Additive rhythm and divisive rhythm

[1]Winold recommends that, "metric structure is best described through detailed analysis of pulse groupings on various levels rather than through attempts to represent the organization with a single term".

which so felicitously exploits accentual and metrical variation and irregularity, and no more subtle rhythmic construction of any kind than that which is set in motion at the beginning of the 'Laudate Pueri,’ if, that is, the music is sung according to the verbal accents instead of... the editor's bar-lines".

[11][12] 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.

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 118, 44 and 78 on the bridge".

[13] "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".

[14] 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.

According to the composer's note, the 128 time signature "serves only as a guideline, the actual meter consists of 36 quavers (three 'bars'), divided asymmetrically".

These beat schemes, in their generic forms, are simple divisions of the same musical period in equal units, producing varying rhythmic densities or motions.

[18]The African rhythmic structure which generates the standard pattern is a divisive structure and not an additive one … the standard pattern represents a series of attack points that outline the onbeat three-against-two / offbeat three-against-two sequence, not a series of durational values".

"Tresillo" is also found within a wide geographic belt stretching from Morocco in North Africa to Indonesia in South Asia.

Use of the pattern in Moroccan music can be traced back to slaves brought north across the Sahara Desert from present-day Mali.

Because of its irregular pattern of attack-points, "tresillo" in African and African-based musics has been mistaken for a form of additive rhythm.

Those who wish to convey a sense of the rhythm's background [main beats], and who understand the surface morphology in relation to a regular subsurface articulation, will prefer the divisive format.