Quartal and quintal harmony

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In music, quartal harmony is the building of harmonic structures built from the intervals of the perfect fourth, the augmented fourth and the diminished fourth. For instance, a three-note quartal chord on C can be built by stacking perfect fourths, C–F–B.

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Quartal and quintal harmony

Quintal harmony is harmonic structure preferring the perfect fifth, the augmented fifth and the diminished fifth. For instance, a three-note quintal chord on C can be built by stacking perfect fifths, C–G–D.

Quartal and quintal harmony

Properties

Quartal and quintal harmony
Notes in a quartal chord on A can be arranged to form a thirteenth chord on B. [1]

Use of the terms quartal and quintal arises from a contrast, compositional or perceptual, with traditional tertian harmonic constructions. Listeners familiar with music of the European common practice period perceive tonal music as that which uses major and minor chords and scales, wherein both the major third and minor third constitute the basic structural elements of the harmony.

Regarding chords built from perfect fourths alone, composer Vincent Persichetti writes that:

Chords by perfect fourth are ambiguous in that, like all chords built by equidistant intervals (diminished seventh chords or augmented triads), any member can function as the root. The indifference of this rootless harmony to tonality places the burden of key verification upon the voice with the most active melodic line. [2]

Quintal harmony (the harmonic layering of fifths specifically) is a lesser-used term, and since the fifth is the inversion or complement of the fourth, it is usually considered indistinct from quartal harmony. Because of this relationship, any quartal chord can be rewritten as a quintal chord by changing the order of its pitches.

Like tertian chords, a given quartal or quintal chord can be written with different voicings, some of which obscure its quartal structure. For instance, the quartal chord, C–F–B, can be written as

Quartal and quintal harmony

History

In the Middle Ages, simultaneous notes a fourth apart were heard as a consonance. During the common practice period (between about 1600 and 1900), this interval came to be heard either as a dissonance (when appearing as a suspension requiring resolution in the voice leading) or as a consonance (when the root of the chord appears in parts higher than the fifth of the chord). In the later 19th century, during the breakdown of tonality in classical music, all intervallic relationships were once again reassessed. Quartal harmony was developed in the early 20th century as a result of this breakdown and reevaluation of tonality.

Precursors

The Tristan chord is made up of the notes F, B, D and G and is the first chord heard in Wagner's opera Tristan und Isolde .

Quartal and quintal harmony

The bottom two notes make up an augmented fourth, while the upper two make up a perfect fourth. This layering of fourths in this context has been seen as highly significant. The chord had been found in earlier works, [3] notably Beethoven's Piano Sonata No. 18, but Wagner's use was significant, first because it is seen as moving away from traditional tonal harmony and even towards atonality, and second because with this chord Wagner actually provoked the sound or structure of musical harmony to become more predominant than its function, a notion which was soon after to be explored by Debussy and others.( [4]

Despite the layering of fourths, it is rare to find musicologists identifying this chord as "quartal harmony" or even as "proto-quartal harmony", since Wagner's musical language is still essentially built on thirds, and even an ordinary dominant seventh chord can be laid out as augmented fourth plus perfect fourth (F–B–D–G). Wagner's unusual chord is really a device to draw the listener into the musical-dramatic argument which the composer is presenting to us.

At the beginning of the 20th century, quartal harmony finally became an important element of harmony. Scriabin used a self-developed system of transposition using fourth-chords, like his Mystic chord (shown below) in his Piano Sonata No. 6.

Quartal and quintal harmony

Scriabin wrote this chord in his sketches alongside other quartal passages and more traditional tertian passages, often passing between systems, for example widening the six-note quartal sonority (C–F–B–E–A–D) into a seven-note chord (C–F–B–E–A–D–G). Scriabin's sketches for his unfinished work Mysterium show that he intended to develop the Mystic chord into a huge chord incorporating all twelve notes of the chromatic scale. [5]

In France, Erik Satie experimented with planing in the stacked fourths (not all perfect) of his 1891 score for Le Fils des étoiles . [6] Paul Dukas's The Sorcerer's Apprentice (1897) has a rising repetition in fourths, as the tireless work of out-of-control walking brooms causes the water level in the house to "rise and rise".

20th- and 21st-century classical music

Composers who use the techniques of quartal harmony include Claude Debussy, Francis Poulenc, Alexander Scriabin, Alban Berg, Leonard Bernstein, Arnold Schoenberg, Igor Stravinsky, Joe Hisaishi and Anton Webern. [7]

Schoenberg

Arnold Schoenberg's Chamber Symphony Op. 9 (1906) displays quartal harmony: the first measure and a half construct a five-part fourth chord with the notes (highlighted in red in the illustration) A–D–F–B–E–A distributed over the five stringed instruments (the viola must tune down the lowest string by a minor third, and read in the unfamiliar tenor clef).

Vertical quartal-harmony in the string parts of the opening measures of Arnold Schoenberg's Chamber Symphony Op. 9 SchoenbergOp9.png
Vertical quartal-harmony in the string parts of the opening measures of Arnold Schoenberg's Chamber Symphony Op. 9
Six-note horizontal fourth chord in Arnold Schoenberg's Chamber Symphony Op. 9 Schonberg Kammersymhonie 9 for wikipedia.png
Six-note horizontal fourth chord in Arnold Schoenberg's Chamber Symphony Op. 9

The composer then picks out this vertical quartal harmony in a horizontal sequence of fourths from the horns, eventually leading to a passage of triadic quartal harmony (i.e., chords of three notes, each layer a fourth apart).[ citation needed ]

Schoenberg was also one of the first to write on the theoretical consequences of this harmonic innovation. In his Theory of Harmony (Harmonielehre) of 1911, he wrote:

The construction of chords by superimposing fourths can lead to a chord that contains all the twelve notes of the chromatic scale; hence, such construction does manifest a possibility for dealing systematically with those harmonic phenomena that already exist in the works of some of us: seven, eight, nine, ten, eleven, and twelve-part chords… But the quartal construction makes possible, as I said, accommodation of all phenomena of harmony. [8]

For Anton Webern, the importance of quartal harmony lay in the possibility of building new sounds. After hearing Schoenberg's Chamber Symphony, Webern wrote "You must write something like that, too!" [9]

Others

In his Theory of Harmony: [10] "Besides myself my students Dr. Anton Webern and Alban Berg have written these harmonies (fourth chords), but also the Hungarian Béla Bartók or the Viennese Franz Schreker, who both go a similar way to Debussy, Dukas and perhaps also Puccini, are not far off."

Fourths in Bela Bartok's Mikrokosmos V, No. 131, Fourths (Quartes) Bartok Mikrokosmos Quartes for wikipedia.png
Fourths in Béla Bartók's Mikrokosmos V , No. 131, Fourths (Quartes)

French composer Maurice Ravel used quartal chords in Sonatine (1906) and Ma mère l'Oye (1910), while American Charles Ives used quartal chords in his song "The Cage" (1906).

Quartal harmony in "Laideronnette" from Ravel's Ma mere l'Oye. The top line uses the pentatonic scale Ravel Ma Mere l'Oye Laideronnette.PNG
Quartal harmony in "Laideronnette" from Ravel's Ma mère l'Oye . The top line uses the pentatonic scale
Introduction to Charles Ives's "The Cage" from 114 Songs Ives - 114 Songs, The Cage introduction.png
Introduction to Charles Ives's "The Cage" from 114 Songs

Hindemith constructed large parts of his symphonic work Symphony: Mathis der Maler by means of fourth and fifth intervals. These steps are a restructuring of fourth chords (C–D–G becomes the fourth chord D–G–C), or other mixtures of fourths and fifths (D–A–D–G–C in measure 3 of the example).

Hindemith was, however, not a proponent of an explicit quartal harmony. In his 1937 writing Unterweisung im Tonsatz (The Craft of Musical Composition,Hindemith 1937) he wrote that "notes have a family of relationships, that are the bindings of tonality, in which the ranking of intervals is unambiguous," so much so, indeed, that in the art of triadic composition "...the musician is bound by this, as the painter to his primary colours, the architect to the three dimensions." He lined up the harmonic and melodic aspects of music in a row in which the octave ranks first, then the fifth and the third, and then the fourth. "The strongest and most unique harmonic interval after the octave is the fifth, the prettiest nevertheless is the third by right of the chordal effects of its Combination tones."

Quartal harmony in Hindemith's Flute Sonata, II with tonal center on B established by descent in left hand in Dorian and repeated B's and F#'s Hindemith, Flute Sonata, II quartal harmony.png
Quartal harmony in Hindemith's Flute Sonata, II with tonal center on B established by descent in left hand in Dorian and repeated B's and F's

The works of the Filipino composer Eliseo M. Pajaro  [ it; nl; tl ] (1915–1984) are characterised by quartal and quintal harmonies, as well as by dissonant counterpoint and polychords. [14]

As a transition to the history of jazz, George Gershwin may be mentioned. In the first movement of his Concerto in F altered fourth chords descend chromatically in the right hand with a chromatic scale leading upward in the left hand.

Jazz

The style of jazz, having an eclectic harmonic orbit, was in its early days overtaken (until perhaps the Swing of the 1930s) by the vocabulary of 19th-century European music.[ clarification needed ] Important influences come thereby from opera, operetta, military bands as well as from the piano music of Classical and Romantic composers, and even that of the Impressionists. Jazz musicians had a clear interest in harmonic richness of colour, for which quartal harmony provided possibilities, as used by pianists and arrangers like Jelly Roll Morton, Duke Ellington, Art Tatum, Bill Evans, [15] Milt Buckner, [15] Chick Corea, [7] [16] Herbie Hancock, [7] [16] and especially McCoy Tyner. [7] [17]

ii-V-I cadence
fourth-suspension or sus chord II V I for wikipedia.png
ii–V–I cadence fourth-suspension or sus chord
Typical hard bop brass part, from Horace Silver's "Senor Blues" SenorBlues.png
Typical hard bop brass part, from Horace Silver's "Señor Blues"

The hard bop of the 1950s made new applications of quartal harmony accessible to jazz.[ citation needed ] Quintet writing in which two brass instruments (commonly trumpet and saxophone) may proceed in fourths, while the piano (as a uniquely harmonic instrument) lays down chords, but sparsely, only hinting at the intended harmony. This style of writing, in contrast with that of the previous decade, preferred a moderate tempo. Thin-sounding unison bebop horn sections occur frequently, but these are balanced by bouts of very refined polyphony such as is found in cool jazz.

The "So What" chord uses three intervals of a fourth. So What chord.png
The "So What" chord uses three intervals of a fourth.

On his watershed record Kind of Blue , Miles Davis with pianist Bill Evans used a chord consisting of three perfect fourth intervals and a major third on the composition "So What". This particular voicing is sometimes referred to as a So What chord, and can be analyzed (without regard for added sixths, ninths, etc.) as a minor seventh with the root on the bottom, or as a major seventh with the third on the bottom. [18]

From the outset of the 1960s, the employment of quartal possibilities had become so familiar that the musician now felt the fourth chord existed as a separate entity, self standing and free of any need to resolve. The pioneering of quartal writing in later jazz and rock, like the pianist McCoy Tyner's work with saxophonist John Coltrane's "classic quartet", was influential throughout this epoch. Oliver Nelson was also known for his use of fourth chord voicings. [19] Floyd claims that the "foundation of 'modern quartal harmony'" began in the era when the Charlie Parker–influenced John Coltrane added classically trained pianists Bill Evans and McCoy Tyner to his ensemble. [20]

Jazz guitarists cited as using chord voicings using quartal harmony include Johnny Smith, Tal Farlow, Chuck Wayne, Barney Kessel, Joe Pass, Jimmy Raney, Wes Montgomery, however all in a traditional manner, as major 9th, 13th and minor 11th chords [20] (an octave and fourth equals an 11th). Jazz guitarists cited as using modern quartal harmony include Jim Hall (especially Sonny Rollins's The Bridge ), George Benson ("Sky Dive"), Pat Martino, Jack Wilkins ("Windows"), Joe Diorio, Howard Roberts, Kenny Burrell, Wes Montgomery, Henry Johnson, Russell Malone, Jimmy Bruno, Howard Alden, Paul Bollenback, Mark Whitfield, and Rodney Jones. [20]

Quartal harmony was also explored as a possibility under new experimental scale models as they were "discovered" by jazz.[ citation needed ] Musicians began to work extensively with the so-called church modes of old European music, and they became firmly situated in their compositional process. Jazz was well-suited to incorporate the medieval use of fourths to thicken lines into its improvisation. The pianists Herbie Hancock, and Chick Corea are two musicians well known for their modal experimentation. Around this time, a style known as free jazz also came into being, in which quartal harmony had extensive use due to the wandering nature of its harmony.

Fourths in Herbie Hancock's "Maiden Voyage" Maiden Voyage2.png
Fourths in Herbie Hancock's "Maiden Voyage"

In jazz, the way chords were built from a scale came to be called voicing, and specifically quartal harmony was referred to as fourth voicing.

ii-V-I turnaround with fourth voicings: all chords are in fourth voicings.
They are often ambiguous as, for example, the Dm11 and G9sus chords are here voiced identically and will thus be distinguished for the listener by the root movement of the bassist. Quartal voicings.png
ii–V–I turnaround with fourth voicings: all chords are in fourth voicings. They are often ambiguous as, for example, the Dm11 and G9sus chords are here voiced identically and will thus be distinguished for the listener by the root movement of the bassist.

Thus when the m11 and the dominant 7th sus (9sus above) chords in quartal voicings are used together they tend to "blend into one overall sound" sometimes referred to as modal voicings, and both may be applied where the m11 chord is called for during extended periods such as the entire chorus. [22]

Rock music

Disliking the sound of thirds (in equal-temperament tuning), Robert Fripp builds chords with perfect intervals in his new standard tuning. Robert Fripp.jpg
Disliking the sound of thirds (in equal-temperament tuning), Robert Fripp builds chords with perfect intervals in his new standard tuning.

Quartal and quintal harmony have been used by Robert Fripp, rhythm guitarist of King Crimson. Fripp dislikes minor thirds and especially major thirds in equal temperament tuning, which is used by non-experimental guitars. Of course, just intonation's perfect octaves, perfect fifths, and perfect fourths are well approximated in equal temperament tuning, and perfect fifths and octaves are highly consonant intervals. Fripp builds chords using perfect fifths, fourths, and octaves in his new standard tuning  (NST), a regular tuning having perfect fifths between its successive open strings.( [23] !--The specific page citation is needed here; the inclusive page numbers of the interview are found in the list of References, 88–103, so the publication is not unpaginated, even if the version on the weblink is.-->)

Tarkus by Emerson, Lake & Palmer uses quartal harmony. [24]

Examples of quartal pieces

Classical

Parallel fourths evoking organum in Debussy's "The Sunken Cathedral" opening Parallel fourths evoking organum in Debussy's "The Sunken Cathedral" opening 02.png
Parallel fourths evoking organum in Debussy's "The Sunken Cathedral" opening

Jazz

Folk

On her 1968 debut album Song to a Seagull , Joni Mitchell used quartal and quintal harmony in "Dawntreader", and she used quintal harmony in the title track Song to a Seagull. [63]

Rock

See also

Related Research Articles

In music theory, the term minor scale refers to three scale patterns – the natural minor scale, the harmonic minor scale, and the melodic minor scale – rather than just one as with the major scale.

Harmony Aspect of music

In music, harmony is the process by which the composition of individual sounds, or superpositions of sounds, is analysed by hearing. Usually, this means simultaneously occurring frequencies, pitches, or chords.

Atonality Music that lacks a tonal center or key

Atonality in its broadest sense is music that lacks a tonal center, or key. Atonality, in this sense, usually describes compositions written from about 1908 to the present day, where a hierarchy of pitches focusing on a single, central tone is not used, and the notes of the chromatic scale function independently of one another. More narrowly, the term atonality describes music that does not conform to the system of tonal hierarchies that characterized classical European music between the seventeenth and nineteenth centuries. "The repertory of atonal music is characterized by the occurrence of pitches in novel combinations, as well as by the occurrence of familiar pitch combinations in unfamiliar environments".

In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones. For instance, the interval from F up to the B above it is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, and A–B. According to this definition, within a diatonic scale there is only one tritone for each octave. For instance, the above-mentioned interval F–B is the only tritone formed from the notes of the C major scale. A tritone is also commonly defined as an interval spanning six semitones. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the above-mentioned C major scale contains the tritones F–B and B–F. In twelve-equal temperament, the tritone divides the octave exactly in half as 6 of 12 semitones or 600 of 1200 cents.

Perfect fourth musical interval

A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth is the fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, because the note F is the fifth semitone above C, and there are four staff positions between C and F. Diminished and augmented fourths span the same number of staff positions, but consist of a different number of semitones.

Perfect fifth musical interval

In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.

Chord (music) Harmonic set of three or more notes

A chord, in music, is any harmonic set of pitches/frequencies consisting of multiple notes that are heard as if sounding simultaneously. For many practical and theoretical purposes, arpeggios and broken chords, or sequences of chord tones, may also be considered as chords in the right musical context.

Emancipation of the dissonance

The emancipation of the dissonance was a concept or goal put forth by composer Arnold Schoenberg and others, including his pupil Anton Webern. The phrase first appears in Schoenberg's 1926 essay "Opinion or Insight?". It may be described as a metanarrative to justify atonality. Jim Samson describes:

As the ear becomes acclimatized to a sonority within a particular context, the sonority will gradually become 'emancipated' from that context and seek a new one. The emancipation of the dominant-quality dissonances has followed this pattern, with the dominant seventh developing in status from a contrapuntal note in the sixteenth century to a quasi-consonant harmonic note in the early nineteenth. By the later nineteenth century the higher numbered dominant-quality dissonances had also achieved harmonic status, with resolution delayed or omitted completely. The greater autonomy of the dominant-quality dissonance contributed significantly to the weakening of traditional tonal function within a purely diatonic context.

In Western musical theory, a cadence is "a melodic or harmonic configuration that creates a sense of resolution [finality or pause]". A harmonic cadence is a progression of two chords that concludes a phrase, section, or piece of music. A rhythmic cadence is a characteristic rhythmic pattern that indicates the end of a phrase.

Minor third musical interval

In music theory a minor third is a musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions. The minor third is one of two commonly occurring thirds. It is called minor because it is the smaller of the two: the major third spans an additional semitone. For example, the interval from A to C is a minor third, as the note C lies three semitones above A. Coincidentally, there are three staff positions from A to C. Diminished and augmented thirds span the same number of staff positions, but consist of a different number of semitones. The minor third is a skip melodically.

Root (chord)

In music theory, the concept of root is the idea that a chord can be represented and named by one of its notes. It is linked to harmonic thinking—the idea that vertical aggregates of notes can form a single unit, a chord. It is in this sense that one speaks of a "C chord" or a "chord on C"—a chord built from C and of which the note C is the root. When a chord is referred to in Classical music or popular music without a reference to what type of chord it is, it is assumed a major triad, which for C contains the notes C, E and G. The root need not be the bass note, the lowest note of the chord: the concept of root is linked to that of the inversion of chords, which is derived from the notion of invertible counterpoint. In this concept, chords can be inverted while still retaining their root.

Tertian

In music theory, tertian describes any piece, chord, counterpoint etc. constructed from the intervals of thirds. An interval such as that between the notes A and C encompasses 3 semitone intervals and is termed a minor third while one such as that between C and E encompasses 4 semitones and is called a major third. Tertian harmony principally uses chords based on thirds; the term is typically used to contrast with quartal and quintal harmony which uses chords based on fourths or fifths.

A suspended chord is a musical chord in which the third is omitted and replaced with a perfect fourth or, less commonly, a major second. The lack of a minor or a major third in the chord creates an open sound, while the dissonance between the fourth and fifth or second and root creates tension. When using popular-music symbols, they are indicated by the symbols "sus4" and "sus2". For example, the suspended fourth and second chords built on C (C–E–G), written as Csus4 and Csus2, have pitches C–F–G and C–D–G, respectively.

In music, the mystic chord or Prometheus chord is a six-note synthetic chord and its associated scale, or pitch collection; which loosely serves as the harmonic and melodic basis for some of the later pieces by Russian composer Alexander Scriabin. Scriabin, however, did not use the chord directly but rather derived material from its transpositions.

Guitar chord

In music, a guitar chord is a set of notes played on a guitar. A chord's notes are often played simultaneously, but they can be played sequentially in an arpeggio. The implementation of guitar chords depends on the guitar tuning. Most guitars used in popular music have six strings with the "standard" tuning of the Spanish classical guitar, namely E-A-D-G-B-E' ; in standard tuning, the intervals present among adjacent strings are perfect fourths except for the major third (G,B). Standard tuning requires four chord-shapes for the major triads.

Consecutive fifths

In music, consecutive fifths, or parallel fifths, are progressions in which the interval of a perfect fifth is followed by a different perfect fifth between the same two musical parts : for example, from C to D in one part along with G to A in a higher part. Octave displacement is irrelevant to this aspect of musical grammar; for example, parallel twelfths are equivalent to parallel fifths.

Consonance and dissonance Categorizations of simultaneous or successive sounds

In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpleasantness, or unacceptability, although there is broad acknowledgement that this depends also on familiarity and musical expertise. The terms form a structural dichotomy in which they define each other by mutual exclusion: a consonance is what is not dissonant, and a dissonance is what is not consonant. However, a finer consideration shows that the distinction forms a gradation, from the most consonant to the most dissonant. In casual discourse, as Hindemith stressed, "The two concepts have never been completely explained, and for a thousand years the definitions have varied". The term sonance has been proposed to encompass or refer indistinctly to the terms consonance and dissonance.

Harmonic major scale

In music theory, the harmonic major scale is a musical scale found in some music from the common practice era and now used occasionally, most often in jazz. In George Russell's Lydian Chromatic Concept it is the fifth mode (V) of the Lydian Diminished scale. It corresponds to the Raga Sarasangi in Indian Carnatic music.

In music theory, the word inversion describes certain types of changes to intervals, chords, voices, and melodies. In each of these cases, "Inversion" has a distinct but related meaning. The concept of inversion also plays an important role in musical set theory.

Post-tonal music theory is the set of theories put forward to describe music written outside of, or 'after', the tonal system of the common practice period. It revolves around the idea of 'emancipating dissonance', that is, freeing the structure of music from the familiar harmonic patterns that are derived from natural overtones. As music becomes more complex, dissonance becomes indistinguishable from consonance.

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Sources

Further reading