Tritone

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:

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.