rhythmic unit

Rhythm (from Greek , ''rhythmos'', "any regular recurring motion, symmetry") generally means a " movement marked by the regulated succession of strong and weak elements, or of opposite or different conditions". This general meaning of regular recurrence or pattern in time can apply to a wide variety of cyclical natural phenomena having a periodicity or frequency of anything from microseconds to several seconds (as with the riff in a rock music song); to several minutes or hours, or, at the most extreme, even over many years.

Rhythm is related to and distinguished from pulse, meter, and beats:

In the performance arts, rhythm is the timing of events on a human scale; of musical sounds and silences that occur over time, of the steps of a dance, or the meter of spoken language and poetry. In some performing arts, such as hip hop music, the rhythmic delivery of the lyrics is one of the most important elements of the style. Rhythm may also refer to visual presentation, as "timed movement through space" and a common language of pattern unites rhythm with geometry. For example, architects often speak of the rhythm of a building, referring to patterns in the spacing of windows, columns, and other elements of the façade. 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, Godfried Toussaint, William Rothstein, Joel Lester, and Guerino Mazzola.

Anthropology

In his television series ''How Music Works'', Howard Goodall presents theories that human rhythm recalls the regularity with which we walk and the heartbeat. Other research suggests that it does not relate to the heartbeat directly, but rather the speed of emotional affect, which also influences heartbeat. Yet other researchers suggest that since certain features of human music are widespread, it is "reasonable to suspect that beat-based rhythmic processing has ancient evolutionary roots". Justin London writes that musical metre "involves our initial perception as well as subsequent anticipation of a series of beats that we abstract from the rhythm surface of the music as it unfolds in time". The "perception" and "abstraction" of rhythmic measure is the foundation of human instinctive musical participation, as when we divide a series of identical clock-ticks into "tick-tock-tick-tock".

Joseph Jordania recently suggested that the sense of rhythm was developed in the early stages of hominid evolution by the forces of natural selection. Plenty of animals walk rhythmically and hear the sounds of the heartbeat in the womb, but only humans have the ability to be engaged ( entrained) in rhythmically coordinated vocalizations and other activities. According to Jordania, development of the sense of rhythm was central for the achievement of the specific neurological state of the battle trance, crucial for the development of the effective defense system of early hominids. Rhythmic war cry, rhythmic drumming by shamans, rhythmic drilling of the soldiers and contemporary professional combat forces listening to the heavy rhythmic rock music all use the ability of rhythm to unite human individuals into a shared collective identity where group members put the interests of the group above their individual interests and safety.

Some types of parrots can know rhythm. Neurologist Oliver Sacks states that chimpanzees and other animals show no similar appreciation of rhythm yet posits that human affinity for rhythm is fundamental, so that a person's sense of rhythm cannot be lost (e.g. by stroke). "There is not a single report of an animal being trained to tap, peck, or move in synchrony with an auditory beat", Sacks write, "No doubt many pet lovers will dispute this notion, and indeed many animals, from the Lipizzaner 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." Human rhythmic arts are possibly to some extent rooted in courtship ritual.

The establishment of a basic beat requires the perception of a regular sequence of distinct short-duration pulses and, as a subjective perception of loudness is relative to background noise levels, a pulse must decay to silence before the next occurs if it is to be really distinct. For this reason, the fast-transient sounds of percussion instruments lend themselves to the definition of rhythm. Musical cultures that rely upon such instruments may develop multi-layered polyrhythm and simultaneous rhythms in more than one time signature, called polymeter. Such are the cross-rhythms of Sub-Saharan Africa and the interlocking ''kotekan'' rhythms of the gamelan.

For information on rhythm in Indian music see Tala (music). For other Asian approaches to rhythm see Rhythm in Persian music, Rhythm in Arabic music and ''Usul''—Rhythm in Turkish music and Dumbek rhythms.

Terminology

Pulse, beat and measure

Most music, dance and oral poetry establishes and maintains an underlying "metric level", a basic unit of time that may be audible or implied, the pulse or ''tactus'' of the mensural level, or ''beat level'', sometimes simply called the beat. This consists of a (repeating) series of identical yet distinct periodic short-duration stimuli perceived as points in time. The "beat" pulse is not necessarily the fastest or the slowest component of the rhythm but the one that is perceived as fundamental: it has a tempo to which listeners entrain as they tap their foot or dance to a piece of music. It is currently most often designated as a crotchet or quarter note in western notation (see time signature). Faster levels are ''division levels'', and slower levels are ''multiple levels''. Maury Yeston clarified "Rhythms of recurrence" arise from the interaction of two levels of motion, the faster providing the pulse and the slower organizing the beats into repetitive groups. "Once a metric hierarchy has been established, we, as listeners, will maintain that organization as long as minimal evidence is present".

Unit and gesture

A durational pattern that synchronises with a pulse or pulses on the underlying metric level may be called a ''rhythmic unit''. These may be classified as:
*Metric – even patterns, such as steady eighth notes or pulses;
*Intrametric – confirming patterns, such as dotted eighth-sixteenth note and swing patterns;
*Contrametric – non-confirming, or syncopated patterns; and
*Extrametric – irregular patterns, such as tuplets.

A rhythmic gesture is any durational pattern that, in contrast to the rhythmic unit, does not occupy a period of time equivalent to a pulse or pulses on an underlying metric level. It may be described according to its beginning and ending or by the rhythmic units it contains. Rhythms that begin on a strong pulse are ''thetic'', those beginning on a weak pulse are ''anacrustic'' and those beginning after a rest or tied-over note are called ''initial rest''. Endings on a strong pulse are ''strong'', on a weak pulse, ''weak'' and those that end on a strong or weak upbeat are ''upbeat''.

Alternation and repetition

Rhythm is marked by the regulated succession of opposite elements: the dynamics of the strong and weak beat, the played beat and the inaudible but implied rest beat, or the long and short note. As well as perceiving rhythm humans must be able to anticipate it. This depends on repetition of a pattern that is short enough to memorize.

The alternation of the strong and weak beat is fundamental to the ancient language of poetry, dance and music. The common poetic term "foot" refers, as in dance, to the lifting and tapping of the foot in time. In a similar way musicians speak of an upbeat and a downbeat and of the "on" and "off" beat. These contrasts naturally facilitate a dual hierarchy of rhythm and depend on repeating patterns of duration, accent and rest forming a "pulse-group" that corresponds to the poetic foot. Normally such pulse-groups are defined by taking the most accented beat as the first and counting the pulses until the next accent. A rhythm that accents another beat and de-emphasises the downbeat as established or assumed from the melody or from a preceding rhythm is called syncopated rhythm.

Normally, even the most complex of meters may be broken down into a chain of duple and triple pulses either by addition or division. According to Pierre Boulez, beat structures beyond four, in western music, are "simply not natural".

Tempo and duration

The tempo of the piece is the speed or frequency of the ''tactus'', a measure of how quickly the beat flows. This is often measured in 'beats per minute' ( bpm): 60 bpm means a speed of one beat per second, a frequency of 1 Hz. A rhythmic unit is a durational pattern that has a period equivalent to a pulse or several pulses. The duration of any such unit is inversely related to its tempo.

Musical sound may be analyzed on five different time scales, which Moravscik has arranged in order of increasing duration.
*Supershort: a single cycle of an audible wave, approximately – second (30–10,000 Hz or more than 1,800 bpm). These, though rhythmic in nature, are not perceived as separate events but as continuous musical pitch.
*Short: of the order of one second (1 Hz, 60 bpm, 10–100,000 audio cycles). Musical tempo is generally specified in the range 40 to 240 beats per minute. A continuous pulse cannot be perceived as a musical beat if it is faster than 8–10 per second (8–10 Hz, 480–600 bpm) or slower than 1 per 1.5–2 seconds (0.6–0.5 Hz, 40–30 bpm). Too fast a beat becomes a drone, too slow a succession of sounds seems unconnected. This time frame roughly corresponds to the human heart rate and to the duration of a single step, syllable or rhythmic gesture.
*Medium: ≥ few seconds, this median durational level "defines rhythm in music" as it allows the definition of a rhythmic unit, the arrangement of an entire sequence of accented, unaccented and silent or "rest" pulses into the cells of a ''measure'' that may give rise to the "briefest intelligible and self-existent musical unit", a ''motif'' or '' figure''. This may be further organized, by repetition and variation, into a definite ''phrase'' that may characterise an entire genre of music, dance or poetry and that may be regarded as the fundamental formal unit of music.
*Long: ≥ many seconds or a minute, corresponding to a durational unit that "consists of musical phrases"—which may make up a melody, a formal section, a poetic stanza or a characteristic sequence of dance moves and steps. Thus the temporal regularity of musical organisation includes the most elementary levels of musical form.
*Very long: ≥ minutes or many hours, musical compositions or subdivisions of compositions.

Curtis Roads takes a wider view by distinguishing nine-time scales, this time in order of decreasing duration. The first two, the infinite and the supra musical, encompass natural periodicities of months, years, decades, centuries, and greater, while the last three, the sample and subsample, which take account of digital and electronic rates "too brief to be properly recorded or perceived", measured in millionths of seconds (microseconds), and finally the infinitesimal or infinitely brief, are again in the extra-musical domain. Roads' Macro level, encompassing "overall musical architecture or form" roughly corresponds to Moravcsik's "very long" division while his Meso level, the level of "divisions of form" including movements, sections, phrases taking seconds or minutes, is likewise similar to Moravcsik's "long" category. Roads' Sound object: "a basic unit of musical structure" and a generalization of note ( Xenakis' mini structural time scale); fraction of a second to several seconds, and his Microsound (see granular synthesis) down to the threshold of audible perception; thousandths to millionths of seconds, are similarly comparable to Moravcsik's "short" and "supershort" levels of duration.

Rhythm–tempo interaction

One difficulty in defining rhythm is the dependence of its perception on tempo, and, conversely, the dependence of tempo perception on rhythm. Furthermore, the rhythm–tempo interaction is context dependent, as explained by Andranik Tangian using an example of the leading rhythm of ″Promenade″ from Moussorgsky's ''Pictures at an Exhibition'':(

This rhythm is perceived as it is rather than as the first three events repeated at a double tempo (denoted as R012 = repeat from 0, one time, twice faster):

However, the motive with this rhythm in the Moussorgsky's piece

is rather perceived as a repeat

This context-dependent perception of rhythm is explained by the principle of correlative perception, according to which data are perceived in the simplest way. From the viewpoint of Kolmogorov's complexity theory, this means such a representation of the data that minimizes the amount of memory.

The example considered suggests two alternative representations of the same rhythm: as it is, and as the rhythm-tempo interaction – a two-level representation in terms of a generative rhythmic pattern and a "tempo curve". Table 1 displays these possibilities both with and without pitch, assuming that one duration requires one byte of information, one byte is needed for the pitch of one tone, and invoking the repeat algorithm with its parameters R012 takes four bytes. As shown in the bottom row of the table, the rhythm without pitch requires fewer bytes if it is "perceived" as it is, without repetitions and tempo leaps. On the contrary, its melodic version requires fewer bytes if the rhythm is "perceived" as being repeated at a double tempo.

Thus, the loop of interdependence of rhythm and tempo is overcome due to the simplicity criterion, which "optimally" distributes the complexity of perception between rhythm and tempo. In the above example, the repetition is recognized because of additional repetition of the melodic contour, which results in a certain redundancy of the musical structure, making the recognition of the rhythmic pattern "robust" under tempo deviations. Generally speaking, the more redundant the "musical support" of a rhythmic pattern, the better its recognizability under augmentations and diminutions, that is, its distortions are perceived as tempo variations rather than rh