Quartal and quintal harmony

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In music, quartal harmony is the building of chordal and melodic structures with a distinct preference for intervals of fourths. ( Listen). Quintal harmony is harmonic structure preferring fifths.

Use of the term 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 the major and minor chords ( Listen), wherein both the major third and minor third ( Listen) intervals constitute the basic harmonic structural-elements.

Quartal harmonic sound, however, stood already on the threshold of the more coherent European polyphonic music of the Middle Ages, but was replaced by the triadic harmony of tonality as it developed in the Renaissance. Again at the beginning of the 20th century, it played a strong role in contemporary music-styles. Quartal harmony imbued modern music with structural commonalities, laying parts more widely separated in space and/or time, allowing for a very different sound.

Quintal harmony is a lesser-used term, and since the fifth is the inversion of the fourth, it is usually considered indistinct from quartal harmony.

Contents 1 Introduction: Intervals and Chord symbols 2 Elements of Quartal harmony 2.1 Short history of the fourth 2.2 Definition 2.3 Properties of Quartal harmonies 2.4 Analytical problems 3 History 3.1 Middle Ages 3.2 Renaissance and Baroque 3.3 Classical and Romantic 3.4 Impressionism 3.5 20th century Music 3.5.1 "Art Music" 3.5.2 Jazz 3.5.3 Rock Music 3.5.4 Latin American Music 4 See also 5 Further reading 5.1 Overall 5.2 Medieval, Renaissance, Baroque 5.3 Classical and Romantic 5.4 20th century music 5.5 Jazz, Rock, and Latin music 6 References 7 External links

[edit] Introduction: Intervals and Chord symbols

Main articles: Interval (music) and Chord symbol

Harmony is that part of music theory concerned with the properties of simultaneously sounding tones. In pitch-difference between tones (Latin intervals), the perfect fourth amounts to five semitones ( Listen); The name fourth comes from the fact that in most common scales, this interval is the distance from the fourth tone to its tonic ( Listen: the first four notes of several diatonic scales).

The interval concept refers to the pitch-distance between two successively or simultaneously sounding tones. Under inversion one finds those intervals which together make up an octave; a third inverts to a sixth. The term descending fourth (or descending fifth, third, etc.) is used for intervals displaced into the octave below. A rising fifth C - G, for example, inverts to the descending fourth G - C.

In this article, Chord symbols will have a capital letter for the Fundamental or Tonic, which indicates a major third and fifth above forming a Major Triad. The addition of m stands for Minor, in which a minor instead of a major third sounds against the tonic. Also, with the addition add, extra tones at a specified distance from the tonic sound. In C6 or C(add6) appear the tones C - E - G - A. C7 refers to a C-major chord with an additional Minor seventh, having the tones C - E - G - B♭. This chord functions in classical tonality as the Dominant seventh chord.

The addition maj7 (an abbreviation of major seventh) extends the triad with an additional Major seventh. Both seventh chords can be even further extended with a major Ninth, written as C9 or Cmaj9, respectively. The abbreviation sus4 (suspended fourth, a Suspended chord) indicates that the expected third in a stable major or minor triad is replaced by a fourth instead. In modern music this chord is often used in a distinct way so it can also stand for itself and not function as an altered triad.

[edit] Elements of Quartal harmony

[edit] Short history of the fourth

Main article: Perfect fourth

The ancient Greeks defined the group of "symphonia", the beautiful intervals, naming the fourth "syllabe" (Greek: fastened together) and later Diatessaron (Greek: by four, from four). This interval became the framework upon which the tetrachords of Greek music theory were built.

In the Middle Ages the fourth was considered a concord, as was the unison, octave, fifth, and later the third. After the 12th century, music theorists sometimes classified the fourth as a dissonance requiring resolution.

In the 13th century, the fourth and fifth together were the concordantiae mediae (middle consonances) after the unison and octave, and before the thirds and sixths. In the 15th century it was considered dissonant, and removed from the group of concords.

Modern acoustic theory supports the medieval interpretation insofar as the intervals of a unison, octave, fifth and fourth have particularly simple frequency ratios. The octave has the ratio of 2:1, for example the interval between A' at A440 and A'' at 880 Hz, giving the ratio 880:440, or 2:1. The fifth has a ratio of 3:2, and its complement has the ratio of 3:4. Ancient and medieval music theorists were familiar with these ratios, for example with experiments on the Monochord.

In the years that followed, the frequency ratios of these intervals would change slightly as different systems of tuning, such as meantone temperament, well temperament, and equal temperament came into favor.

In the history of western polyphony, these simpler intervals were plainly favoured, but in its development between the 12th and 16th centuries:

1. At first these simple intervals occur so frequently that they appear to be the favourite sound of composers.
2. These intervals become increasingly considered "obsolete", as the more "complex" intervals (thirds, sixths, and tritones) move gradually from the margins to the centre of musical interest.
3. With the end of the Middle Ages, new rules for voice leading had been laid, disestablishing the importance of these intervals or at least handling them in a more restricted fashion (for instance, the later forbidding of parallel octaves and fifths).

The music of the 20th century for the most part discards the rules of "classical" western tonality. For instance, composers such as Erik Satie borrowed stylistic elements from the Middle Ages, but some composers even found innovative uses for these intervals. It became very common in the 20th century for the fourth to be used as a structural element.

[edit] Definition

The concept of Quartal harmony outlines a formal harmonic structure based on the use of the interval of a perfect fourth in substitution of traditional structuring of chords in thirds. As in the tonality pervading European music (between about 1600 and 1900) such quartal sounds appear mainly as a suspension in the voice leading, which is handled harmonically as a special case, unrelated to its use observable in later music. Jazz and Rock apply quartal harmony in the 1960s with a fondness. Corresponding to this vertical structuring of chords is a melodically oriented (horizontal) usage of fourths; the parallel theory of quartal melody however has not been put across as of yet. A wider theory is that of quartal coupling. This indicates that a fourth may be used to enrich an existing chord, added much as one could add a third, octave, or sixth to a chord.

Theoretical systems and models in which the harmonic interpretation of fourth-chord, fifth-chords, and larger structures such as movements are described (as they have been in tertian harmony with functional harmony or diatonic theory and the concept of cadences) have not yet been developed. In the literature, one finds reference to concepts of quartal stratification, quartal towers, and quartal chords which have minute differences.

[edit] Properties of Quartal harmonies

Quartal chord sounds have a somewhat "erratic" function, in that they have a tendency to forget which key they are in. The fourth is the complement of the perfect fifth, which means that both intervals "fuse" with another to become the octave. When one arranges a circle of fifths in its "cadential order" (G -> C -> F -> B♭ and so on), one has also produced in reverse a sequence of ascending fourths (this is the reason that modern theoreticians may speak of a "circle of fourths"). The integral design of cadential models - G functions as the dominant of C, this extends again to F and so on - explains why fourths have this property, giving quartal harmony a new tonal centre corresponding to the original by a less stable ratio.

[edit] Analytical problems

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. Both interpretations may be valid, and either may lead to interesting consequences.

The 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, where the fourth does not require resolution. Fsus4, a second inversion (6/4) chord, would also be a plausible label. Extending quartal chords to four or more notes generate still more possibilities of a similar nature. A four-tone chord C - F - B♭ - E♭ can be seen, for example 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), or many other things. The possibilities are quite numerous.

As part of a tonally directed listening there are also many interpretations of the fourth chords. The tones C - F - B♭, for instance, can easily be heard as a fourth-suspension in F major, also C7sus4. In a five-tone "quartal tower" having the tones C - F - B♭ - E♭ - A♭ the ear may hear an A♭ major or F minor sound with additional embellishing tones.

The question of which strategy of analysis is advisable must be given an answer that is refined by the particular details: given one interpretation, and the progression of harmony including the preceding and following chords, and the overall musical development, is there a comprehensible and audibly functional meaning to the interpretation, or is it simply a mental exercise forcing the music into a Procrustean bed? It can be an important criteria to note whether these suspensions and chromatic mutations of chord tones (alterations) are resolved functionally as the interpretation dictates. Surely it must also be significant, whether it takes many listenings (or a study of the score) for the listener to understand the harmonic situation arranged by the interpretation.

[edit] History

Quartal harmony has had parallel developments in both vocal and instrumental music, but has also occurred in the traditional music of many non-western cultures. Some people who have put good use of this have been... Nicholas Weatherburn, Michael Shafer and David Liao

[edit] Middle Ages

In medieval music, the tonality of the common practice period had not yet developed, and many examples may be found with harmonic structures that favour quartal harmonies. The Musica enchiriadis of the mid 10th century, a guidebook for musical practice of the time, described singing in parallel fourths, fifth and octaves. This development continued, and the music of the Notre Dame school may be considered the apex of a coherent harmony in this style.

For instance, in this Alleluia (Listen) by Pérotin, the fourth is favoured. This example from the score shows that the interval of a fourth constitutes over fifteen percent of the interval relationships. Elsewhere in parallel organum at the fourth, the upper line would be accompanied a fourth below. Also important was the practice of Fauxbourdon, which is a three voice technique (not infrequently improvisatory) in which the two lower voices proceed parallel to the upper voice at a fourth and sixth below. Fauxbourdon, while making extensive use of fourths, is also an important step towards the later triadic harmony of tonality, as it may be seen as a first inversion (or 6/3) triad.

This parallel 6/3 triad was incorporated into the contrapuntal style at the time, in which sometimes parallel fourths were considered problematic, and written around with ornaments or other modifications to Fauxbourdon. An example of this is the start of the Marian-Antiphon Ave Maris Stella (Listen) by Guillaume Du Fay, a master of Faurxbourdon.

In medieval thought, contemplation of the musical intervals was frequently expressed from theological perspectives. Pope John XXII issued a bull in 1324 forbidding most contrapuntal practice, but permitting on solemn occasions an enrichment of the plainchant by the concord of the octave which he described as a symbol for the perfect beauty and holiness of God, sounding out over earthly imperfection and infertility, along with the fifth and fourth which have a similar purity.

[edit] Renaissance and Baroque

The development of tonality continued through the Renaissance until it was fully realized at last by composers of the Baroque era. In Josquin Des Prez's 1515 Mass Missa Pange Lingua Listen) or the two-part Domine, dominus noster it still feels sparse. Ascending and descending lines in the individual parts of the following example outline a fourth interval with their range.

As time progressed through the late Renaissance and early Baroque, the fourth became more understood as an interval that needed resolution. Increasingly the harmonies of fifths and fourths yielded to uses of thirds and sixths. In the example, cadence forms from works by Orlando Lasso and Giovanni Pierluigi da Palestrina show the fourth being resolved as a suspension. (Listen)

In the early Baroque music of Claudio Monteverdi, Palestrina and Girolamo Frescobaldi triadic harmony was thoroughly utilized. Diatonic and chromatic passages strongly outlining the interval of a fourth appear in the Lamento genre, and often in Passus duriusculus passages of chromatic descent. In the madrigals of Claudio Monteverdi and Carlo Gesualdo the intensive interpretation of the text (Word painting) frequently highlights the shape of a fourth as an extremely delayed resolution of a fourth suspension. Also, in Frescobaldi's Chromatic Toccata of 1635 the outlined fourths overlap, bisecting various church modes.

In the first third of the 18th century, ground-laying theoretical work on composition and harmony were written. Jean-Philippe Rameau completed his treatise Le Traité de l'harmonie réduite à ses principes naturels (French: the theory of harmony reduced to its natural principles) in 1722 which was supplemented by his work of four years earlier, Nouveau Système de musique theoretique (French: new system of music theory), which together may be considered the cornerstone of modern Music theory in view of consonance and harmony. The Austrian composer Johann Joseph Fux published in 1725 his powerful treatise on composition of Counterpoint in the style of Palestrina under the title Gradus ad Parnassum (Latin: The Steps to Parnassus). He outlined various types of counterpoint (e.g. Note against note), and suggested a careful application of the fourth as to avoid dissonance.

This older style of counterpoint was often overlaid with a fully formed tonality in the works of the High Baroque. In the Cruxifixus of Johann Sebastian Bach's Mass in B Minor the intervals of the ascending fourth and descending fifth are thoroughly emphasized. His keyboard works, such as the Fugue No.22 in the first book of the Well-Tempered Clavier or the Sinfonia no.9 (Listen) there is an extreme density of imitation (very often at the interval of a fourth) with such great care taken to maintain coherent harmony that Paul Hindemith would refer to Bach's counterpoint as a "harmony preserving carnival-mirror" („wahres harmonische Vexierspiel“) in his teachings.

[edit] Classical and Romantic

The blossoming of tonality and establishment of well temperament in Bach's time had a continuing effect up to the late Romantic period, and the tendencies of quartal harmony were somewhat suppressed. An increasingly refined cadence, and triadic harmony defined the musical work of this era. Counterpoint was simplified to favour an upper line with a clear accompanying harmony. Still, there are many examples of dense counterpoint in this style, commonly as part of the background urging the harmonic expression in a passage along to a climax.

Mozart in his so-called Dissonance Quartet KV 465 (Listen) used Chromatic and Whole tone scales to outline fourths. Arch shaped lines emphasizing fourths in the first Violin (C - F - C) and the Violoncello (G - C - C' - G') are combined with lines emphasizing fifths in the second Violin and Viola. Over the barline between the second and third measures of the example a fourth-suspension can be seen in the second violin's tied C. In another of his String quartets, KV 464, such fourth-suspensions are also very prominent.

Examples of the tonal language are often taken from classical String quartets and Piano music, as in these compositions all of the elements and problems of tonality occur just as in larger works, but the simplicity of instrumentation makes them easier to see. The theme of the fourth movement of Beethoven's Piano sonata op. 110 (Listen) opens with three ascending fourths (A♭ -> D♭ - B♭ -> E♭ - C -> F) and them downwards in gestures outlining fourths (i.e. F - E♭ - D♭ - C). This counterpoint has two themes working together to highlight the fourth.

To begin the second movement of his String Quartet in A Minor op. 132 (Listen) Beethoven exposes the fourth in a three note gesture (G♯ - A - C♯) four times, with all instruments playing in unison. In measure 5 this motive is combined with an inverted variation (outlining a descending fifth) in mixed rhythm.

From 1850 to 1900 the expression of tonality by composers of the Late Romantic such as Anton Bruckner, Richard Wagner, Gustav Mahler and Claude Debussy, began to dissolve, and as the 20th century began with tonality no longer a strong binding force, quartal harmony was given more room to breathe.

Quartal harmony became important in the work of Slavic and Scandinavian composers such as Modest Mussorgsky, Leoš Janáček, and Jean Sibelius.

They 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 somewhat quartal harmony in a way that was relatively hard and modern. Even in the preceding example from Mussorgsky's Piano-cycle Pictures at an Exhibition (Избушка на курьих ножках (Баба-Яга) - The Hut on Fowl's Legs) (Listen) the fourth always has an "unvarnished" entrance. Rudiments of quartal harmony appear in Janáček's Rhapsody Taras Bulba, his Opera Věc Makropulos (The Makropulos Affair) and Z Mrtvého Domu (From the House of the Dead), and descending fourths and sevenths can be found dominating the writing.

The Freiburg musicologist Christian Berger pointed out in his writing Atonality and Tradition - Anton Webern's Four Pieces for Violin and Clarinet op. 8 („Atonalität und Tradition – Anton Weberns Vier Stücke für Geige und Klavier op. 7“) a connection between Richard Wagner's so-called Liebestod-Melody (Love-Death) from the second act of the opera Tristan und Isolde and Webern's work. Both works set in the leap of a fourth (E♭ - A♭) two semitones downwards (A♭ - G - G♭). The target of this descending line becomes a starting point for the next upward fourth (G♭ - C♭), and this procedure is repeated many times. In Webern's use of this device, Berger found eight consecutive fourths set in this way.

[edit] Impressionism

The Romantic composers Frédéric Chopin and Franz Liszt, use the special "thinned out" sound of a fourth-chord in late works for Piano (Nuages gris (Fr: Grey Clouds), La lugubre gondola (Fr: The Mournful Gondola), and other works).

The Impressionists would make much more use of this chord, even allowing it as a place of relaxation, altering its perception in the context of harmonic function and winning its status as an autonomous chord.

These would become 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 Maurice Ravel, Claude Debussy and others. In the fourth piece from the first book of Debussy's Préludes, Les sons et les parfums tournent dans l'air du soir (Fr: Sounds and Perfumes Stir in the Evening Air), triadic fourth chords in the right hand over "normal" four-note chords in the left hand (Listen). Further examples are Debussy's orcehstral work La Mer (Fr: The Sea), La cathédrale engloutie (Fr: The Sunken Cathedral) of the Préludes, as well as Pour les quartes (Fr: For Fourths) (Listen (Opening)) and Pour les arpéges composées (Fr: For Composite Arpeggios) from his Etudes.

In this example from the 1897 work The Sorcerer's Apprentice (L'Apprenti sorcier) by Debussy's colleague composer Paul Dukas, we see 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 Maurice Ravel's Sonatine and Ma Mère l'Oye (Fr: Mother Goose) would follow a few years later.

[edit] 20th century Music

[edit] "Art Music"

At the beginning of the 20th century quartal structure 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 6th Piano Sonata. This was best realized by his work Prometheus - The Poem of Fire. Earlier sketches left by Scriabin indicate that the composer apparently first intended that the work develop from a single non-transposed tonal centre.

Scriabin wrote this chord in his sketches as well as quartal and more traditional tertian writing, often passing between systems, for example widening the six-tone quartal sonority (C - F♯ - B♭ - E - A - D) into a seven-tone chord (C - F♯ - B♭ - E - A - D - G). There was a growing need for a theory of quartal harmony in the context of the music of Scriabin and Liszt; Leonid Sabanejew published in 1912 a work on Scriabin's theoretical ideas about Prometheus: Poem of Fire in the periodical Der Blaue Reiter (The Blue Rider), but they 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." („Dabei wurde übersehen, dass erstens Akkorde aus reinen Quarten (wie zum Beispiel in Arnold Schönbergs hierfür mit Recht vielzitierter Kammersinfonie) nicht ohne weiteres mit Mischungen aus übermäßigen, verminderten und reinen Quarten gleichzusetzen ist und zweitens, dass Skrjabin selbst seinen sogenannten mystischen Akkord keineswegs als Quartenakkord sondern vielmehr als eine Wiederspiegelung der Obertöne ansah.“)

Arnold Schoenberg's influential Chamber Symphony Op. 9 from the year 1906 (Listen) is a milestone in 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 appearing tones C - F - B♭ - E♭ - A♭ distributed over several instruments. The composer then leaves this vertical quartal harmony with a horizontal sequence of fourths C - F - B♭ - E♭ - A♭ - D♭ from the horns, eventually leading to a triadic harmony.

Schoenberg was also one of the first to write on the theoretical consequences of this harmonic innovation. In his Theory of Harmony of 1912, he wrote: "The quartal construction of chords can lead to a chord containing all twelve tones 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 phenomenona of harmony (...)" („Der quartenweise Aufbau der Akkorde kann zu einem Akkord führen, der sämtliche zwölf Töne der chromatischen Skala enthält, und damit immerhin eine Möglichkeit der systematischen Betrachtung jener harmonischen Phänomene erzielen, die in Werken von einigen von uns schon vorkommen: sieben-, acht- neun-, zehn-, elf-, zwölfstimmige Akkorde. (...) Der quartenweise Aufbau ermöglicht (...) die Unterbringung aller Phänomene der Harmonie (...)“)

For Anton Webern the importance of quartal harmony lay in the possibility of building new sounds. He wrote in the year 1912: "With alteration the fourth-chord never need belong to tonal harmony, but can be free of all tonal relationships." („Durch Alteration werden die Quartenakkorde zu noch nie gehörten Harmonien, die frei von jeder tonalen Beziehung sind.“)

After seeing Schoenberg's Chamber Symphony he felt: "You must write something like that, too!" („So was mußt du auch machen!“) (Page 48 of his book The Path to the New Music (52 of Der Weg zur Komposition)) Shortly after, he wrote his Four Pieces for Violin and Piano Op. 7, using quartal harmony as a formal principle, which was realized in other works as well.

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 of 114 songs), in which the piano part contained four-part fourth chords accompanying a vocal line which moves in whole tones: (Listen).

Also other composers, for example Béla Bartók with his piano work Mikrokosmos (Listen) and Music for Strings, Percussion and Celesta, Paul Hindemith, Carl Orff and Igor Stravinsky employed quartal harmony. They joined romantic elements with baroque music, folk songs and their peculiar rhythm and harmony with the open harmony of fourths and fifths.

Hindemith constructed, for example, large parts of his symphonic work Mathis der Maler (Mathis the Painter) (Listen) 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 ("Understanding of Tone-motion") he wrote: "Tones have a family of relationships, that are the bindings of tonality, in which the ranking of intervals is unambiguous," („dass die Töne eine Familienzugehörigkeit besitzen, die sich in der Bindung an tonale Haupttöne äußert, die eine unzweideutige Rangliste der Tonverwandschaften aufstellt.“) so much that in the art of triadic composition "...the musician is bound by this, as the painter to his primary colours, the architecht to the three dimensions.". („... der Musiker ist an ihn gebunden, wie der Maler an die primären Farben, der Architekt an die drei Dimensionen.“) He lined up the harmonic and melodic craft in a row where first appears the octave, then fifth and thirdm 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." („Das stärkste und eindeutige harmonische Intervall ist nächst der alleinstehenden Oktave die Quinte, das schönste jedoch die Terz wegen ihrer in den Kombinationstönen begründeten Akkordwirkung.“)

In his Theory of Harmony („Harmonielehre“) of 1922 Schoenberg remarked on page 407 (pg 487 in the cited German version): "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. („Außer mir haben meine Schüler Dr. Anton Webern und Alban Berg solche Klänge [gemeint sind Quartenklänge] geschrieben. Aber auch der Ungar Bela Bartok oder der Wiener Franz Schreker, die beide einen ähnlichen Weg gehen wie Debussy, Dukas und vielleicht auch Puccini, sind wohl nicht weit davon entfernt.“)

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 Mieczyslaw 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 wholetones, tritones with semitones, or other possibilities.

In the first movement of Olivier Messiaen's Turangalîla Symphony a six-tone combination is constructed in pieces from fourths and tritones, much like Schoenberg and Scriabin's. Much of Messiaen's work applies quartal harmony, moderated by his development of "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 "Two conversations for Organ" of the year 1942), Ivan Wyschnegradsky, Toru 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 Piano Concerto in F (Listen) altered fourth chords descend chromatically in the right hand with a chromatic scale leading upward in the left hand.

[edit] 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. Important influences come thereby from Opera, Operetta, Military bands as much as Piano music of Classical, Romantic composers, and somewhat 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 and Art Tatum. 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, 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 shown here, 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. Throughout the 1940s quartal harmony is employed as ongoing practice.

The Hard bop of the 1950s made new applications of quartal harmony accessible to Jazz. Quintet writing with two brass instruments, commonly Trumpet and Saxophone may proceed in fourths, whereas the Piano as a uniquely harmonic instrument lays down chords, but sparsely, only to hint at the intended harmony. See Horace Silver's Señor Blues (Listen). This style of writing, in contrast with the decade previous, preferred a moderate tempo. "Thin" sounding "unison" Bebop horn sections occur frequently, but it is balanced by bouts of very refined polyphony as in Cool Jazz, though many felt this music was not "hard" or expressive enough.

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. (Listen)

From the outset of the 1960s, the employment of quartal possibilities had become so familiar that the musician now felt the fourth chord as belonging on its own, self standing, free of any need to resolve as a supension. 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 (Corozine 2002, p.12).

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 quartal harmony into improvisation. The pianists Herbie Hancock, and Chick Corea are two musicians well known for their modal experimentation. At this time a phenomenon known as Free Jazz also came into being, in which the 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. At about 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.

[edit] Rock Music

In Rock Music quartal harmony became part of the compositional framework, between Riffs and Power chords which often use fifths and fourths instead of triadic harmony.

In Funk, there is a well loved stylistic device, interjecting fourths in syncopation by the guitars, keyboards, or brass section. Consider the following riff from the song "Flashlight" (Listen) by George Clinton's band Parliament, 1977. In Hard Rock and Heavy Metal whole songs were often built up from riffs of fourths and fifths on the Electric guitar.

See Ritchie Blackmore's song "Man on the Silver Mountain" (Listen) played by his band Rainbow in 1975, with a riff completely composed of fourths. This preference for fourths in Rock stems directly from the chosen "high instrument of Rock Music", the guitar, on which they are very simple to play.

The 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. For example the opening of Tarkus (Eruption) by Emerson, Lake & Palmer (Listen) has such an ostinato in the bass. Here a sequence of fourths on F (F - B♭ - E♭ - B♭ - A♭ - E♭ - B♭) is followed a semitone higher on F♯ with E - B - F♯.

Some support from classical principles of composition was taken by Gentle Giant in their a cappella vocals in the song "Design" (Listen). 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 Music 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). Quartal harmony comes most commonly the role in a fourth suspension (as in Classical music), for example in Elton Johns rock ballad Burn Down the Mission.

[edit] Latin American Music

The Popular music of Latin American countries is interrelated with the development in the USA, due to considerable cultural exchange.

Latin music has a tendency toward a slightly faster tempo than music in the US. Quartal harmony found its way into salsa and Latin jazz from the Jazz practice (such as the playing of John Coltrane), but also due to the concept of rhythm in the Afro-cuban tradition. The guitarist Carlos Santana became world-known by combining these influences together.

In the Música Popular Brasileira of Brazil, the guitar has a similarly central role as the harmonic instrument as 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 art music.

[edit] See also

• Secundal
• Tertian
• Polychord
• List of quartal pieces

[edit] Further reading

[edit] Overall

• Diether de la Motte: Harmonielehre. dtv, München 1997 (10. Auflage) Erstauflage 1976, ISBN 3-423-04183-8 (Theory of Harmony)
• Urs Martin Egli: Hören und Nachdenken - Eine reale Harmonielehre. HBS Nepomuk, Aarau 2003, ISBN 3-907117-15-8 (Hearing and Contemplation - A Real Theory of Harmony)
• Zsolt Gardonyi und Hubert Nordhoff: Harmonik. Karl Heinrich Möseler Verlag, Wolfenbüttel Neuausgabe 2002 (Erstdruck 1990), ISBN 3-7877-3035-4 (Harmony)

[edit] Medieval, Renaissance, Baroque

• Rudolf Flotzinger: Perotinus musicus. Schott, Mainz 2000, ISBN 3-7957-0431-6 (Music of Perotin)
• Claus Ganter: Kontrapunkt für Musiker - Gestaltungsprinzipien der Vokal- und Instrumentalpolyphonie des 16. und 17. Jahrhunderts in der Kompositionspraxis von Josquin-Desprez, Palestrina, Lasso, Froberger, Pachelbel u.a.. Musikverlag Emil Katzbichler, München - Salzburg 1994, ISBN 3-87397-130-5 (Conterpoint for Musicians - Formal Principles of Vocal and Instrumental Polyphony of the 16th and 17th Centuries in the Compositional Practice of Josquin Desprez, Palestrina, Lasso, Froberger, Pachelbel et al.)
• Martin Geck: Johann Sebastian Bach, Rowohlt, Reinbek 2002, ISBN 3-499-50637-8
• Peter Niedermüller: "Contrapunto" und "effetto" - Studien zu den Madrigalen Carlo Gesualdos. Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-27908-6 (Counterpoint and Effect - Studies of the Madrigals of Carlo Gesualdo)

[edit] Classical and Romantic

• Zsolt Gardonyi und Siegfried Mauser: Virtuosität und Avantgarde - Untersuchungen zum Klavierwerk Franz Liszts. Schott, Mainz 1988, ISBN 3-7957-1797-3 (Virtuosity and the Avant Garde - Investigating the Piano Work of Franz Liszt)
• Theodor Helm: Beethovens Streichquartette: Versuch einer technischen Analyse dieser Werke im Zusammenhange mit ihrem geistigen Gehalt. M. Sändig, Wiesbaden 1971, ISBN 3-500-23600-6 (Beethoven's String Quartets: A Technical Analytical Approach to These Works in the Context of His Intellectual Principles)
• Theo Hirsbrunner: Claude Debussy und seine Zeit. Laaber-Verlag, 2002, ISBN 3-89007-533-9 (Claude Debussy and His Time)

[edit] 20th century music

• Hermann Danuser: Amerikanische Musik seit Charles Ives. Laaber 1987, ISBN 3-89007-117-1 (The American Music of Charles Ives)
• Gottfried Eberle: Zwischen Tonalität und Atonalität - Studie zur Harmonik Alexander Skrjabins. Musikverlag Emil Katzbichler, München – Salzburg 1978, ISBN 3-87397-044-9 (Between Tonality and Atonality - Study of Alexander Skriabin's Harmony)
• Ekkehard Kreft: Harmonische Prozesse im Wandel der Epochen (3.Teil) Das 20. Jahrhundert. Peter Lang, Frankfurt am Main 1999, ISBN 3-631-47141-6 (Harmonic Processes in Change Between Epochs, Bool 3: The 20th Century)
• Arnold Schönberg: Theory of Harmony. Belmont Music Publishers, Los Angeles 1912/1978, ISBN 0-520-04944-6

[edit] Jazz, Rock, and Latin music

• David N. Baker: Jazz Improvisation. Frangipani, Bloomington (Indiana) 1983, ISBN 0-89917-397-7
• Wolf Burbat: Die Harmonik des Jazz. dtv Bärenreiter, Kassel 1998, ISBN 3-423-30140-6 or ISBN 3-423-04472-1 (The Harmony of Jazz)
• Rebeca Mauleón: Salsa Guidebook. For piano and ensemble. Sher Music, Petaluma (Kalifornien) 1993, ISBN 0-9614701-9-4
• David H. Rosenthal: Hard Bop. Jazz and Black music 1955-1965. Oxford University Press (USA), New York 1993, ISBN 0-19-508556-6

[edit] References

This article incorporates text translated from the corresponding German Wikipedia article as of July 20, 2006.

• Vince Corozine. Arranging Music for the Real World: Classical and Commercial Aspects. Alfred Publishing, Los Angeles 2002.

[edit] External links

• Quartalharmony with notes and listening examples
• Quartal voicing for the guitar
• Program notes for Arnold Schoenberg's Chamber Symphony for 15 Solo Instruments op. 9

v • d • e Chords
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