Tritone (Part 1)

What is a tritone?

A tritone is an interval that spans 6 semitones from any single note (in equaltemperament).

It is exactly half-way between an octave. It can sound erring and offensive to our ears.

Every tritone will usually contain an accidental, a sharp or a flat, for example, C-F#

or Gb which can be said to be either an augmented fourth or a diminished fifth.

Ab-D is another type of tritone interval. However, there is only one interval that

does not have any sharps of flats and that is B-F. Hence, as history progressed

they were given the accidentals first making them Bb (to F) or F# (from B). The

tritone in chords give us tension which is then resolved in the following chords. For

example, the V7 chord in C major is said to be G-B-D-F, the B-F resolves to C-E in

the C major tonic chord C-E-G-C and this tension and release is the ground for

music in tonal harmony (This is only regarding modern/contemporary music that works in 12 equal-temperament) (Adam Neely, 2017).

This very interval has been known to be called, “The Devilʼs Interval” or in Latin "Diabolus In Musica” [The Devil In Music] (Adam Neely, 2017). There are an infinite number of many historical articles that discusses about this very specific interval both mathematically

and musically. In the following sub-topics I shall discuss about some of the historic

details and significance of the intervals, giving some microtonal ratios, as well as a

very-near approximation of the 600 cent in the harmonic series (as it does not

occur naturally), and some of my favorite songs that include such intervals.

What is the history behind such an interval?

The history behind an interval like the tritone is complicated and vast. However,

tritone being banned and not used in Churches or in chant music are erroneous.

There is just not enough context or material that would say otherwise. The tritone was

generally avoided but far from being banned. There have been musical pieces that

date back to the 13th century that include tritone, although, fairly rarely and in

places that have context. This specific dissonant interval was not at all banned but

used in a more meaningful manner to enlighten the piece (Margo Schulter, personal communication, Sep 5th, 2019).

Some historical ideas:

The mention of the of “Diabolus In Musica” was mentioned approximate 400 years

after Medieval practices, in a counterpoint treaties called, Gradus ad Parnassum

by Johann Joseph Fux around the 18th century (Schulter, n.d., para. 1).

Tritone along with the minor second and major seventh (inversion of the minor

2nd) were considered a perfect discord — the harshness and cruel sounding

interval was generally avoided but still occurred (Schulter, n.d., para. 8).

There was a solution, a rather different one, “one solution was a scale with

accidentals making it impossible to sing other than perfect fifths” (Schulter, n.d., para. 6).

What this means?

(Margo Schulter, 2019)

While there is a TTST pattern happen, there is no avoiding the tritone as shown as

C4-F#4, for example. This method generally allowed two singers to sing without

hitting a tritone, for instance, if a singer started from C3 another could start from

G3 never to hitting a tritone if they go in parallel fifths. However, this can

introduced augmented octaves i.e. C4-C#5 or F3-F#4 (Margo Schulter, personal communication, Sep 5th, 2019).

Tritone can be viewed as an interval that is unavoidable in the world of music, it is

a part of the tonal system and has been used with zeal as centuries passed.

A few common pieces that I have been able to gather from friends and sources

that feature tritone melodically are as follows:

Machaut's piece Amours Me Fait Desirer,

Alfonso El Sabio piece De Grad, Cantiga 253,

Adam De La Halle piece Dieus Soit En Cheste Maison,

Pérotin piece Dum Sigillum Summi Patris,

A vertical tritone can be found in Alleluia Posui Adiutorium by Pérotin. There are many other undiscovered pieces, both in chants and organum pieces

(polyphonic).

During the 13th and 14th century the tritone resolution cadential was prominent

however, it did move in parallel motion while other intervals moved in contrary motion (Schulter, n.d., para. 13). For example,

(Margo Schulter, n.d.)

The triads move in parallel motion, in this case the notes B3 and F4 move in

parallel to C4 and G4. Hence, they go in parallel fifths which was later avoided

during counterpoint composition. In Rock music, and Jazz parallel fifths are open

and free to use.

However, with the other examples, the moves independently move away from each

other. The G3 moves down to F3, the Bb3 moves up to C4, the D4 moves down to

C4, and the E4 moves up to F4. Contrary motion was much preferred as it gave

voices independence of movement.

Here is the original image that was later reinterpreted in music notation

The (min3-1) just means the minor third interval B3-D4 moves to the unison of

the next chord, C4-C4. While, (m3-5) the minor third from D4-F4 moves to the

five of the next chord which is C4-G4.

The same goes for next chord,

• The lower two voices move G3-Bb3 to F3-C4, from minor third to fifth (min3-5),

• The two middle voices move Bb3-D4 to C4-C4, from major third to fifth (Maj3-5),

• The upper two voices move D4-E4 to C4-F4, from major second to fourth (Maj2-4),

• The two outer voices move G3-E4 to F3-F4, from major sixth to octave (Maj6-8),

So, this can be written (Maj6-8 + min3-5 + Maj3-1 + Maj2-4) (Margo Schulter, personal communication, Sep 5th, 2019).

[Please ignore the F2 note, it does NOT exist. The cursor automatically highlighted the note lightly indicating that F2 would be the note in that space/area].

All of this just proves that tritone was indeed used, while some composers such as

Monteverdi used the tritone in a way that was not following the rules, others like Artusi made sure to use it in good authority.

(Victor, n.d., pg. 1)

I have taken upon myself to include a second part for this blog topic. Stay on a look-out to catch different microtonal intervals that produce a tritone in the harmonic series, what "third" tone a tritone produces when it is put through distortion (combination tones), and some of my favorite pieces of music that include tritones.

REFERENCES:

Adam Neely. (June 5th, 2017). The Devil in music (an untold history of the Tritone) [Video File]. Retrieved from https://www.youtube.com/watch?v=eR5yzCH5CsM

Margo Schulter (n.d.). Diminished 7ths [Image]. Retrieved from http://www.medieval.org/emfaq/harmony/tritone.html

Schulter, M. (n.d.) Tritones in early music: Were they always prohibited? Retrieved from http://www.medieval.org/emfaq/harmony/tritone.html

Victor, z. (n.d.). Giovanni Maria Artusi, On the Imperfections of Modern Music (1600), and Claudio and Giulio Cesare Monteverdi, Scherzi musicali (1607) [PDF]. Retrieved from https://www.cengage.com/music/book_content/049557273X_wrightSimms/assets/ITOW/7273X_28_%20ITOW_Artusi-Monteverdi.pdf

APPENDIX:

Collins, C. (2015). Medieval Tritone Superstitions Proved Popular in 19th-Century Music. Retrieved from https://www.cmuse.org/medieval-tritone-superstitions-proved-popular-in-19th-century-music/

Longdon. V. (2018). What is a tritone and why was it nicknamed the devil’s interval? Retrieved from https://www.classicfm.com/discover-music/music-theory/what-is-a-tritone/

Schulter, M. (2010). Regions of the Interval Spectrum. Retrieved from http://www.bestii.com/~mschulter/IntervalSpectrumRegions.txt

To understand different SATB motions (Soprano, Alto, Tenor & Bass voices): Rick Beato. (Oct 17th, 2017). Tonal HARMONY | The SECRETS of Four Part Writing (SATB) [Video File]. Retrieved from https://www.youtube.com/watch?v=HuSKULck394