Quartal and quintal harmony

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Quartal and quintal harmony is a compositional technique which employs fourths (or their inversions, fifths) as the constituants of harmony, rather than the thirds used in a traditional tonal context. These can also appear in melodic lines as often occurring intervals. As the interval of a fifth is very similar to the interval of a fourth (by inversion), quartal and quintal harmony can be considered the same procedure, much like harmony in sixths could be considered the same procedure as harmony in thirds. It can be used as an enrichment of other harmonic languages, and can also be seen as an expansion of common practice tertian harmony.

Chords created with quartal/quintal hrmony

While triadic harmony is based on the chord made of three stacked thirds and its extensions (further stacking of thirds creating seventh chords, ninth chords, etc.), quartal/quintal harmony is based on the stacking of fourths/fifths to create harmonic entities. A basic quartal chord (a stacking of three perfect fourths) is demonstrated below, along with its construction using fifths:

<music> \meterOff \cadenzaOn <d g c>1 \bar "|" <c g' d'>1 \bar "|" </music>

The augmented fourth/diminished fifth is also usable as an interval, displacing one perfect fourth/fifth (a stacking of two tritones does not introduce any new tones to the chord):

<music> \meterOff \cadenzaOn <ees a d>1 \bar "|" <d a' ees'> \bar "|" </music>

A chord that uses more than three fourths/fifths can easily be constructed (one must pay attention to not stack two consecutive tritones, though, as previously explained):

<music> \meterOff \cadenzaOn <c f b e ais>1 \bar "|" <ais e' b' f' c'>1 \bar "|" </music>

Inversions

Quartal/quintal chords can be used in inversions, and there are no particular guidelines for the usage of such inversions. Below, a chord of four fourths is presented in a few inversions:

Consonance and dissonance

With the fourth/fifth being the basic interval in quartal/quintal harmony instead of the third, the following holds true:

the stacking of two fourths (a tertian seventh) is considered consonant (analogous to stacking two thirds in tertian harmony)
the stacking of two fifths (a tertian ninth) is similarly considered consonant
the third stacking of a fourth/fifth is considered dissonant (analogous to stacking three thirds - a seventh chord)
- the third stacking of a fourth/fifth may resemble a tertian third or fourth, but it not to be treated as such.

Guidelines for voice-leading inspired by common-practice triadic principles can be thus formulated and applied to a quartal/quintal harmonic system. Examples would include: "resolution" of thirds, avoidance of parallel sevenths, and preferance for contrary motion. This is but a possibility, though, and much music that employs quartal/quintal harmony does not follow such guidelines.

Usage of quartal/quintal harmony

Quartal/quintal harmony can be used in many different ways, and no one common usage prevails. Quartal and quintal chords used during the common-practice period were but a phenomenon of voice-leading, usually suspensions above a triad. However, as music became freer and new compositional techniques flourished at the turn of the 20th century, independent harmony built on fourths became a possibility.

Quartal harmony as a component of tonality

A potential use of quartal/quintal harmony is to enrich tertian harmony while maintaining a sense of tonality. A simple example is shown below: In C major, we have a I - VI7 - V - I progression enriched by a quartal chord on C following the tonic. The progression is undeniably tonal, however the second chord is unidentifiable as a triad or seventh chord.

Quartal/quintal harmony may also be used on its own, independently of tertian harmony, while still maintaining a tonal center. The following example maintains a Bb tonal center, using various quartal/quintal chords that relate to the diatonic scale degrees:

Quartal/quintal harmony is also a notable feature of jazz, referred to as "stacking fourths". Modal jazz makes extensive use of quartal/quintal harmony adjacent to tertian harmony, as can be observed in the music of Nikolai Kapustin.

Quartal/quintal harmony outside of a tonal context

It is of common use to employ quartal/quintal harmony without adhering to a strict sense of tonality. Many augemented and diminished intervals can make up a multi-part quartal/quintal chord that bears no tonal significance (Scriabin's Mystic Chord being such an example), and atonal melodic movement may be present connecting such chords. Below is a short example of atonal quartal/quintal harmony:

While consonant and respecting certain harmonic principles relating to tonality, quartal/quintal harmony can be used in a consonant and locally tonal/modal style, all the while being either constantly modulatory and very chromatic or an element of chord planing (such that the melodic movement of voices may be tonal, but the overall harmonic result an atonal planing of chords). Such examples may be found in the music of Claude Debussy, and among other works of the impressionistic/late romantic period, primarily in descriptive (program) music. Below is an example, using planing of the same chord along a whole tone scale beginning on D (highlighted in red):

History of quartal\quintal harmony

In the period of medieval polyphony preceding the advent of the Common-practice period, the use of thirds and triads was not the primary means of constructing harmony. Rather, much melodic emphasis would be placed on fourths and fifths, while some texts would be sung a fourth and an octave below the first voice (a common practice known as Fauxbourdon ). Thus, many harmonies used during that period may be termed quartal or quintal (although whether a harmonic entity composed of a fourth and octave constitutes an actual chord is debatable). When tertian harmony became the primary method of constructing harmony during the Rennaissance and Baroque periods, however, the natural emphasis on the fourth and fifth in music faded away, a phenomenon exacerbated by the tight voice-leading guidelines of the Baroque and Classical periods. Quartal and quintal harmony remained mere by-products of voice-leading until the early 20th century, when composers actively sought new means of expression. The works of impressionists such as Claude Debussy saw the renewed use of quartal and quintal harmony independently from tertian harmony, and the compositions of Arnold Schoenberg and Anton Webern (both figureheads of the Second Viennese school) use much quartal harmony in a freer atonal (or tonally extended) context (see Webern's Four Pieces for Violin and Piano, Op. 7 and Schoenberg's Chamber Symphony, Op. 9). The availability of quartal\quintal harmony as a compositional technique has persisted through today, as can be demonstrated by more contemporary works such as Charles Ives's The Cage.

Quartal and quintal harmony

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