A Survey of Music Theory for the College Classroom: Chromatic Harmony 2 and 20th Century Music

Rhythm in the 20th Century

Overview

Music written during the 20th and 21st centuries has included greater rhythmic freedom and complexity than at any time during the past. Many conventions of western art music during the Common Practice Period such as four measure phrases, the expectation of regular metric downbeats and accents, and the use of standard time signatures and symmetrical meters, have been modified or jettisoned as composers explored new avenues of rhythmic organization. Additionally, the rhythmic practices of nonwestern cultures have continued to make inroads into western art music. The following surveys some of the rhythmic practices that composers of western art music have increasingly used or developed since the late 19th century.

Syncopation   

Syncopation happens when a rhythmic pattern obscures the strong beats implied in a time signature, thus creating heightened interest in the music because of the disruption of the normal flow of metric accents. Syncopation has been a feature of many musical styles and genres over the past few centuries and is widely used in 20th and 21st century art music. Syncopation can be used in any meter, at any tempo, and within any level of subdivision of the beat.

A classic and often used example of syncopation is where the usual metric accent pattern is shifted by half a beat. This syncopation can be contained within a bar or can be extended over the bar line by using ties.

syncopation

Syncopation can also take place within smaller subdivisions of a beat, as shown below.

advanced syncopation

Hemiola

The hemiola, sometimes called cross-rhythm, is the rhythmic ratio of 3:2. Whether expressed vertically in two parts, or horizontally in one part, the important effect is that of 3 in the space of 2, as illustrated in the next examples.

hemiola

Displaced Accents (Shifting Accents)

Another method of achieving flexibility in rhythm is through using shifting accents, in which accents are placed on a beat or division of a beat that does not match with the usual metric accent pattern found within that meter. When used consistently, displaced accents can even begin to suggest a different meter. In the following example, a simple duple signature is implied.

displaced accents

Igor Stravinsky used displaced accents in his monumental piece The Rite of Spring. In the episode The Augurs of Spring it is used in a simple duple meter, and in the episode Ritual of Abduction in a compound triple meter. In The Firebird, Stravinsky combines highly syncopated rhythms and displaced accents to radically alter the perception of the meter in the section Infernal Dance of King Kashchei.

Asymmetric/Irregular Meters

A very common way of avoiding the metrical regularity of simple and compound meters is to use asymmetrical meters in which exist groupings of subdivisions of both 2 and 3, making patterns such as 2+3, 3+2, 3+2+2, 2+3+2, and 2+2+3. The two most common asymmetric meters are \(\begin{smallmatrix} 7 \\ 8 \end{smallmatrix}\) and \(\begin{smallmatrix} 5 \\ 8 \end{smallmatrix}\), although others such as \(\begin{smallmatrix} 10 \\ 8 \end{smallmatrix}\) and \(\begin{smallmatrix} 11 \\ 8 \end{smallmatrix}\) are sometimes seen. It is also possible to use the quarter note as the division value, creating meters such as \(\begin{smallmatrix} 5 \\ 4 \end{smallmatrix}\) and \(\begin{smallmatrix} 7 \\ 4 \end{smallmatrix}\). Much less frequently found is the use of the 16th note or smaller values as the division. A piece that features many noteworthy rhythmic devices including meters such as \(\begin{smallmatrix} 18 \\ 16 \end{smallmatrix}\) is Debussy’s Sonata for Flute, Viola, and Harp

The following example illustrates \(\begin{smallmatrix} 5 \\ 8 \end{smallmatrix}\) and \(\begin{smallmatrix} 7 \\ 8 \end{smallmatrix}\) meters. Note that appropriate beaming makes clear the patterns in these asymmetrical meters.

asymmetric meters

Complex meters, sometimes called composite meters, are based on more traditional numbers of divisions such as 8 or 9 but that feature beats of unequal length. For instance, the eight 8th notes of \(\begin{smallmatrix} 4 \\ 4 \end{smallmatrix}\) are grouped in four groups of two (2+2+2+2), but in \(\begin{smallmatrix} 8 \\ 8 \end{smallmatrix}\) meter the 8th notes can be expressed in groups of 2+3+3, 3+2+3, and 3+3+2. An example of this occurs in Bartok’s Mikrokosmos, No. 153, Dance in Bulgarian Rhythm. A meter such as \(\begin{smallmatrix} 9 \\ 8 \end{smallmatrix}\) can be transformed into grouping such as 4+2+3. These complex meters are usually notated in the manner shown in the following examples.

complex meters

Changing Meters/Time Signatures

The use of frequent time signatures changes became common in 20th century music. This practice, also called shifting meter and mixed meter, allows composers to keep the elements of traditional time signatures such as bar lines and metric accents while injecting a fresh and often impelling vibrancy into the music. These shifts in time signature can be very rapid, occurring as often as every measure. For example, the chamber piece Fuging Machine by the author of this text, features a constant shift between \(\begin{smallmatrix} 7 \\ 8 \end{smallmatrix}\)and \(\begin{smallmatrix} 3 \\ 4 \end{smallmatrix}\) throughout most of the work. Another example can be seen in the episode Ritual of Abduction in Stravinsky’s Rite of Spring. While not a requirement, mixed meter often occurs at faster tempos, which helps the listener to perceive the differences in beats, subdivisions of beats, and metric accents. Composers such as Claude Debussy often combined shifting meters, asymmetric meters, and other rhythmic devices in a more gentle and supple manner, as displayed in the previously mentioned Sonata for Flute, Viola, and Harp.

The next example shows a single melodic line that employs shifting meters. As earlier, notice that the beaming makes clear the patterns in the asymmetrical meters (3+2, 2+2+3, etc.).

changing time signatures

Ametric/Nonmetric Rhythms

Ametric or nonmetric rhythms occur when a composer writes music that has no audible bar lines or meter. This can include music that uses standard time signatures but in which the music is written in such a way as to obscure the metric accents implied by the time signature, as Edgard Varèse does in his famous piece for solo flute, Density 21.5. An example without time signatures is Charles Ives' Piano Sonata No. 2, Concord, Massachusetts, 1840-1860.

It is also possible to employ all manner of electronic, aleatoric, notational, and improvisational techniques to create music without a perceivable repeating pulse or audible meter.

Added Values

In his book The Technique of My Musical Language, the French composer Olivier Messiaen examines innovative rhythmic ideas and procedures that he used in his own music. These include the techniques of added values, nonretrogradable rhythms, and augmentation and diminution. 

In an added value, a short rhythmic value is added to a standard or traditional rhythm. The added value can be accomplished through adding a dot, note, or rest to a rhythmic pattern. The music is ametric and free in feel but is precisely notated.

Messiaen uses added values in Dance of Fury for Seven Trumpets from Quartet for the End of Time, a piece written when he was a POW in a German military prison camp. The bar lines do not indicate a specific number of beats or divisions, but instead serve as visual aids to performance, to mark phrase divisions, and to cancel accidentals.

Non-retrogradable Rhythms

A palindrome is a word that is spelled the same backward as forward, such as madam, level, and racecar. A musical palindrome is a rhythm, melody, pitch pattern, or chord progression (for ex., I – ii – V – ii – I) that sounds the same when played forward and backward, and non-retrogradable rhythms are rhythmic palindromes. It is possible to have rather simple non-retrogradable rhythms as well as to combine concepts such as the added value to create more complex examples. Non-retrogradable rhythms can stretch over multiple measures and can conceivably encompass an entire piece. Messiaen is noted for his use of non-retrogradable rhythms.

A simple non-retrogradable rhythm includes this example of syncopation.

simple nonretrogradable rhythm

Next is a longer and more complex example.

complex nonretrogradable rhythm

Augmentation and Diminution

Augmentation and diminution are techniques for varying a melody and/or a rhythm and not are new to the 20thcentury, having been used by composers such as J.S. Bach during the Baroque period. Classic or conventional augmentation refers to the doubling of a duration (for ex., quarter notes expanding to half notes) while diminution refers to halving the duration (for ex., quarter notes contracting to eighth notes). Messiaen, in his text The Technique of My Musical Language, includes more complex possibilities by using added values. 

Tempo Modulation

In tempo modulation, sometimes called metric modulation, a rhythmic value in the first tempo becomes equal to a new rhythmic value in the second tempo. While it is possible for the time signatures to change, it is not necessary. The following example uses eighth-note triplets to affect the transition, but the device can be extended to other meters and to other tuplets such as quintuplets. Elliott Carter is noted for his use of this technique.

tempo modulation

Polyrhythm, Polymeter and Polytempo

The concept of polyrhythm or cross-rhythm has already been touched upon in the section on hemiola. When a hemiola occurs vertically, i.e. in two parts, the effect is that of two distinct rhythmic lines. This practice can be extended to other relationships, such as 5:4 (for ex. a quintuplet vs. eighth notes), 5:2, 7:2 and so forth. To experiment with various ratios, polyrhythm generators can be found online.

Polymeter occurs when two or more meters are used at one time. It is possible to use different time signatures with matching bar lines, or to have two different time signatures with different bar lines. Examples of polymeter in which different time signatures with matching bar lines are used are found in Stravinsky’s ballet score Petrushka at rehearsal 3 (“Introduction”) and rehearsal 14 (“The Crowds”) in the First Tableau: The Shrovetide Fair, and in the Third Tableau: The Moor’s Room at rehearsal 72 (“Waltz”). This piece is also rife with examples of shifting and asymmetric meters. An example of polymeter in which different time signatures are used with different bar lines is the second movement of Maurice Ravel's Piano Trio, in which \(\begin{smallmatrix} 4 \\ 2 \end{smallmatrix}\) is matched with \(\begin{smallmatrix} 3 \\ 4 \end{smallmatrix}\).

Polytempo occurs when two or more tempos are used at a time. A relatively simple example of this is seen in Charles Ives’s chamber early 20th century work The Unanswered Question

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