the work results from its title and the context.
• For the eerie "lure calls" of the witch in the middle of the Baba Yaga hut in Mussorgski's Pictures at an Exhibition
• several times in the War Requiem by Benjamin Britten
• In Richard Wagner's opera The Flying Dutchman in the Dutch monologue of the prelude
• In Richard Wagner's musical drama Siegfried in the prelude and in vocal passages by the dragon Fafner (is not resolved)
• As a central thematic and structure-forming element in the 4th Symphony by Jean Sibelius
• West Side Story : Maria (ascending tritone from 1st to 2nd note of the theme)
• In the "raptor motif" of John Williams' score for Jurassic Park
• At several points in the score for Star Trek II: The Wrath of Khan and Star Trek III: In Search of Mr. Spock by James Horner
• In the credits of the Muppet Show (descending tritone from the penultimate to the last note)
• In the theme music of the Simpsons (is then resolved to the fifth )
• As an introduction to Jimi Hendrix 's Purple Haze
• As an ostinato accompaniment to the song Black Sabbath by Black Sabbath
• At the beginning of the song YYZ the band Rush is IATA airport code of the airport of Toronto addressed in Morse code as Tritonusriff at the 5/4-time.
• The typical “piggy chords” of the band Voivod
• In the song Rockin 'All over the World by Status Quo
• Is used excessively by the band Primus , whereby no resolutions take place, but rather a sound that is as disharmonious as possible is sought (the best-known example is the title melody from South Park )
• The experimental guitarist Buckethead also makes frequent use of this to make certain passages appear "unnatural" or "robotic". Part of the solo in his song Jordan consists almost entirely of this interval.
• In the intro of the song Blind by Korn .
• The bands Mägo de Oz (Diabolus in musica) and Linea 77 even dedicated entire songs to this interval.
• The album Diabolus in Musica by the thrash metal band Slayer is named after the interval.
• The beginning of the Sonata op.1 for piano by Alban Berg begins with a perfect fourth, followed by a tritone (gc-f sharp)
• In the intro of Liar by Emilie Autumn
• In the main riff of the song Enter Sandman by Metallica .
• In the main riff of the song Broken Mirrors by Rise Against
• At the end of Into the Fire by Deep Purple .
• As the title melody of the antagonist G-Cis Harmonia (whose name is itself a tritone) from Pokémon Black / White and Black 2 / White 2.
• At the beginning of the song Bastard by Tyler, The Creator , where he uses a play on words relating to the devil because of the designation as the devil interval in place of a tritone.
• In the film music for “Ben Hur”: March through the desert (Jesus hands a bowl of water)

See also

• Tritone paradox
• Tritone substitution
• Tritone content

Web links

Commons : Augmented fourths  - collection of images, videos and audio files

Wiktionary: tritone  - explanations of meanings, word origins, synonyms, translations

Remarks

1. ↑ Some dictionaries claim that the tritone only exists as a singular. This is counteracted by the numerous occurrences of the plural form Tritoni in specialist literature, as a corresponding Google book search shows.
2. ↑ If the tuning is equal , excessive fourths and diminished fifths are equal at 600 cents. It is different in the pure tuning : the tritone , the excessive fourth C-F sharp can be intoned as follows :

   First the fifth C – G, then a semitone lower to C – F sharp .

   The frequency ratio is ${\displaystyle {\frac {3}{2}}\cdot {\frac {15}{16}}={\frac {45}{32}}\,\,{\widehat {\approx }}\,\,590{\text{ Cent.}}}$

   The diminished fifth C-Ges can be intoned as follows:

   First the fourth C – F, then a semitone higher to C – Ges .

   The frequency ratio is ${\displaystyle {\frac {4}{3}}\cdot {\frac {16}{15}}={\frac {64}{45}}\,\,{\widehat {\approx }}\,\,610{\text{ Cent.}}}$

   The two intervals differ by the Diaschima with 20 cents, in a mid-tone tuning even by the small diesis = 41 cents. (See tone structure (mathematical description) .)
3. ↑ The intonation of the excessive fourth C – F sharp occurs, for example, via the fifth (3/2) C – G (to be introduced) and then a semitone (16/15) G – F sharp back. The diminished fifth C-Gb , on the other hand, takes place via the fourth (4/3) C-F (to be introduced) and then a semitone (16/15) F-Gb after that.
4. ↑ Incidentally, the same expression has occasionally been used to designate the chromatic semitone b – b , such as B. Andreas Werckmeister , at the beginning of the 18th century:

   "It also shines that the Italians introduce wolten more characters [...] present day, which still nowhere to be profitable seynd, insonderheit because they the ♮ quadratum sit where it's Locum has not [... (76) ...] And because this clavis ♮ doesn't look too different from the Latin h , the organists have even given it the name H to distinguish the b rotundi […] because there is a big difference here, because Mi contra fa, est diabolus in Musica : ♮ major and B flat minor is a big difference. "

   - Andreas Werckmeister : Musical Paradoxal Discourse. Theodor Philipp Calvisius, Quedlinburg 1707, OCLC 21261004 , pp. 75–76 (in Fraktur , transcription orthographically slightly aligned, Latin letters in transcription italic; scan in Google book search)

   In Werckmeister's other treatise, the expression “diabolus in musica” refers to other (also chromatic) semitones f – f sharp (under “fingerings” Werckmeister understands all kinds of accords, both intervals and chords):

   “As already mentioned, the tertiae majores and minores must be distinguished for all grips . Then when the singer or violist strikes the f sharp (as the composer has set) on the d and the organist wanted to take f , a nasty constellation (I wanted to say "co-ordination") would arise; and this is actually the mi contra fa, of which the ancients said, est diabolus in musica . Quite a few have also understood the tritonos and the relationes nonharmonicas, such as the old Autoribus, can be looked up. "

   - Andreas Werckmeister : Harmonologia musica. Theodor Philipp Calvisius, Frankfurt / Leipzig 1702, OCLC 46171904 , p. 6 (in Fraktur, transcription orthographically slightly aligned, Latin letters in transcription in italics; scan in Google book search
5. ↑ The term BP Quarte refers to the fourth level of a diatonic Bohlen-Pierce scale in pure tuning ( lambda scale), see English Wikipedia
6. ↑ In addition, the tritone appears in many other parts of the West Side Story . It is even part of the leitmotif consisting of a fourth and a tritone , which is often heard in a whistled form and symbolizes the conflict between the two rival youth gangs Jets and Sharks . The fourth stands for the Sharks (cf. e.g. the song America ), the tritone for the jets (cf. e.g. the song Cool ).

Individual evidence

1. ↑ ^{a b} List of German interval names. In: huygens-fokker.org, accessed on November 3, 2017.