page_title: Additive rhythm and divisive rhythm
section_title: Additive rhythm
hierarchical_section_title: Additive rhythm and divisive rhythm / Additive rhythm
caption_attribution_description: English: Additive rhythm 3+3+2 over 8
context_page_description: In music, the terms additive and divisive are used to distinguish two types of both rhythm and meter:
  A divisive rhythm is a rhythm in which a larger period of time is divided into smaller rhythmic units or, conversely, some integer unit is regularly multiplied into larger, equal units.
  This can be contrasted with additive rhythm, in which larger periods of time are constructed by concatenating a series of units into larger units of unequal length, such as a meter produced by the regular alternation of and.
  When applied to meters, the terms perfect and imperfect are sometimes used as the equivalents of divisive and additive, respectively.
  For example, 4 may be evenly divided by 2 or reached by adding 2 + 2. In contrast, 5 is only evenly divisible by 5 and 1 and may be reached by adding 2 or 3. Thus, is divisive while is additive.
  The terms additive and divisive originate with Curt Sachs's book Rhythm and Tempo, while the term aksak rhythm was introduced for the former concept at about the same time by Constantin Brăiloiu, in agreement with the Turkish musicologist Ahmed Adnan Saygun.
context_section_description: Additive rhythm features nonidentical or irregular durational groups following one another at two levels, within the bar and between bars or groups of bars (Agawu 2003, 86). This type of rhythm is also referred to in musicological literature by the Turkish word aksak, which means "limping" (Brăiloiu 1951; Fracile 2003, 198). In the special case of time signatures in which the upper numeral is not divisible by two or three without a fraction, the result may alternatively be called irregular, imperfect, or uneven meter, and the groupings into twos and threes are sometimes called long beats and short beats (Beck and Reiser 1998, 181–82).
  The term additive rhythm is also often used to refer to what are also incorrectly called asymmetric rhythms and even irregular rhythms – that is, metres which have a regular pattern of beats of uneven length. For example, the time signature  indicates each bar is eight quavers long, and has four beats, each a crotchet (that is, two quavers) long. The asymmetric time signature , on the other hand, while also having eight quavers in a bar, divides them into three beats, the first three quavers long, the second three quavers long, and the last just two quavers long.
  These kinds of rhythms are used, for example, by Béla Bartók, who was influenced by similar rhythms in Bulgarian folk music. Stravinsky's Octet for Wind Instruments "ends with a jazzy 3+3+2 = 8 swung coda" (Walsh 1988, 127). Additive patterns also occur in some music of Philip Glass, and other minimalists, most noticeably the "one-two-one-two-three" chorus parts in Einstein on the Beach. They may also occur in passing in pieces which are on the whole in conventional metres. In jazz, Dave Brubeck's song "Blue Rondo à la Turk" features bars of nine quavers grouped into patterns of 2+2+2+3 at the start. George Harrison’s song “Here Comes the Sun” on the Beatles’ album Abbey Road features a rhythm "which switches between 11/8, 4/4 and 7/8 on the bridge" (Margotin and Guesdon 2013, 576). "The special effect of running even eighth notes accented as if triplets against the grain of the underlying backbeat is carried to a point more reminiscent of Stravinsky than of the Beatles" (Pollack n.d.).
  Olivier Messiaen made extensive use of additive rhythmic patterns, much of it stemming from his close study of the rhythms of Indian music. His "Danse de la fureur, pour les sept trompettes" from The Quartet for the End of Time is a bracing example. A gentler exploration of additive patterns can be found in "Le Regard de la Vierge" from the same composer's piano cycle Vingt Regards sur l'enfant-Jésus.
caption: Additive rhythm 3+3+2
  8 time. 1 whole note = 8 eighth notes = 3 + 3 + 2.
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