Additive rhythm and divisive rhythm

rdf:langString Additive rhythm and divisive rhythm

rdf:langString Winold, Allen . "Rhythm in Twentieth-Century Music". In Aspects of Twentieth-Century Music, edited by Gary Wittlich, Englewood Cliffs, New Jersey: Prentice-Hall. . pp. 208-269.

rdf:langString Beck, Jill, and Joseph Reiser . Moving Notation: A Handbook of Musical Rhythm and Elementary Labanotation for the Dancer. Performing Arts Studies 6. Amsterdam: Harwood Academic Publishers. ; .

rdf:langString Margotin, Philippe, and Jean-Michel Guesdon . All the Songs: The Story Behind Every Beatles Release. New York: Black Dog and Leventhal. .

rdf:langString London, Justin . "Rhythm". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.

rdf:langString Read, Gardner . Music Notation: A Manual of Modern Practice, second edition. Boston: Allyn and Bacon, Inc.

rdf:langString Pollack, Alan . "Notes on 'Here Comes the Sun'" .

rdf:langString Walsh, Stephen . The Music of Stravinsky. London: Routledge.

rdf:langString Brăiloiu, Constantin. 1951. "Le rythme Aksak" Revue de Musicologie 33, nos. 99 and 100 : 71–108.

rdf:langString Ladzekpo, C. K. . "The Myth of Cross-Rhythm", Foundation Course in African Dance-Drumming .

rdf:langString Peñalosa, David . The Clave Matrix; Afro-Cuban Rhythm: Its Principles and African Origins. Redway, California: Bembe Inc. .

rdf:langString Fracile, Nice . "The 'Aksak' Rhythm, a Distinctive Feature of the Balkan Folklore". Studia Musicologica Academiae Scientiarum Hungaricae 44, nos. 1 and 2:197–210.

rdf:langString In music, the terms additive and divisive are used to distinguish two types of both rhythm and meter: * A divisive (or, alternately, multiplicative) 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 (joining end to end) a series of units into larger units of unequal length, such as a 58 meter produced by the regular alternation of 28 and 38. 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, 48 (or, more commonly, 24) is divisive while 58 is additive. The terms additive and divisive originate with Curt Sachs's book Rhythm and Tempo (1953), 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 Ahmet Adnan Saygun. The relationship between additive and divisive rhythms is complex, and the terms are often used in imprecise ways. In his article on rhythm in the second edition of the New Grove Dictionary of Music and Musicians, Justin London states that: [i]n discussions of rhythmic notation, practice or style, few terms are as confusing or used as confusedly as ‘additive’ and ‘divisive’. … These confusions stem from two misapprehensions. The first is a failure to distinguish between systems of notation (which may have both additive and divisive aspects) and the music notated under such a system. The second involves a failure to understand the divisive and additive aspects of meter itself. 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". Sub-Saharan African music and most European (Western) music is divisive, while Indian and other Asian musics may be considered as primarily additive. However, many pieces of music cannot be clearly labeled divisive or additive.