Editing Rhythm (section)

==Terminology==

===Pulse, beat and measure===

{{Further|Pulse (music)|Beat (music)}}
[[File:Metric levels.svg|thumb|right|upright=1.15|[[Metric level]]s: beat level shown in middle with division levels above and multiple levels below.]]

{{Blockquote|As a piece of music unfolds, its rhythmic structure is perceived not as a series of discrete independent units strung together in a mechanical, additive, way like beads [or "pulses"], but as an organic process in which smaller rhythmic motives, whole possessing a shape and structure of their own, also function as integral parts of a larger ["architectonic"] rhythmic organization.{{sfn|Cooper|Meyer|1960|p=2}}}}

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 (music)|pulse]] or ''tactus'' of the [[mensural level]],{{sfn|Berry|1987|p=349}}{{sfn|Lerdahl and Jackendoff|1983}}{{sfn|Fitch and Rosenfeld|2007|p=44}} or ''beat level'', sometimes simply called the [[beat (music)|beat]]. This consists of a (repeating) series of identical yet distinct [[Frequency|periodic]] short-duration [[stimulus (physiology)|stimuli]] perceived as points in time.{{sfn|Winold|1975|p=213}} 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 [[Entrainment (biomusicology)|entrain]] as they tap their foot or dance to a piece of music.{{sfn|Handel|1989}} 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''.{{sfn|Winold|1975|p=213}} [[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.{{sfn|Yeston|1976|p=50–52}} "Once a metric hierarchy has been established, we, as listeners, will maintain that organization as long as minimal evidence is present".{{sfn|Lester|1986|p=77}}

===Unit and gesture===

A [[Duration (music)|durational pattern]] that synchronises with a [[pulse (music)|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 note]]s or pulses;
*Intrametric – confirming patterns, such as [[dotted note|dotted]] [[eighth note|eighth]]-[[sixteenth note]] and [[swung note|swing]] patterns;
*Contrametric – non-confirming, or [[syncopated]] patterns; and
*Extrametric – irregular patterns, such as [[tuplet]]s.

{{Image frame|border=no|caption=From left to right: ''metric'', ''intrametric'', ''contrametric'', and ''extrametric'' rhythmic units|align=center|content=<score lang="lilypond" sound="1">
<<
    \new RhythmicStaff {
    \set Score.tempoHideNote = ##t \tempo 8 = 108
    \set Staff.midiInstrument = #"woodblock"
        \xNotesOn
        \time 2/4
        \bar "||" [c16 16 16 16] [16 16 16 16] \bar "||" [16 16 16 16] [16 16 16 16] |
        \bar "||" [16 16 16 16] [16 16 16 16] \bar "||" [16 16 16 16] [16 16 16 16]
    }
    \new RhythmicStaff {
    \set Staff.midiInstrument = #"agogo"
        [c8 8 8 8] | 8. 16 8. 16 |
        16 8 16~16 8 16 | \tuplet 3/4{16 16 16} \tuplet 3/4{16 16 16}
    }
>></score>}}

A rhythmic gesture is any [[Duration (music)|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''.{{sfn|Winold|1975|p=239}}

===Alternation and repetition===
Rhythm is marked by the regulated succession of opposite elements: the [[dynamics (music)|dynamics]] of the [[Accent (music)|strong and weak]] beat, the played beat and the inaudible but implied [[rest (music)|rest beat]], or the long and short note. As well as perceiving rhythm humans must be able to anticipate it. This depends on [[repetition (music)|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 [[Foot (prosody)|poetic term "foot"]] refers, as in dance, to the [[Arsis and thesis|lifting and tapping]] of the foot in time. In a similar way musicians speak of an [[Beat (music)#Upbeat|upbeat]] and a [[Beat (music)#Downbeat|downbeat]] and of the [[Beat (music)#On-beat and off-beat|"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 [[foot (poetry)|poetic foot]]. Normally such pulse-groups are defined by taking the most accented beat as the first and [[counting (music)|counting]] the pulses until the next accent.{{sfn|MacPherson|1930|p=5}}{{harvnb|Scholes|1977b}} 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 [[Syncopation|syncopated]] rhythm.

Normally, even the most complex of meters may be broken down into a chain of duple and triple pulses{{sfn|MacPherson|1930|p=5}}{{sfn|Scholes|1977b}} either by [[Additive and divisive rhythm|addition or division]]. According to [[Pierre Boulez]], beat structures beyond four, in western music, are "simply not natural".{{sfn|Slatkin|n.d.|loc=at 5:05}}

===Tempo and duration===
{{Further|Tempo|Duration (music)}}

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' ([[Tempo|bpm]]): 60&nbsp;bpm means a speed of one beat per second, a frequency of 1&nbsp;Hz. A [[#Unit and gesture|rhythmic unit]] is a durational pattern that has a period equivalent to a pulse or several pulses.{{sfn|Winold|1975|p=237}} 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.{{sfn|Moravcsik|2002|p=114}}
*Supershort: a single cycle of an audible wave, approximately {{frac|1|30}}–{{frac|1|10,000}} second (30–10,000&nbsp;Hz or more than 1,800&nbsp;bpm). These, though rhythmic in nature, are not perceived as separate events but as continuous [[pitch (music)|musical pitch]].
*Short: of the order of one second (1&nbsp;Hz, 60&nbsp;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&nbsp;Hz, 480–600&nbsp;bpm) or slower than 1 per 1.5–2 seconds (0.6–0.5&nbsp;Hz, 40–30&nbsp;bpm). Too fast a beat becomes a [[drone (music)|drone]], too slow a succession of sounds seems unconnected.<ref>{{harvnb|Fraisse|1956}}{{Page needed|date=July 2014}}; {{harvnb|Woodrow|1951}}{{Page needed|date=July 2014}}, both quoted in {{harvnb|Covaciu-Pogorilowski|n.d.}}</ref> This time frame roughly corresponds to the human [[heart rate]] and to the duration of a single step, syllable or [[#Unit and gesture|rhythmic gesture]].
*Medium: ≥ few seconds, this median durational level "defines rhythm in music"{{sfn|Moravcsik|2002|p=114}} as it allows the definition of a rhythmic unit, the arrangement of an entire sequence of accented, unaccented and silent or "[[rest (music)|rest]]" pulses into the [[cell (music)|cells]] of a ''measure'' that may give rise to the "briefest intelligible and self-existent musical unit",{{sfn|Scholes|1977c}} a ''[[motif (music)|motif]]'' or ''[[figure (music)|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.{{sfn|MacPherson|1930|p={{Page needed|date=July 2014}}}}
*Long: ≥ many seconds or a minute, corresponding to a durational unit that "consists of musical phrases"{{sfn|Moravcsik|2002|p=114}}—which may make up a melody, a formal section, a poetic [[stanza]] or a characteristic [[Sequence dance|sequence]] of [[Dance move|dance moves and steps]]. Thus the temporal regularity of musical organisation includes the most elementary levels of [[form (music)|musical form]].{{sfn|MacPherson|1930|p=3}}
*Very long: ≥ minutes or many hours, musical compositions or subdivisions of compositions.

[[Curtis Roads]]{{sfn|Roads|2001}} takes a wider view by distinguishing nine-time scales, this time in order of decreasing duration. The first two, the [[Infinity|infinite]] and the supra musical, encompass natural periodicities of months, years, decades, centuries, and greater, while the last three, the [[sample (music)|sample]] and subsample, which take account of digital and electronic rates "too brief to be properly recorded or perceived", measured in millionths of seconds ([[microsecond]]s), and finally the [[infinitesimal]] or infinitely brief, are again in the extra-musical domain. Roads' Macro level, encompassing "overall musical architecture or [[musical form|form]]" roughly corresponds to Moravcsik's "very long" division while his Meso level, the level of "divisions of form" including [[movement (music)|movements]], [[section (music)|sections]], [[phrase (music)|phrases]] taking seconds or minutes, is likewise similar to Moravcsik's "long" category. Roads' [[Sound object]]:{{Citation needed|date=December 2023}} "a basic unit of musical structure" and a generalization of [[note (music)|note]] ([[Iannis Xenakis|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===
{{Undue weight section|date=January 2021}}
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 [[Modest Mussorgsky|Moussorgsky]]'s ''[[Pictures at an Exhibition]]'':({{sfn|Tanguiane|1993}}{{sfn|Tanguiane|1994|pages=465–502}}
{{box|type=transparent|spacing=1em|border size=0em|{{music|quarter}} {{music|quarter}} {{music|quarter}}}}{{box|type=transparent|spacing=0.2em|border size=0em|{{music|quaver}} {{music|quaver}} {{music|quaver}}}}

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):
{{box|type=transparent|spacing=1em|border size=0em|{{music|quarter}} {{music|quarter}} {{music|quarter}}}}{{box|type=transparent|spacing=0em|border size=0em|'''R012'''}}
However, the motive with this rhythm in the Moussorgsky's piece
{{box|type=transparent|spacing=1em|border size=0em| <sup>{{music|quarter}} <sup>{{music|quarter}}</sup></sup> <sub>{{music|quarter}}</sub>}}{{box|type=transparent|spacing=0.2em|border size=0em|<sup>{{music|quaver}} <sup>{{music|quaver}}</sup></sup> <sub>{{music|quaver}}</sub> }}
is rather perceived as a repeat
{{box|type=transparent|spacing=1em|border size=0em| <sup>{{music|quarter}} <sup>{{music|quarter}}</sup></sup> <sub>{{music|quarter}}</sub>}}{{box|type=transparent|spacing=0em|border size=0em|'''R012'''}}

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 [[Andrey Kolmogorov|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.

{| class="wikitable" width="auto" style="text-align:left;"
|+ Complexity of representation of time events
|-
|!style="text-align:left;" |
!colspan="2"| Rhythm only
||
!colspan="2"| Rhythm with pitch
|-
|
!Complete coding
!Coding as repeat
||
!Complete coding
!Coding as repeat
|-
|
!{{box|type=transparent|spacing=1em|border size=0em|{{music|quarter}} {{music|quarter}} {{music|quarter}}}}{{box|type=transparent|spacing=0.2em|border size=0em|{{music|quaver}} {{music|quaver}} {{music|quaver}}}}
!{{box|type=transparent|spacing=1em|border size=0em|{{music|quarter}} {{music|quarter}} {{music|quarter}}}} R012
||
!{{box|type=transparent|spacing=1em|border size=0em|<sup>{{music|quarter}} <sup>{{music|quarter}}</sup></sup> <sub>{{music|quarter}}</sub>}} {{box|type=transparent|spacing=0.2em|border size=0em|<sup>{{music|quaver}} <sup>{{music|quaver}}</sup></sup> <sub>{{music|quaver}}</sub> }}
!{{box|type=transparent|spacing=1em|border size=0em|<sup>{{music|quarter}} <sup>{{music|quarter}}</sup></sup> <sub>{{music|quarter}}</sub>}} R012
|-
! style="text-align:left;" |Complexity of rhythmic pattern
||6 bytes||3 bytes|| ||12 bytes ||6 bytes
|-
! style="text-align:left;" |Complexity of its transformation
||0 bytes||4 bytes|| ||0 bytes || 4 bytes
|-
! style="text-align:left;" |Total complexity
|| 6 bytes||7 bytes|| || 12 bytes ||10 bytes
|}
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 rhythmic changes:

{{blockquote|By taking into account melodic context, homogeneity of accompaniment, harmonic pulsation, and other cues, the range of admissible tempo deviations can be extended further, yet still not preventing musically normal perception. For example, [[Alexander Scriabin|Skrjabin]]'s own performance of his ''Poem'' op. 32 no. 1 transcribed from a piano-roll recording contains tempo deviations within {{music|dottedquarter}} {{=}} 19/119, a span of 5.5 times.{{sfn|Skrjabin|1960}} Such tempo deviations are strictly prohibited, for example, in Bulgarian or Turkish music based on so-called additive rhythms with complex duration ratios, which can also be explained by the principle of correlativity of perception. If a rhythm is not structurally redundant, then even minor tempo deviations are not perceived as ''accelerando'' or ''ritardando'' but rather given an impression of a change in rhythm, which implies an inadequate perception of musical meaning.{{sfn|Tanguiane|1994|p=480}}}}

===Metric structure===
{{Further|Metre (music)|Bar (music)|Metre (poetry)}}

[[File:Claves-detail.gif|thumb|left|upright=1.35|Notation of a [[Clave (rhythm)|clave rhythm pattern]]: Each cell of the grid corresponds to a fixed duration of time with a resolution fine enough to capture the timing of the pattern, which may be counted as two bars of four beats in divisive (metrical or symmetrical) rhythm, each beat divided into two cells. The first bar of the pattern may also usefully be counted additively (in measured or [[asymmetrical rhythm]]) as {{serif|'''3 + 3 + 2'''}}.]]

The study of rhythm, stress, and [[pitch (music)|pitch]] in [[speech]] is called [[prosody (linguistics)|prosody]] (see also: [[prosody (music)]]): it is a topic in [[linguistics]] and [[poetics]], where it means the number of lines in a [[verse (poetry)|verse]], the number of syllables in each line and the arrangement of those syllables as long or short, accented or unaccented. Music inherited the term "[[Meter (music)|meter or metre]]" from the terminology of poetry.{{sfn|Scholes|1977b}}{{sfn|Scholes|1977c}}{{sfn|Latham|2002}})

The metric structure of music includes meter, tempo and all other rhythmic aspects that produce temporal regularity against which the foreground details or [[Duration (music)|durational patterns]] of the music are projected.{{sfn|Winold|1975|pp=209–210}} The terminology of western music is notoriously imprecise in this area.{{sfn|Scholes|1977b}} MacPherson preferred to speak of "time" and "rhythmic shape",{{sfn|MacPherson|1930|p=3}} [[Imogen Holst]] of "measured rhythm".{{sfn|Holst|1963|p=17}}

[[File:Phenakistoscope 3g07690d.gif|thumb|An [[Phenakistoscope|early moving picture]] demonstrates the [[waltz]], a dance in triple metre.]]

Dance music has instantly recognizable patterns of beats built upon a characteristic tempo and measure. The Imperial Society of Teachers of Dancing defines the [[Tango music|tango]], for example, as to be danced in {{music|time|2|4}} time at approximately 66 beats per minute. The basic slow step forwards or backwards, lasting for one beat, is called a "slow", so that a full "right–left" step is equal to one {{music|time|2|4}} measure.{{sfn|Imperial Society of Teachers of Dancing|1977|p={{Page needed|date=July 2014}}}} (''See [[Dance#Rhythm|Rhythm and dance]]''.)

[[File:clavepattern.svg|thumb|right|upright=1.35|Notation of three measures of a clave pattern preceded by one measure of steady quarter notes. This pattern is noted in [[double time]] relative to the one above, in one instead of two four-beat measures.[[File:Clave pattern.ogg|thumb|none|Four beats followed by three clave patterns]]]]

The general classifications of ''metrical rhythm'', ''measured rhythm'', and ''free rhythm'' may be distinguished.{{sfn|Cooper|1973|p=30}} Metrical or divisive rhythm, by far the most common in Western music calculates each time value as a multiple or fraction of the beat. Normal accents re-occur regularly providing systematical grouping (measures). Measured rhythm ([[additive rhythm]]) also calculates each time value as a multiple or fraction of a specified time unit but the accents do not recur regularly within the cycle. Free rhythm is where there is neither,{{sfn|Cooper|1973|p=30}} such as in Christian [[chant]], which has a basic pulse but a freer rhythm, like the rhythm of prose compared to that of verse.{{sfn|Scholes|1977c}} ''See [[Free time (music)]]''.

Finally some music, such as some graphically scored works since the 1950s and non-European music such as [[Honkyoku]] repertoire for [[shakuhachi]], may be considered ''ametric''.{{sfn|Karpinski|2000|p=19}} ''Senza misura'' is an Italian musical term for "without meter", meaning to play without a beat, using time to measure how long it will take to play the bar.{{sfn|Forney and Machlis|2007|p={{Page needed|date=December 2009}}}}