Simultaneity

Marcel Duchamp's `Nude Descending a Staircase, No. 3.` The nude figure is presented from the neck down with narrow beige and tan rectangles representing thighs, shins, upper arms and forearms, and a rounded shape representing various her pelvis. The implied motion of the figure is demonstrated by 10-15 roughly-drawn iterations of each shape as it makes the necessary movements for walking down a dark brown staircase, the motion sometimes accentuated with an arc drawn to show the shape's path. Nude Descending a Staircase, No. 2, a 1912 oil painting by French artist Marcel Duchamp. Duchamp used multiple images of the subject's body in various poses to imply motion.
(Philadelphia Museum of Art | Public Domain)

Music almost always involves the combination of multiple sounds, from a simple chord on a piano to strains of a thousand-person choir. While these combinations are often consonant, the dissonance of incongruent sounds can drive a piece in different and interesting ways.

Polychords

A polychord consists of two unrelated chords being juxtaposed harmonically. These chords can be difficult to resolve aurally as a single sound, often presenting something similar to a figure-ground problem for the listener.

The most successful polychords consist of distantly related chords, such as those separated by three or more degrees on the circle of fifths. The combination of closely related chords will likely not be heard as polychords but as extended harmonies.

Three circles of fifths; one with C and F highlighted, one with C and E flat highlighted, and one with C and C sharp/D flat highlighted. In the center of each circle the two corresponding major triads are shown as a polychord in traditional music notation. Below the circles, under the label `Aural Perception,` equivalent chords are notated: F major 7 for the C/F polychord, C 7 sharp 9 over D sharp for the C/E flat polychord. The C/C sharp polychord is notated identically below the label.
Figure 1: Three different polychords shown with how the chords might be perceived aurally. Closely related chords are heard as extended harmonies; distantly related chords are heard as polychords.

Composers generally combine triads to create polychords, as combining larger chords blurs the perceived duality. The illusion of simultaniety can be produced using tremolo.

Measures 33 and 34 of Petrushka by Igor Stravinsky in condensed score, showing flutes, oboes, piano and strings playing a tremolo between an F sharp major triad and a C major triad. Clarinets and Bassoons are playing scalar passages on thiry-second notes, and the brass have a simple melody of a quarter note tied to eighth-note triplets.
Figure 2: Measures 33 and 34 of the second tableau of Petrushka a 1911 ballet by Russian composer Igor Stravinsky. In this passage, Petrushka, a puppet, curses the magician which has caused him to come to life. The polychord played by flutes, oboes, piano and strings — the combination of a C major triad and an F# major triad — is used thematically throughout the ballet and is known to theorists as the Petrushka chord.

Because of their dissonance, polychords usually do not have a strong tonal function, but this can be overcome by using orchestration or voicing to place one chord in a subsidiary role.

Measure 1 of `A Hard Day's Night` by The Beatles, showing an F9 chord in the electric and acoustic guitars, a D3 in the electric bass, a D-G-D chord in the piano, and a combined snare and ride cymbal in the drum set.
Figure 3: The opening chord of the 1964 song A Hard Day's Night, by the English band The Beatles. This chord, which starts the album, featured acoustic guitarist John Lennon and electric guitarist George Harrison playing an F9 chord, electric bassist Paul McCartney playing a D3, pianist George Martin playing a G power chord, and drummer Ringo Starr striking the snare drum and ride cymbal. The result, an F major/G major polychord, comes across as a dominant D7 chord because of the D in the bass and the various harmonics involved.

Polychords are notated in jazz lead sheets as a special type of slash chord, with both chord symbols shown. While rare, these chords are generally shown with a horizontal bar, as opposed to the slash used for inverted chords.

Measures 17 to 20 of Alice Coltrane's changes for John Coltrane's `A Love Supreme,` showing two alterations of F minor 11 and a combined G minor and F minor 7 polychord.
Figure 4: Measures 17–20 of American composer and saxophonist John Coltrane's 1965 piece A Love Supreme, as harmonized by his wife, composer and pianist Alice Coltrane, showing use of polychords in a jazz context.

Polytonality

Whereas polychords are individual sound events, polytonality is the use of multiple, simultaneous key centers over a longer period of time. Polytonality can be thought of as the melodic counterpart to polychordal harmony, and of course polychords can often be found in a polytonal texture.

Because it occurs over a longer period of time, polytonality tends to be more dissonant and jarring to the listener. Because of this, the technique is less common and is often used to portray conflict or other types of disparity.

Measures 3 to 6 of `What The Hell Happened` by Bruce Hornsby, with the lyrics `Look at my momma, look at my pop, look at my brother, makin' them little girls' jaws drop.` The piece's vocal line and left hand of the piano are drawn from C sharp major, but cast against a pedal C natural in the piano left hand.
Figure 6: Measures 3–6 of the 2004 song What The Hell Happened by American singer-songwriter Bruce Hornsby. This passage juxtaposes C# major in the vocals and piano right hand with a C natural in the piano left hand, and uses other examples of polytonality throughout to reflect the narrator bemoaning his marked ugliness.

Bitonality

Like polychordalism, polytonality requires some harmonic distance to create an effective, dissonant juxtaposition. The use of simultaneous keys which are more closely related is called bitonality, and can still create a feeling of duality though in a less dissonant way. In fact, bitonal passages generally sound traditionally tonal, with their ambiguous tonal center becoming apparent only through closer analysis.

Measures 33 to 43 of `Waltz #2 (XO)` by Elliott Smith, showing the chords of the piece analyzed in both G minor and B flat major. The chords are diatonic in both keys, with the exception of measures 38 and 39, which have a rarely-seen dominant of the subtonic moving to a subtonic in G minor, and a dominant of the dominant moving to the dominant in B flat major.
Figure 7: Measures 33–43 of the 1998 song Waltz #2 (XO) by American singer-songwriter Elliott Smith. The verse is bitonal, moving smoothly between G minor and Bb major without specific points of modulation. Though the beginning and ending of the phrase shown is centered on G minor, chords in the middle of the phrase make more sense in Bb major.

Polyrhythm

A polyrhythm is a combination of multiple unaligned rhythms within a single beat. To create the effect of simultaneity, at least one of the rhythms must represent an irregular division of the beat (tuplets).

The one-measure ostinato figure of Mykola Leontovych's `Carol of the Bells,` repeated four times. The top line shows one bell ringer's pattern, repeated B flat dotted quarter notes. The second line shows another bell ringer's pattern, a quarter note descending sequence of B flat, A, G. The bottom line shows the melody of the carol, a combination of both bells.
Figure 8: The ostinato melodic pattern of the 1914 song Carol of the Bells, by Ukranian composer Mykola Leontovych. The familiar melody is actually a polyrhythm of two ringing bells; one in 6/8 time and one in 3/4 time.

Polyrhythms are common in metal music, where they fit well with the rhythmic complexity and intensity of the genre.

Figure 9: The Swedish band Meshuggah's 2008 song Lethargica. Meshuggah is well-known for their consistent use of complex meters and polyrhythms as part of their signature sound.

Polymeter

Polyrhythms involve metrical dissonance between two or more voices within a beat, but the prevailing beats are still aligned between the voices. When the beats themselves are not aligned, the result is polymeter: the combination of more than one meter simultaneously.

Polymeters can occur by each voice accenting different downbeats, or by melodic phrasing enforcing different meters.

Three measures of notated piano music, written in 4/4 time. The left hand part consists of eighth notes in a strict 4/4 pattern, and the right hand has repeated eighth notes with an accented chord on every fifth note.
Figure 11: A polymetric rhythm created through dynamic accents.
Three measures of notated piano music, written in 4/4 time. The left hand part consists of eighth notes in a strict 4/4 pattern, and the right hand has descending scalar melody which repeats every six notes.
Figure 12: A polymetric rhythm created through tonic accents.

Polymetrical sections can be notated in a number of different ways: by relying on accents and/or melody alone, through beaming (sometimes across barlines), or through lines with independent time signatures.

A repeated three-eighth-note ostinato written three different ways: first, in a 4/4 structure, beamed in groups of four; second, in a 4/4 structure, but beamed in groups of three; lastly, in a 3/8 structure.
Figure 13: A polymetric rhythm notated in three different ways: first, beamed in 4/4 time; second, notated in a 4/4 structure but beamed as a 3/8 rhythm; lastly, notated in 3/8, which misaligns measures with the other parts.

Polymeters can sometimes involve phasing, where patterns of different lengths move out of sync with each other and eventually re-align. This is demonstrated in the 1974 song Kashmir by the English band Led Zeppelin, in which the guitars and orchestra play a 3/8 pattern which repeats eight times over the course of three 4/4 measures played by the drums.

Measures 7 through 12 of `Kashmir` by Led Zeppelin. The example shows the vocal line, which is in 4/4 time, and the guitar part, which is in 3/8.
Figure 14: Measures 7–12 of Kashmir by Led Zeppelin.

Polymeter plays an important role in Ewe music, in which a percussion ensemble performs a repeated pattern (which itself is often polyrhythmic) while a lead drum performs rhythms which are often in a different meter than that the ensemble.

Figure 15: Residents of Atsiekpui, Ghana perform the Agbadza, an Ewe dance accompanied by a percussion ensemble comprised of drums, axatses (beaded gourds used as rattles) and gankogui (cowbell-like instruments). In this performance, performed as part of a funeral for a community member, the lead drummer — situated to the left of the other musicians — plays polymetric patterns over the repeated beat of the ensemble.

Simultaneity: Summary

  • Polychords consist of two simultaneous chords, usually triads, which have a dissonant relationship.
    • Polychordal components are most effective when they are separated by at least three degrees on the circle of fifths.
  • Polytonality is the simultaneous performance of melodies from distantly-related keys.
    • Music which can be perceived in two different but related keys, such as a piece which feels simultaneously in C major and A minor, is called bitonal.
  • Polyrhythms are multiple divisions of a beat played simultaneously.
  • Music in which parts are playing in different meters which do not align with one another is called polymetric.

Exercises

Exercise 1: Analyzing Percy Grainger's Lincolnshire Posy

Exercise 2: Writing an Passage Incorporating Simultaneity