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Quartal and quintal harmony
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===Precursors=== The [[Tristan chord]] is made up of the notes F{{music|natural}}, B{{music|natural}}, D{{music|sharp}} and G{{music|sharp}} and is the first chord heard in [[Richard Wagner|Wagner]]'s [[opera]] ''[[Tristan und Isolde]]''. :<score override_ogg="Wagner Tristan opening (orchestral).ogg"> { \new PianoStaff << \new Staff << \new Voice \relative c'' { \clef treble \key a \minor \time 6/8 \voiceOne \partial8 r8 R2. \once \override NoteHead.color = #red gis4.->(~ gis4 a8 ais8-> b4~ b8) r r } \new Voice \relative c' { \override DynamicLineSpanner.staff-padding = #4.5 \once \override DynamicText.X-offset = #-5 \voiceTwo \partial8 a\pp( f'4.~\< f4 e8 \once \override NoteHead.color = #red dis2.)(\> d!4.)~\p d8 r r } >> \new Staff << \relative c { \clef bass \key a \minor \time 6/8 \partial8 r8 R2. \once \override NoteHead.color = #red <f b>2.( <e gis>4.)~ <e gis>8 r r } >> >> } </score> 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,{{sfn|Vogel|1962|loc=12}} notably [[Ludwig van Beethoven|Beethoven]]'s [[Piano Sonata No. 18 (Beethoven)|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 [[Functional harmony|function]], a notion which was soon after to be explored by [[Claude Debussy|Debussy]] and others.{{sfn|Erickson|1975|p={{Page needed|date=June 2012}}}} 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. [[Alexander Scriabin|Scriabin]] used a self-developed system of transposition using fourth-chords, like his [[Mystic chord]] (shown below) in his [[Piano Sonata No. 6 (Scriabin)|Piano Sonata No. 6]]. :<score sound="1"> { \override Score.TimeSignature #'stencil = ##f \relative c' { \clef treble \time 4/4 <c fis bes e a d>1 } } </score> 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{{music|sharp}}–B{{music|flat}}–E–A–D) into a seven-note chord (C–F{{music|sharp}}–B{{music|flat}}–E–A–D–G). Scriabin's sketches for his unfinished work ''[[Mysterium (Scriabin)|Mysterium]]'' show that he intended to develop the Mystic chord into a huge chord incorporating all twelve notes of the [[chromatic scale]].{{sfn|Morrison|1998|loc=316}} In France, [[Erik Satie]] experimented with [[Parallel harmony|planing]] in the stacked fourths (not all perfect) of his 1891 score for ''[[Le Fils des étoiles]]''.{{sfn|Solomon|2003}} [[Paul Dukas]]'s ''[[The Sorcerer's Apprentice (Dukas)|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".
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