In music, quartal harmony is the building of harmonic structures with a distinct preference for the intervals of the perfect fourth, the augmented fourth and the diminished fourth. Quintal harmony is harmonic structure preferring the perfect fifth, the augmented fifth and the diminished fifth. In modern tuning, the augmented fourth and the diminished fifth are identical and are often called the tritone because the interval between the two notes is three tones.
Use of the terms quartal and quintal arises from a contrast, compositional or perceptual, with traditional tertian harmonic constructions. Listeners familiar with music during and after the 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.
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. Indeed, a circle of fifths can be arranged in fourths (G -> C -> F -> B♭ etc. are fifths when played downwards and fourths when played upwards); this is the reason that modern theoreticians may speak of a "circle of fourths".
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The concept of quartal harmony outlines a formal harmonic structure based on the use of the interval of a perfect fourth to form chords. The fourth, thus, substitutes for the third as used in chords based on major and minor thirds. Although the fourth replaces the third in chords, quartal harmony rarely replaces tertian harmony in full works. Instead, the two types of harmony are found side-by-side. Since the distance between the lower and the higher notes of a stack of two perfect fourths is a minor seventh and this interval inverts to a major second, quartal harmony necessarily also includes these intervals. Whether one hears these chords and intervals as consonant or dissonant is a matter of personal interpretation.
There is a question whether a chord built from fourths should be interpreted as a quartal-harmony structure, or if it is more meaningful to interpret is as part of the traditional functional harmony.
A quartal chord composed of the notes C - F - B♭ may be regarded using traditional theory as a C dominant seventh chord (with an omitted fifth) in the midst of a 4-3 suspension, or as C7sus4 (see suspended chord), where the fourth does not require resolution. Fsus4, a suspended second inversion chord, would also be a plausible label. Extending quartal chords to four or more notes generate still more possibilities of a similar nature. The four-note chord C - F - B♭ - E♭ can be interpreted as a C minor chord with a minor seventh and embellishing fourth (Cm7add4 or Cm11), or as an inversion of an E-flat major chord with a second-suspension and embellishing sixth—E♭sus2(add6), among other interpretations.
There are other interpretations of fourth chords. The notes C - F - B♭, for instance, can easily be heard as a fourth-suspension in F major, also C7sus4. In a five-note "quartal tower" having the notes C - F - B♭ - E♭ - A♭ the ear may hear an A♭ major or F minor sound with additional embellishing notes.
The question of which strategy of analysis is advisable is hard to answer since it is refined by the particular details: given one interpretation, and the progression of harmony through the preceding and following chords, and the overall musical development, is there a comprehensible and audibly functional meaning to the interpretation? It is important to question whether these suspensions, chromatic chords and altered chords are resolved as part of the functional harmony or whether they remain non-functional and unresolved.
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 tonic 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. Jazz and rock of the 1960s frequently used quartal harmony.
The Romantic composers Frédéric Chopin and Franz Liszt used the special "thinned out" sound of fourth-chords in late works for piano (Nuages gris, La lugubre gondola, and other works).
The Tristan chord is made up of the notes F♮, B♮, D♯ and G♯ and is the very first chord heard in Richard Wagner's opera Tristan und Isolde. The bottom two notes make up an augmented fourth 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[2][3] (notably Beethoven's Piano Sonata No. 18) but Wagner's usage 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] Beethoven's usage of the chord is of short duration and it resolves in the accepted manner; whereas Wagner's usage lasts much longer and resolves in a highly unorthodox manner for the time. 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 in to the musical-dramatic argument that the composer in presenting us with. However, fourths become important later in the opera, especially in the melodic development.
From 1850 to 1900, the application of tonality began to dissolve as evidenced in the works of composers of the Late Romantic such as Wagner, Anton Bruckner, Gustav Mahler and Claude Debussy, and as the 20th century began with tonality no longer a strong binding force, quartal harmony became one of the new means of expression. At the beginning of the 20th century, fourth-based chords finally became an important element of harmony.
Alexander Scriabin used a self-developed system of transposition using fourth-chords, like his Mystic chord in his Sixth Piano Sonata. Earlier sketches of his symphonic composition, Prometheus: The Poem of Fire, indicate that he first intended that the work develop from a single non-transposed tonal centre. 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).
In 1912, Leonid Sabaneyev published a work on Scriabin's theoretical ideas about Prometheus: The Poem of Fire in the periodical Der Blaue Reiter, but his opinions may not have been appropriate. As Hugo Riemann wrote in his Music Lexicon: "Firstly, chords from pure fourths (for example those in Arnold Schoenberg's well cited Chamber Symphony) without extension or mixture are used in the same way as diminished fourths, and secondly, that Scriabin himself looked upon his so-called Mystic Chord not as a quartal structure but as a reflection of the overtone series." 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]
Fourth-based harmony became important in the work of Slavic and Scandinavian composers such as Modest Mussorgsky, Leoš Janáček, and Jean Sibelius. These composers used this harmony in a pungent, uncovered, almost archaic way, often incorporating the folk music of their particular homelands. Sibelius' Piano Sonata in F-Major, op. 12 of 1893 used tremolo passages of near-quartal harmony in a way that was relatively hard and modern. Even in the example below from Mussorgsky's piano-cycle Pictures at an Exhibition, the fourth always makes an "unvarnished" entrance. Rudiments of quartal harmony appear in Janáček's rhapsody Taras Bulba, and his operas The Makropulos Affair and From the House of the Dead. Descending fourths and sevenths can be found dominating the writing.
The Impressionists would make much more use of chords built from fourths, even allowing them as a places of relaxation, altering our perception of them in the context of harmonic function and winning them their status as autonomous chords. Fourth-chords became consolidated with ninth chords, the whole tone scale, the pentatonic scale, and polytonality as part of the language of Impressionism, and quartal harmony became an important means of expression in music by Debussy, Maurice Ravel, and others. Examples are found in Debussy's orchestral work La Mer and in his piano works, in particular La cathédrale engloutie from his Préludes for piano, Pour les quartes and Pour les arpéges composées from his Etudes. Also of note is the opening of Ravel's ballet Daphnis et Chloé: a pile of fifths is generated in the orchestra above which is added a pair of fourth chords.
In the 1897 work Paul Dukas's The Sorcerer's Apprentice, we hear 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". Quartal harmony in Ravel's Sonatine and Ma Mère l'Oye would follow a few years later.
The use of fourth-chords is also found in the works of Mahler. His Seventh Symphony, in particular, uses harmony based on fourths alongside those based on thirds.
Composers who use the techniques of quartal harmony include Claude Debussy, Alexander Scriabin, Alban Berg, Leonard Bernstein, Arnold Schoenberg, Igor Stravinsky, and Anton Webern.[7] Arnold Schoenberg's Chamber Symphony Op. 9 (1906) displays quartal harmony. The work begins not from tonal harmony, but instead begins with a fictitious tonal-centre: the first measures construct a five-part fourth chord with the notes C - F - B♭ - E♭ - A♭ distributed over several instruments. 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).
Schoenberg was also one of the first to write on the theoretical consequences of this harmonic innovation. In his Theory of Harmony (Harmonielehre) of 1912,[8] he wrote: "The quartal construction of chords can lead to a chord containing all twelve notes of the chromatic scale, and with that comes a possibility for the systematic use of those harmonic phenomena that have already been obtained in some recent works having seven, eight, nine, ten, eleven, and twelve-part chords. (...) The quartal construction allows (...) the accommodation of all possible phenomena of harmony (...)." Other examples of quartal harmony appear in Schoenberg's String Quartet No. 1.
For Anton Webern, the importance of quartal harmony lay in the possibility of building new sounds. In 1912, he wrote, "With alteration the fourth-chord never need belong to tonal harmony, but can be free of all tonal relationships." After hearing Schoenberg's Chamber Symphony, Webern wrote "You must write something like that, too!" (Page 48 of his book The Path to the New Music) Shortly after, he wrote his Four Pieces for Violin and Piano Op. 7, using quartal harmony as a formal principle, which was also used in later works.
Uninfluenced by the theoretical and practical work of the Second Viennese School, the American Charles Ives meanwhile wrote in 1906 a song called "The Cage" (No. 64 of his collection, 114 songs), in which the piano part contained four-part fourth chords accompanying a vocal line which moves in whole tones.
Other 20th century composers, like Béla Bartók with his piano work Mikrokosmos and Music for Strings, Percussion and Celesta, as well as Paul Hindemith, Carl Orff and Igor Stravinsky, employed quartal harmony in their work. These composers joined Romantic elements with Baroque music, folk songs and their peculiar rhythm and harmony with the open harmony of fourths and fifths.
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[9] (The Craft of Musical Composition), 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."
In his Theory of Harmony,[8] Schoenberg remarked on page 407: "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.
British composer Sir Michael Tippett also employed quartal harmonies extensively in works from his middle period. Examples are his Piano Concerto and the opera The Midsummer Marriage. An almost constant quartal harmony is used by Bertold Hummel in his Second Symphony of 1966. A similarly obvious example is the work of Mieczysław Weinberg. Hermann Schroeder alternated in his works using fragments of Gregorian Chant between quintal and quartal harmony. Also the Polish composer Witold Lutosławski devised a usage that allows many harmonic combinations to be applied to a single part, having several combinations that may be tried against it, like fourths with whole tones, tritones with semitones, or other possibilities.
In the first movement of Olivier Messiaen's Turangalîla-Symphonie, a six-note combination is constructed in pieces from fourths and tritones, much like in the music of Schoenberg and Scriabin. Much of Messiaen's work applies quartal harmony, moderated by his development of what he called "Modes of limited transposition".
A preference for quartal harmony is present in the works of Leo Brouwer (10 Etudes for Guitar), Robert Delanoff (Zwiegespräche für Orgel), Ivan Vïshnegradsky, Tōru Takemitsu (Cross Hatch) and Hanns Eisler (Hollywood-Elegy). In the 1960s, the use of tone clusters juxtaposing minor and major seconds pushed aside quartal harmony somewhat. The orchestral work of György Ligeti, Atmosphères of 1961, makes extensive use of such sounds.
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.
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. 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,[11][12] Milt Buckner,[12] Chick Corea,[7][11] Herbie Hancock,[7][11] and especially McCoy Tyner.[7][11] Nevertheless, the older jazz usually handled fourths in the customary manner (as a suspension needing resolution).
Bebop brought an aesthetic change to modern jazz: the chords which before had a relative identity (as major and minor, dominant, etc.) gave way to block transpositions, with a fleeting, smooth flowing tonality, having the colours of chords blurred and strongly ambiguous. A prevalent example for this is the beloved ii-V-I cadence of modern jazz.
In the figure to the right, the musician plays the same outer voices as in a traditional cadence, but substitutions have been made in the inner voices. These altered voices still exhibit normal voice leading but within the extended harmony of jazz. The multiplicity of possibilities available can be used as a framework for improvisation. In addition, compositions of this time often had a frantic tempo, allowing more leeway in the harmony of fleeting chords (because they are not sounding for very long). Quartal harmony was employed throughout the jazz of the 1940s.
The hard bop of the 1950s made new applications of quartal harmony accessible to jazz. 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.
On his watershed record Kind of Blue, Miles Davis with his sextet applied a self-standing, free fourth chord for the composition "So What". This particular voicing is sometimes referred to as a So What chord.[13]
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.[14] Floyd claims that the "foundation of 'modern quartal harmony'" begin in the era when the Charlie Parker influenced John Coltrane added classically trained pianists Bill Evans and McCoy Tyner to his ensemble.[15]
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[15] (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 ("Skydive"), Pat Martino, Jack Wilkins ("Windows"), Joe Diorio, Howard Roberts ("Impressions"), Kenny Burrell ("So What"), Wes Montgomery ("Little Sunflower"), Henry Johnson, Russell Malone, Jimmy Bruno, Howard Alden, Paul Bollenback, Mark Whitfield, and Rodney Jones.[15]
Quartal harmony was also explored as a possibility under new experimental scale models as they were "discovered" by jazz. 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 usage 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 usage due to the wandering nature of its harmony.
Between these intensive experiments with quartal harmony, the search for new applications for it in jazz was quickly exhausted. Around 1970, quartal harmony had become part of the canon of everyday practice. 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.
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.[17]
Quartal harmony is part of the compositional framework of rock music, especially in riffs and power chords, which often use fifths and fourths instead of triadic harmony. In hard rock and heavy metal, whole songs were often built up from riffs of fourths and fifths on the electric guitar.
In funk, there is a stylistic device of interjecting fourths in syncopation by the guitars, keyboards, or brass section, as with the riff in the song "Flash Light" by George Clinton's band Parliament, 1977.
The song "Man on the Silver Mountain" recorded in 1975 by the band Rainbow includes a riff completely composed of fourths.
Progressive rock bands like King Crimson, Gentle Giant or Emerson, Lake & Palmer show likewise a fondness for melody and harmony combined into a single structure, the ostinato, often in fourths. Tarkus by Emerson, Lake & Palmer is almost entirely based on quartal harmony, from the ostinato in the opening bass figure to the parallel harmony in "Aquatarkus". Also Guitar Synthesis composers such as Chuck Hammer began to layer fourths and fifths in Guitarchitecture pieces such as "Glacial Guitars", in order to explore sustain as a compositional component. Some classical principles of composition utilized by Gentle Giant in their a cappella vocals for the song "Design". Over two alternating fourth chords (F - B♭ - D - A♭ and D - G - C - E) three voices move one after another in canonic imitation. This imitation allows harsh clashes between the parts to appear as a tension-generating device without disrupting the continuity of the passage.
However, the multitude of examples of quartal harmony must not be used to overlook the facts of the matter: rock and pop cover a wide field with a great deal of variety, but in most music intended to be a commercial success, accessible to the masses, a clear and simple triadic tonality has formed a hegemony (sometimes extended with a seventh or ninth). Fourth chords most commonly appear as fourth suspensions, for example in Elton John's rock ballad "Burn Down the Mission".
The Popular music of Latin American countries is interrelated with the development of "Latin music" in the U.S., due to considerable cultural exchange.
Latin music has a tendency toward a slightly faster tempo than the equivalent music in the USA. Quartal harmony found its way into salsa and Latin jazz via the jazz men (such as the playing of John Coltrane), but the concept of rhythm in the Afro-Cuban tradition was also an influence. The guitarist Carlos Santana became world-known by combining these influences.
In the Música Popular Brasileira of Brazil, the guitar has a central role as the harmonic instrument similar to the instrument's role in Rock. As a result, the quartal oriented playing of the guitar was borrowed and the unique rhythmic tradition adapted to fit (as in Tropicalismo). Even earlier, however, the notable Brazilian composer Heitor Villa-Lobos (1887–1959) wrote pioneering works in the first half of the 20th century combining elements of folk music and the popular music of his homeland with the quartal-harmonic experiments of European and North American classical music.
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