Additive Meter - Complex Time Signatures

Complex Time Signatures

See also: List of musical works in unusual time signatures, Quintuple meter, and Septuple meter

Signatures that do not fit into the usual duple or triple categories are known as "complex", "asymmetric", "irregular", "unusual", or "odd" although these are broad terms, and usually a more specific description is appropriate. The term "odd meter", however, is sometimes used to describe time signatures in which the upper number is simply odd rather than even, including 3/4 and 9/8. Although these more complex meters were and are common in some non-Western music, they were rarely used in formal written Western music until the 19th century. The first deliberate quintuple meter pieces were "apparently published in Spain between 1516 and 1520", although other authorities reckon the Delphic Hymns to Apollo (one by Athenaeus entirely in quintuple meter, the other by Limenius predominantly so), carved on the exterior walls of the Athenian Treasury at Delphi in 128 BC, are probably earlier. The third movement (Larghetto) of Chopin's Piano Sonata No. 1 (1828) is an early, but by no means the earliest, example of 5
4 time in solo piano music. Reicha's Fugue 20 from his Thirty-six Fugues, published in 1803, is also for piano and is in 5
8. The waltz-like second movement of Tchaikovsky's Pathétique Symphony, often described as a "limping waltz", is a notable example of 5
4 time in orchestral music. Examples from the 20th century include Holst's "Mars, the Bringer of War", (5
4) from the orchestral suite The Planets, Paul Hindemith's "Fugue Secunda in G",(5
8) from Ludus Tonalis, the ending of Stravinsky's Firebird (7
4), the fugue from Heitor Villa-Lobos's Bachianas Brasileiras No. 9 (11
8) and the Mission Impossible theme by Lalo Schifrin (also in 5
4).

Examples from the Western popular music tradition include Radiohead's "15 Step" (5
4), "Everything in Its Right Place" (10
4) and "Paranoid Android" (includes 7
8). Progressive rock also made frequent use of unusual time signatures, the best known examples being the use of shifting meters in The Beatles' "Strawberry Fields Forever" (1966) and the use of quintuple meter in their "Within You, Without You" (1967).

The jazz composition "Take Five", written in 5
4 time was one of a number of irregular-meter experiments of The Dave Brubeck Quartet, which also produced compositions in 11
4 ("Eleven Four"), 7
4 ("Unsquare Dance"), and 9
8 ("Blue Rondo à la Turk"), expressed as 2+2+2+3
8, this last being a good example of a work in a signature which, despite appearing to be merely compound triple, is actually more complex.

However, such time signatures are only considered unusual from a Western point of view. In contrast, for example, Bulgarian dances use such meters extensively, including forms with 5, 7, 9, 11, 13, 15, 22, 25 and other numbers of beats per measure. These rhythms are notated as additive rhythms based on simple units, usually 2, 3 and 4 beats, though the notation fails to describe the metric "time bending" taking place; or as compound meters, for example the Bulgarian Sedi Donka, consisting of 25 beats divided 7+7+11, where 7 is subdivided 3+2+2 and 11 is subdivided 2+2+3+2+2 or 4+3+4. See Variants below.