# Meter

 Why am I learning this? The one thing that is most challenging about playing twentieth and twenty-first century music is perhaps the meter. The meter can be asymmetrical, and it can change constantly, as can the beat. There can be multiple meters simultaneously, or there can be no meter at all. Knowing about meter helps you to be sharp and flexible in such situations.

Meter is the grouping of beats into measures. Meters are classified first of all by the number of beats and the number of divisions.

# History and etymology

Although musicians have used something like meter all over the world for millennia, it is only in the eighteenth century that music theorists began to distinguish it clearly from rhythm. The modern division between rhythm and meter in turn has spurred a contrary theory by Christopher Hasty that meter is actually just rhythm after all. But regardless of how distinct they are, they affect one another.

The term meter comes from the Greek metros for measure. Considering that rhythm means measured motion, we see from the etymology how meter is different from rhythm: it is just the measurement without any motion. In other words, it is just the framework of beats, not the notes.

# Basic aspects

Meters are classified first of all by the number of beats and the number of divisions of the beat. Meters with two, three, four, five, six, or seven beats are called duple, triple, quadruple, quintuple, sextuple, or septuple meters. Meters with the beat divided in two are called simple, and meters with the beat divided in three are called compound. Some musicians refer to simple and compound divisions as duple and triple, but this terminological usage obscures the distinction between beats and divisions and should be avoided. If you hear someone use the terms duple and triple this way, just smile and nod; you will never get them to stop. The most common time signatures for simple meters are 2/4, 3/4, 4/4, 5/4, 6/4, and 7/4, and the most common time signatures for compound meters are 6/8, 9/8, and 12/8, although 2, 4, 8, or 16 can appear as the bottom number with either simple or compound meters. The terms quintuple or septuple properly refer to meters with five or seven beats, but they are also used loosely for asymmetrical meters with five or seven divisions (see below).

Divisions of divisions (e.g., sixteenth notes in 4/4) are properly called subdivisions, to distinguish them from divisions of the beat (e.g., eighth notes in 4/4). Nevertheless, many musicians use both terms for both concepts, which causes no end of confusion.

An asymmetrical meter is a meter with unequal beats, typically with both simple and compound division. Common time signatures for asymmetrical meters include 5/8 (grouped as 2+3 or 3+2), 7/8 (grouped as 2+2+3 or 3+2+2), 8/8 (grouped as 3+3+2), 9/8 (grouped as 2+2+2+3), and 10/8 (grouped as 2+3+2+3 or 3+2+3+2). The time signature can also show the separate beats, for example 3+3+2/8. In keeping with such notation, asymmetrical meters are sometimes called additive meters.

Example: Led Zeppelin, “The Ocean,” from Houses of the Holy (1973): The hook is a measure of 4/4 and a measure of 2/4 + 6/16. Toward the end, the 6/16 feeds into a climactic 12/16.

Example: Frank Zappa, “Didja Get Any Onya” from Weasels Ripped My Flesh (1970): 7/8 (2+2+3), then 5/8 (2+3)

Example: Béla Bartók, “Bulgarian Rhythm,” no. 115 of Mikrokosmos (1926–37): 5/8 as 3+2 and 2+3.

Many musicians say that all quintuple and septuple meters are asymmetrical. However, this usage confuses beat and division. There are five equal beats in simple or compound quintuple meter and seven equal beats in simple or compound septuple meter; therefore these meters are not asymmetrical! A truly asymmetrical quintuple meter is, for example, 11/8, grouped as 2+2+3+2+2, as in the Bulgarian dance Kopanitsa.

Tempo modulation is a change of tempo where a pulse other than the old beat is taken as the new beat. For example, a supertriplet in 4/4 at quarter = 80 could become the new beat of 4/4 at quarter = 120. Notice that the meter is still 4/4 in this case: the meter does not have to change in a tempo modulation, although it often does, for which reason tempo modulation is sometimes called metric modulation.

Example: Jimi Hendrix, “Voodoo Chile,” from Electric Ladyland (1968), scroll to 5:57: Toward the end (19:01), the compound subdivisions (not divisions!) are regrouped as divisions (not subdivisions!) in a new double-time compound meter, which leads to the climax.

Example: Elliott Carter, “Canaries,” no. 7 from Eight Pieces for Four Timpani (1950–66)

Polymeter is when there are different meters at once. The different meters may or may not have separate written time signatures. Polymeter may or may not involve polytempo (multiple tempi at once), and vice versa.

Example: Led Zeppelin, “Kashmir,” from Physical Graffiti IV (1975): The song combines 4/4 in the drums and 6/8 in the strings.

Example: Charles Ives, “Putnam’s Camp,” from Three Places in New England (1903–14): The piece depicts two marching bands passing each other. At 5:10, the trumpets are conspicuous in 4/4, and the violins are in 12/8.

Example: Igor Stravinsky, “Marche du soldat,” no. 1 from L’histoire du soldat (1918). The bass maintains a steady 2/4 through the written meter changes.

A very common special case of polymeter is hemiola. Hemiola is when two sets of three pulses coincide with three sets of two pulses (3+3 and 2+2+2). On a small scale, a hemiola is a measure of compound duple (3+3 divisions) and a measure of simple triple (2+2+2 divisions) at the same time. On a larger scale, a hemiola is two measures of simple triple (3+3 beats) and one measure of a slow simple triple (2+2+2 divisions) at the same time.

Example: “Son de la Negra,” Mexican folk song: Small hemiola, 6/8 is overlaid on a fast 3/4.

Example: G. F. Handel, Alla Hornpipe (1715), from Water Music, Suite no. 2 in D major, II (scroll to 2:15): Large hemiola at the cadence.

A related phenomenon is syncopation, when rhythmic accents and/or word stresses are displaced from metric accents. If an entire passage is syncopated in the same way, it can start to resemble polymeter.

Example: Otis Redding, “Hard to Handle,” from The Immortal Otis Redding (1968): The syncopated notes are boxed; they are all displaced a sixteenth note early from what would align with the metric accents. Sing it slowly and tap the eighth notes to sense the syncopation clearly.

Non-metric or ametric music is when there is no steady beat. The marking senza misura means without meter. There may be a marking to play ad libitum (at liberty, i.e., freely), a span of seconds indicated in which to play a passage, an absence of stems and flags, and/or an absence of barlines.

Example: Tangerine Dream, Zeit (1972): Zeit means time, which is suspended, as it were, through the absence of meter

Example: Charles Ives, “The Cage” (1906): The piece depicts a wild animal pacing in a cage. The absence of meter helps to convey the sense of wildness.

Because meter (like everything in music) is an interpretation of sound, music can be basically non-metric to the listener, who cannot necessarily see the score, but metric to the performer. This difference allows for dramatic fake-outs and reveals.

Example: The Police, “Bring on the Night,” from Reggatta de Blanc (1979): At first the hi hat seems to mark the beat, but when the chorus arrives, then it becomes apparent that it actually marks the offbeat (Nathan Hesselink)!

Example: Radiohead, “Pyramid Song,” from Amnesiac (2001): What seems at first to be an erratic series of durations turns out to be a groove in 12/8 (Nathan Hesselink)!

Example: Claude Debussy, Violin Sonata (1917), I, mm. 1–14. What seems at first to be 3/2 with some hiccups should turn out to be 3/4. However, every violinist drags out the rhythm in mm. 9 and 13, retaining the 3/2 feeling too long. Do not submit to the hive mind! Play what is written!

• Stephen Kostka, Materials and Techniques of Post-Tonal Music, Chapter 6
• Miguel Roig-Francolí, Understanding Post-Tonal Music, Chapter 10