Dance is a performing art form consisting of purposefully selected sequences of human movement. This movement has aesthetic and symbolic value, and is acknowledged as dance by performers and observers within a particular culture.[nb 1] Dance can be categorized and described by its choreography, by its repertoire of movements, or by its historical period or place of origin.
An important distinction is to be drawn between the contexts of theatrical and participatory dance,  although these two categories are not always completely separate; both may have special functions, whether social, ceremonial, competitive, erotic, martial, or sacred/liturgical. Other forms of human movement are sometimes said to have a dance-like quality, including martial arts, gymnastics, cheerleading, figure skating, synchronized swimming, marching bands, and many other forms of athletics.
Theatrical dance, also called performance or concert dance, is intended primarily as a spectacle, usually a performance upon a stage by virtuoso dancers. It often tells a story, perhaps using mime, costume and scenery, or else it may simply interpret the musical accompaniment, which is often specially composed. Examples are western ballet and modern dance, Classical Indian dance and Chinese and Japanese song and dance dramas. Most classical forms are centred upon dance alone, but performance dance may also appear in opera and other forms of musical theatre.
Participatory dance, on the other hand, whether it be a folk dance, a social dance, a group dance such as a line, circle, chain or square dance, or a partner dance such as is common in western Western ballroom dancing, is undertaken primarily for a common purpose, such as social interaction or exercise, of participants rather than onlookers. Such dance seldom has any narrative. A group dance and a corps de ballet, a social partner dance and a pas de deux, differ profoundly. Even a solo dance may be undertaken solely for the satisfaction of the dancer. Participatory dancers often all employ the same movements and steps but, for example, in the rave culture of electronic dance music, vast crowds may engage in free dance, uncoordinated with those around them. On the other hand, some cultures lay down strict rules as to the particular dances in which, for example, men, women and children may or must participate.
Dance is generally, though not exclusively, performed with the accompaniment of music and may or may not be performed in time to such music. Some dance (such as tap dance) may provide its own audible accompaniment in place of (or in addition to) music. Many early forms of music and dance were created for each other and are frequently performed together. Notable examples of traditional dance/music couplings include the jig, waltz, tango, disco, and salsa. Some musical genres have a parallel dance form such as baroque music and baroque dance; other varieties of dance and music may share nomenclature but developed separately, such as classical music and classical ballet.
Rhythm and dance are deeply linked in history and practice. The American dancer Ted Shawn wrote; "The conception of rhythm which underlies all studies of the dance is something about which we could talk forever, and still not finish." A musical rhythm requires two main elements; first, a regularly-repeating pulse (also called the "beat" or "tactus") that establishes the tempo and, second, a pattern of accents and rests that establishes the character of the metre or basic rhythmic pattern. The basic pulse is roughly equal in duration to a simple step or gesture.
A basic tango rhythm
Dances generally have a characteristic tempo and rhythmic pattern. The tango, for example, is usually danced in 2
4 time at approximately 66 beats per minute. The basic slow step, called a "slow", lasts for one beat, so that a full "right–left" step is equal to one 2
4 measure. The basic forward and backward walk of the dance is so counted - "slow-slow" - while many additional figures are counted "slow - quick-quick.
Just as musical rhythms are defined by a pattern of strong and weak beats, so repetitive body movements often depends on alternating "strong" and "weak" muscular movements. Given this alternation of left-right, of forward-backward and rise-fall, along with the bilateral symmetry of the human body, it is natural that many dances and much music are in duple and quadruple meter. However, since some such movements require more time in one phase than the other - such as the longer time required to lift a hammer than to strike - some dance rhythms fall equally naturally into triple metre. Occasionally, as in the folk dances of the Balkans, dance traditions depend heavily on more complex rhythms. Further, complex dances composed of a fixed sequence of steps always require phrases and melodies of a certain fixed length to accompany that sequence.
Lululaund - The Dancing Girl (painting and silk cloth. A.L. Baldry 1901, before p.107), The inscription reads; "Dancing is a form of rhythm/ Rhythm is a form of music/ Music is a form of thought/ And thought is a form of divinity."
The very act of dancing, the steps themselves, generate an "initial skeleton of rhythmic beats" that must have preceded any separate musical accompaniment, while dance itself, as much as music, requires time-keeping just as utilitarian repetitive movements such as walking, hauling and digging take on, as they become refined, something of the quality of dance.
Musical accompaniment therefore arose in the earliest dance, so that ancient Egyptians attributed the origin of the dance to the divine Athotus, who was said to have observed that music accompanying religious rituals caused participants to move rhythmically and to have brought these movements into proportional measure. The same idea, that dance arises from musical rhythm, is still found in renaissance Europe in the works of the dancing master Guglielmo Ebreo da Pesaro who speaks of dance as a physical movement that arises from and expresses inward, spiritual motion agreeing with the "measures and perfect concords of harmony" that fall upon the human ear,  while, earlier, Mechthild of Magdeburg, seizing upon dance as a symbol of the holy life foreshadowed in Jesus' saying "I have piped and ye have not danced",  writes;
I can not dance unless thou leadest. If thou wouldst have me spring aloft, sing thou and I will spring, into love and from love to knowledge and from knowledge to ecstasy above all human sense
Thoinot Arbeau's celebrated 16th century dance-treatise Orchésographie, indeed, begins with definitions of over eighty distinct drum-rhythms.
As has been shown above, dance has been represented through the ages as having emerged as a response to music yet, as Lincoln Kirstein implied, it is at least as likely that primitive music arose from dance. Shawn concurs, stating that dance "was the first art of the human race, and the matrix out of which all other arts grew" and that even the "metre in our poetry today is a result of the accents necessitated by body movement, as the dancing and reciting were performed simultaneously" - an assertion somewhat supported by the common use of the term "foot" to describe the fundamental rhythmic units of poetry.
Scholes, not a dancer but a musician, offers support for this view, stating that the steady measures of music, of two, three or four beats to the bar, its equal and balanced phrases, regular cadences, contrasts and repetitions, may all be attributed to the "incalculable" influence of dance upon music.
Émile Jaques-Dalcroze, primarily a musician and teacher, relates how a study of the physical movements of pianists led him "to the discovery that musical sensations of a rhythmic nature call for the muscular and nervous response of the whole organism", to develop "a special training designed to regulate nervous reactions and effect a co-ordination of muscles and nerves" and ultimately to seek the connections between "the art of music and the art of dance", which he formulated into his system of eurhythmics. He concluded that "musical rhythm is only the transposition into sound of movements and dynamisms spontaneously and involuntarily expressing emotion".
Hence, though doubtless, as Shawn asserts, "it is quite possible to develop the dance without music and... music is perfectly capable of standing on its own feet without any assistance from the dance", nevertheless the "two arts will always be related and the relationship can be profitable both to the dance and to music",  the precedence of one art over the other being a moot point. The common ballad measures of hymns and folk-songs takes their name from dance, as does the carol, originally a circle dance. Many purely musical pieces have been named "waltz" or "minuet", for example, while many concert dances have been produced that are based upon abstract musical pieces, such as 2 and 3 Part Inventions, Adams Violin Concerto and Andantino. Similarly, poems are often structured and named after dances or musical works, while dance and music have both drawn their conception of "measure" or "metre" from poetry.
Shawn quotes with approval the statement of Dalcroze that, while the art of musical rhythm consists in differentiating and combining time durations, pauses and accents "according to physiological law", that of "plastic rhythm" (i.e. dance) "is to designate movement in space, to interpret long time-values by slow movements and short ones by quick movements, regulate pauses by their divers successions and express sound accentuations in their multiple nuances by additions of bodily weight, by means of muscular innervations".
Shawn nevertheless points out that the system of musical time is a "man-made, artificial thing.... a manufactured tool, whereas rhythm is something that has always existed and depends on man not at all", being "the continuous flowing time which our human minds cut up into convenient units", suggesting that music might be revivified by a return to the values and the time-perception of dancing.
The early-20th-century American dancer Helen Moller stated simply that "it is rhythm and form more than harmony and color which, from the beginning, has bound music, poetry and dancing together in a union that is indissoluble.
Concert dance, like opera, generally depends for its large-scale form upon a narrative dramatic structure. The movements and gestures of the choreography are primarily intended to mime the personality and aims of the characters and their part in the plot. Such theatrical requirements tend towards longer, freer movements than those usual in non-narrative dance styles. On the other hand, the ballet blanc, developed in the 19th century, allows interludes of rhythmic dance that developed into entirely "plotless" ballets in the 20th century and that allowed fast, rhythmic dance-steps such as those of the petit allegro. A well-known example is The Cygnets' Dance in act two of Swan Lake.
The ballet developed out of courtly dramatic productions of 16th- and 17th-century France and Italy and for some time dancers performed dances developed from those familiar from the musical suite,  all of which were defined by definite rhythms closely identified with each dance. These appeared as character dances in the era of romantic nationalism.
Ballet reached widespread vogue in the romantic era, accompanied by a larger orchestra and grander musical conceptions that did not lend themselves easily to rhythmic clarity and by dance that emphasised dramatic mime. A broader concept of rhythm was needed, that which Rudolf Laban terms the "rhythm and shape" of movement that communicates character, emotion and intention,  while only certain scenes required the exact synchronisation of step and music essential to other dance styles, so that, to Laban, modern Europeans seemed totally unable to grasp the meaning of "primitive rhythmic movements",  a situation that began to change in the 20th century with such productions as Igor Stravinsky's The Rite of Spring with its new rhythmic language evoking primal feelings of a primitive past.
Indian classical dance styles, like ballet, are often in dramatic form, so that there is a similar complementarity between narrative expression and "pure" dance. In this case, however, the two are separately defined, though not always separately performed. The rhythmic elements, which are abstract and technical, are known as nritta. Both this and expressive dance (nritya), though, are closely tied to the rhythmic system (tala). Teachers have adapted the spoken rhythmic mnemonic system called bol to the needs of dancers.
Japanese classical dance-theatre styles such as Kabuki and Noh, like Indian dance-drama, distinguish between narrative and abstract dance productions. The three main categories of kabuki are jidaimono (historical), sewamono (domestic) and shosagoto (dance pieces). Somewhat similarly, Noh distinguishes between Geki Noh, based around the advancement of plot and the narration of action, and Furyū Noh, dance pieces involving acrobatics, stage properties, multiple characters and elaborate stage action.