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I. Fundamentals
Twentieth-Century Rhythmic Techniques

### Core Idea

Asymmetrical meters contain measures which are divided into unequal groupings of beats or divisions, creating an uneven metrical pulse. Ametric music may or may not have an explicit meter signature, and is not played or sung in a strict metrical style.

### Explanation

Asymmetrical meters contain measures which are divided into unequal groupings of beats or divisions, creating an uneven metrical pulse.

Ametric music may or may not have an explicit meter signature, and is not played or sung in a strict metrical style.

In some cases, the meter written in the score may not be the meter that the listener perceives, which is an issue of perceived versus notated meter.

Changing meter is a method of composition which incorporates any change of meter.

Polymeter occurs when two or more meters are performed simultaneously.

Metric modulation is a rhythmic technique that smooths out abrupt tempo changes by introducing subdivisions or groups of beats in the first tempo that match durations in the new tempo.

Timeline notation is a contemporary metric technique that uses seconds as the measure of time, rather than traditional bar lines and meters.

Feathered beaming is a gradual change in the speed of notes within a single beam.

Ostinato is a repeated rhythmic or pitched musical idea.

Many composers in the twentieth century expanded the traditional rhythmic palette of music in order to explore new musical ideas. Below, nine less traditional rhythmic techniques are discussed.

Asymmetrical Meter

Music in asymmetrical meters contain measures which are divided into unequal groupings of beats or divisions, creating an uneven metrical pulse. Listen to Example 1, whose meter is \begin{smallmatrix}5\\8\end{smallmatrix}. Notice the division of the two beats; one is grouped into three eighth notes, and the other into two eighth notes. This creates a feeling of a long pulse followed by a short pulse:

Example 1. "Ladies In Their Sensitivities" (1979) written by Stephen Sondheim, performed by Peter Polycarpou.

This song is found in the musical Sweeny Todd (1979) whose music is by Stephen Sondheim (1930–2021). The off-kilter feeling of the \begin{smallmatrix}5\\8\end{smallmatrix} meter reinforces the anxious thought process of the singer; he is a servant, recommending his boss for a shave, and is hesitant to do so due to his bootlicking status.

Now listen to Example 2, which is also in \begin{smallmatrix}5\\8\end{smallmatrix} meter. Notice how the division of the two beats is grouped in the opposite manner of the last example, with the first beat divided into two eighth notes, and the second beat into three eighth notes:

Example 2. "Aufbruch" (2008) measures 141–149 written by Rolf Rudin (b.1961), performed by the National Chiayi University Band.

The \begin{smallmatrix}5\\8\end{smallmatrix} measures juxtapose the more metrically typical \begin{smallmatrix}3\\4\end{smallmatrix} measures, creating a call and response texture between the woodwinds and brass. The character of the woodwinds is much more lively and playful as compared to the staunch and powerful brass.

There are other asymmetrical time signatures whose beat division unit is the eighth note, such as \begin{smallmatrix}7\\8\end{smallmatrix}, \begin{smallmatrix}11\\8\end{smallmatrix}, \begin{smallmatrix}13\\8\end{smallmatrix}, etc. Usually we can identify the groupings of the meter's subdivisions by either how the notes are beamed, or via explicit directions written in the music (e.g. a \begin{smallmatrix}7\\8\end{smallmatrix} meter signature may be written as \begin{smallmatrix}(2+2+3)\\8\end{smallmatrix}, \begin{smallmatrix}(3+2+2)\\8\end{smallmatrix}, or another way).

Now listen to Example 3, which is in the time signature \begin{smallmatrix}13\\8\end{smallmatrix} (3+3+3+2+2), beginning at 0:17. Try counting along with the example!

https://open.spotify.com/track/1S5ZrjYFWNbhciAxMrLdjU?si=fa408139359a4512

Example 3. "Skinbleshanks: The Railway Cat" performed by the Cast Of The Motion Picture "Cats" (2019).

This song is found in the musical Cats (1981), with music written by Andrew Lloyd Webber (b. 1948). The \begin{smallmatrix}13\\8\end{smallmatrix} section could have been written in a prototypical \begin{smallmatrix}12\\8\end{smallmatrix} meter; however, adding an extra eighth note reinforces the lively nature of the character by not allowing the listener to fall into a regular rhythmic pattern.

Asymmetrical meters can have other beat units, such as the sixteenth note or quarter note. Some examples you may encounter are \begin{smallmatrix}5\\4\end{smallmatrix}, \begin{smallmatrix}7\\16\end{smallmatrix}, or \begin{smallmatrix}5\\2\end{smallmatrix}. The beats of these time signatures are still divided or grouped unequally, though their beat unit changes. Observe Example 4, which is first written in \begin{smallmatrix}7\\4\end{smallmatrix} and rewritten in \begin{smallmatrix}7\\8\end{smallmatrix}:

Example 4. "Unsquare Dance" (1961) written by the Dave Brubeck Quartet.

This is an excerpt of the "Unsquare Dance" (1961) by the Dave Brubeck Quartet (1951–2012). A typical square dance is in a quadruple meter; however, this "unsquare dance" is in an asymmetrical meter, which diverts the listener's expectations. Notice how the rhythm can be written in both \begin{smallmatrix}7\\4\end{smallmatrix} and \begin{smallmatrix}7\\8\end{smallmatrix} meters, while still sounding the same.

Ametric Music

Music written ametrically does not have any perceivable meter. Ametric music may or may not have an explicit meter signature, and is not necessarily played or sung in a strict metrical style. In other words, the notes may still have rhythmic values, but rhythmic durations might not result in a perceivable beat pattern. This technique may allow for a performer’s own improvisation and phrasing, and is employed in cadenzas, passages of free improvisation, Gregorian chant, and post-tonal music. Listen to Example 5, a post-tonal song that does not have a time signature:

Example 5. "The Cage" (c. 1904) written by Charles Ives (1874–1954), performed by Corinne Curry (soprano) and Luise Vosgerchian (piano).

"The Cage" (circa 1904) is a song written by American composer Charles Ives (1874–1954). The ametric nature of the song supports the anxious beha

### Key Quote

Asymmetrical meters contain measures which are divided into unequal groupings of beats or divisions, creating an uneven metrical pulse.

### Application Scenarios

Music in asymmetrical meters contain measures which are divided into unequal groupings of beats or divisions, creating an uneven metrical pulse. Listen to Example 1, whose meter is \begin{smallmatrix}5\\8\end{smallmatrix}. Notice the division of the two beats; one is grouped into three eighth notes, and the other into two eighth notes. This creates a feeling of a long pulse followed by a short pulse:

Example 1. "Ladies In Their Sensitivities" (1979) written by Stephen Sondheim, performed by Peter Polycarpou.

Now listen to Example 2, which is also in \begin{smallmatrix}5\\8\end{smallmatrix} meter. Notice how the division of the two beats is grouped in the opposite manner of the last example, with the first beat divided into two eighth notes, and the second beat into three eighth notes:

Example 2. "Aufbruch" (2008) measures 141–149 written by Rolf Rudin (b.1961), performed by the National Chiayi University Band.

### Key Terminology

asymmetrical meter metric modulation timeline notation feathered beaming changing meter division unit eighth note modulation polymeter bar lines ostinato measure

### Related Links

Asymmetrical Meter (lcsproductions.net)Introduction to Asymmetrical Meters (Ash Stemke)Compound and Asymmetric Meter (learnmusictheory.net)Creating Interesting Motion with Time Signature Changes (David Bawiec)Advanced Rhythm and Meter/Percieved vs. Notated Meter (Frank Koonce)Songs that use Polymeter and Polyrhythm (David Bennett)Intro to Metric Modulation (Philippe Macnab-Seguin)Metric Modulation (Beyond Music Theory)Feathered Notes (Steinberg.org)Ostinato (Music Theory Academy)
Source: https://viva.pressbooks.pub/openmusictheory/chapter/twentieth-century-rhythmic-techniques/
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