Rhythm (from Greek ῥυθμός – rhythmos, "any regular recurring motion, symmetry") is a "movement marked by the regulated succession of strong and weak elements, or of opposite or different conditions."  In other words, rhythm is simply the timing of the musical sounds and silences. While rhythm most commonly applies to sound, such as music and spoken language, it may also refer to visual presentation, as "timed movement through space."
Rhythm in linguistics
The study of rhythm, stress, and pitch in speech is called prosody; it is a topic in linguistics. Narmour  describes three categories of prosodic rules which create rhythmic successions which are additive (same duration repeated), cumulative (short-long), or countercumulative (long-short). Cumulation is associated with closure or relaxation, countercumulation with openness or tension, while additive rhythms are open-ended and repetitive. Richard Middleton points out this method cannot account for syncopation and suggests the concept of transformation.
A rhythmic unit is a durational pattern which occupies a period of time equivalent to a pulse or pulses on an underlying metric level, as opposed to a rhythmic gesture which does not .
Origins of human appreciation of rhythm
In his series How Music Works, Howard Goodall presents theories that rhythm recalls how we walk and the heartbeat we heard in the womb. More likely is that a simple pulse or di-dah beat recalls the footsteps of another person. Our sympathetic urge to dance is designed to boost our energy levels in order to cope with someone, or some animal chasing us – a fight or flight response. From a less darwinist perspective, perceiving rhythm is the ability to master the otherwise invisible dimension, time. Rhythm is possibly also rooted in courtship ritual.
Neurologist Oliver Sacks posits that human affinity for rhythm is fundamental, so much that a person's sense of rhythm cannot be lost in the way that music and language can (e.g. by stroke). In addition, he states that chimpanzees and other animals show no similar appreciation for rhythm.
Rhythm notation and the oral tradition
Worldwide there are many different approaches to passing on rhythmic phrases and patterns, as they exist in traditional music, from generation to generation.
In the Griot tradition of Africa everything related to music has been passed on orally. Babatunde Olatunji (1927–2003), a Nigerian drummer who lived and worked in the United States, developed a simple series of spoken sounds for teaching the rhythms of the hand drum. He used six vocal sounds: Goon Doon Go Do Pa Ta. There are three basic sounds on the drum, but each can be played with either the left or the right hand. This simple system is now used worldwide, particularly by Djembe players.
It is noteworthy that the debate about the appropriateness of staff notation for African music is a subject of particular interest to outsiders, not insiders. African scholars from Kyagambiddwa to Kongo have for the most part accepted the conventions—and limitations—of staff notation and gone on to produce transcriptions in order to inform and to make possible a higher level of discussion and debate.— Agawu (2003: 52)
John Miller Chernoff 1979 has argued that West African music is based on tension between rhythms. A set of moral values underpins a full musical system based on repetition of relatively simple patterns which meet at distant intervals and call and answer schemes. Values also show up in collective utterances such as proverbs or lineages appear either in phrases that translate as drum talk or in the words of songs. People expect musicians to stimulate participation of all present, notably by reacting to people dancing the music. Appreciation of musicians is related to the effectiveness of their upholding community values.
Indian music has also been passed on orally. Tabla players would learn to speak complex rhythm patterns and phrases before attempting to play them. Sheila Chandra, an English pop singer of Indian descent, made performances based on her singing these patterns. In Indian Classical music, the Tala of a composition is the rhythmic pattern over which the whole piece is structured.
Standard music notation contains rhythmic information and is adapted specifically for drums and percussion instruments. The drums are generally used to keep other instruments in 'time'. They do this by supplying beats/strikes in time at a certain pace, i.e. 70 beats per minute (bpm). In Rock music, a drum beat is used to keep a bass/guitar line in time.
In Western music, rhythms are usually arranged with respect to a time signature, partially signifying a meter. The grouping of the underlying pulse is sometimes called the beat. The tempo is a measure of how quickly the beat flows. The tempo is usually measured in 'beats per minute' (bpm); 60 bpm means a speed of one beat per second. The meter(usually corresponding with measure length), is usually grouped into either two or three beats, which are called duple meter and triple meter, respectively. If the beats in consistently even or odd groups of two, three, or four, it is simple meter, if by admixtures of two and three it iscompound meter. According to Pierre Boulez, beat structures beyond four are "simply not natural".. His reference is to the conventions of western European concert music.
Syncopated rhythms are rhythms that accent parts of the beat not already stressed by counting. Playing simultaneous rhythms in more than one time signature is called polymeter. See also polyrhythm. In recent years, rhythm and meter have become an important area of research among music scholars. Recent work in these areas includes books by Maury Yeston, Fred Lerdahl and Ray Jackendoff, Jonathan Kramer, Christopher Hasty, William Rothstein, and Joel Lester.
Grid notation of single a clave pattern.
Some genres of music make different use of rhythm than others. Sub-Saharan African music traditions and most Western music is based on subdivision, while non-Western music uses more additive rhythm. African music makes heavy use of polyrhythms, specifically cross-rhythm and Indian music uses complex cycles such as 7 and 13, while Balinese music often uses complex interlocking rhythms. By comparison, a lot of Western classical music is fairly rhythmically (or metrically) simple; it stays in a simple meter such as 4/4 or 3/4 and makes little use of syncopation.
Clave is a key pattern (or guide pattern) in African, Cuban music, and Brazilian music.
In the 20th century, composers like Igor Stravinsky, Béla Bartók, Philip Glass, and Steve Reich wrote more rhythmically complex music using odd meters, and techniques such as phasing and additive rhythm. At the same time, modernists such as Olivier Messiaen and his pupils used increased complexity to disrupt the sense of a regular beat, leading eventually to the widespread use of irrational rhythms in New Complexity. This use may be explained by a comment of John Cage's where he notes that regular rhythms cause sounds to be heard as a group rather than individually; the irregular rhythms highlight the rapidly changing pitch relationships that would otherwise be subsumed into irrelevant rhythmic groupings . LaMonte Young also wrote music in which the sense of a regular beat is absent because the music consists only of long sustained tones (drones). In the 1930s, Henry Cowell wrote music involving multiple simultaneous periodic rhythms and collaborated with Léon Thérémin to invent the Rhythmicon, the first electronic rhythm machine, in order to perform them. Similarly, Conlon Nancarrow wrote for the player piano.
^ ῥυθμός, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus project
^ The Compact Edition of the Oxford English Dictionary. II. Oxford University Press. 1971. p. 2537.
^ "Art, Design, and Visual Thinking". http://char.txa.cornell.edu/language/principl/rhythm/rhythm.htm. Retrieved 2010-03-16.
^ Narmour (1980), p. 147–53. Cited in Winold, Allen (1975).
^ Middleton, Richard (1990). Studying Popular Music. Philadelphia: Open University Press. ISBN 0-335-15275-9.
^ Winold, Allen (1975). "Rhythm in Twentieth-Century Music", Aspects of Twentieth-Century Music. Wittlich, Gary (ed.). Englewood Cliffs, New Jersey: Prentice–Hall. ISBN 0-13-049346-5.
^ Mithen, Steven (2005). The Singing Neanderthals: The Origins of Music, Language, Mind and Body.. London: Weidenfeld & Nicolson.. ISBN 0297643177. http://www.epjournal.net/filestore/ep03375380.pdf.
^ Patel, Aniruddh D. (2006), "Musical rhythm, linguistic rhythm, and human evolution not you", Music Perception (Berkeley, California: University of California Press) I (24): 99–104, ISSN 0730-7829, "there is not a single report of an animal being trained to tap, peck, or move in synchrony with an auditory beat." as cited in Sacks, Oliver (2007). "Keeping Time: Rhythm and Movement". Musicophilia, Tales of Music and the Brain. New York • Toronto: Alfred a Knopf. pp. 239–240. ISBN 978-1-4000-4081-0. "No doubt many pet lovers will dispute this notion, and indeed many animals, from the Lippizaner horses of the Spanish Riding School of Vienna to performing circus animals appear to 'dance' to music. It is not clear whether they are doing so or are responding to subtle visual or tactile cues from the humans around them."
^ Agawu, Kofi (2003: 52). Representing African Music: Postcolonial Notes, Queries, Positions. New York: Routledge.
^ Chernoff, John Miller (1979) African Rhythm and African Sensibility -- Aesthetic and Social Action in African Musical Idioms. Chicago: The University of Chicago Press
^ In Discovering Music: Rhythm with Leonard Slatkin at 5:05
^ Yeston, Maury (1976). The Stratification of Musical Rhythm. Yale University Press. ISBN 0300018843.
^ Hasty, Christopher (1997). Meter as Rhythm. Oxford: Oxford University Press. ISBN 0-19-510066-2.
^ Sandow, Greg (2004). "A Fine Madness", p. 257, The Pleasure of Modernist Music. ISBN 1-58046-143-3.
McGaughey, William (2001). Rhythm and Self-Consciousness: New Ideals for an Electronic Civilization. Minneapolis: Thistlerose Publications. ISBN 0-9605630-4-0.
Honing, H. (2002). "Structure and interpretation of rhythm and timing." Tijdschrift voor Muziektheorie [Dutch Journal of Music Theory] 7(3): 227–232.
Humble, M. (2002). The Development of Rhythmic Organization in Indian Classical Music, MA dissertation, School of Oriental and African Studies, University of London.
Lewis, Andrew (2005). Rhythm—What it is and How to Improve Your Sense of It. San Francisco: RhythmSource Press. ISBN 978-0-9754667-0-4.
London, Justin (2004). Hearing in Time: Psychological Aspects of Musical Meter. ISBN 0-19-516081-9.
Williams, C. F. A., The Aristoxenian Theory of Musical Rhythm, (Cambridge Library Collection - Music), Cambridge University Press; 1st edition, 2009.
Toussaint, G. T., “The geometry of musical rhythm,” In J. Akiyama, M. Kano, and X. Tan, editors, Proceedings of the Japan Conference on Discrete and Computational Geometry, Vol. 3742, Lecture Notes in Computer Science, Springer, Berlin/Heidelberg, 2005, pp. 198–212.