Tri-tone - Historical Uses

Historical Uses

The tritone is a restless interval, classed as a 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 hexachordal system, which made B♭ a diatonic note, namely as the fourth degree of the hexachord on F. From then until the end of the Renaissance the tritone, nicknamed the diabolus in musica, was regarded as an unstable interval and rejected as a consonance by most theorists.

The name diabolus in musica ("the Devil in music") has been applied to the interval from at least the early 18th century. Johann Joseph Fux cites the phrase in his seminal 1725 work Gradus ad Parnassum, Georg Philipp Telemann in 1733 describes, "mi against fa", which the ancients called "Satan in music", and Johann Mattheson in 1739 writes that the "older singers with solmization called this pleasant interval 'mi contra fa' or 'the devil in music'". 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. However Denis Arnold, in 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").

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 likely fanciful. At any rate, avoidance of the interval for musical reasons has a long history, stretching back to the parallel organum of the Musica Enchiriadis. In all these expressions, including the commonly cited "mi contra fa est diabolus in musica", the "mi" and "fa" refer to notes from two adjacent hexachords. 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. 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.

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.g., Franz Liszt's use of the tritone to suggest Hell in his 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. Later on, in twelve-tone music, serialism, and other 20th century compositional idioms it came to be considered as a neutral interval. 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 Lendvaï, in his analysis of the use of tonality in the music of Béla Bartók. Tritone relations are also important in the music of George Crumb. George Harrison uses tritones on the downbeats of the opening phrases of the Beatles songs "The Inner Light", "Blue Jay Way" and "Within You Without You", creating a prolonged sense of suspended resolution.

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.

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....

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