Editing Time signature (section)

==Additive meters==
To indicate more complex patterns of stresses, such as [[additive rhythm]]s, more complex time signatures can be used. Additive meters have a pattern of [[Beat (music)|beats]] that subdivide into smaller, irregular groups. Such meters are sometimes called ''imperfect'', in contrast to ''perfect meters'', in which the [[Bar (music)|bar]] is first divided into equal units.<ref>{{cite book|first=Gardner|last=Read|title=Music Notation: A Manual of Modern Practice|location=Boston|publisher=Allyn and Bacon, Inc.|year=1969|isbn=0800854535}}{{Page needed|date=December 2010}}</ref>

For example, the time signature {{music|time|3+2+3|8}} means that there are 8 quaver beats in the bar, divided as the first of a group of three eighth notes (quavers) that are stressed, then the first of a group of two, then first of a group of three again. The stress pattern is usually counted as

:: {{music|time|3+2+3|8}}: '''one''' two three ''one'' two ''one'' two three ...

This kind of time signature is commonly used to notate folk and non-Western types of music. In classical music, [[Béla Bartók]] and [[Olivier Messiaen]] have used such time signatures in their works. The first movement of [[Maurice Ravel]]'s [[Piano Trio (Ravel)|Piano Trio in A Minor]] is written in {{music|time|8|8}}, in which the beats are likewise subdivided into {{serif|'''3+2+3'''}} to reflect [[Basque music|Basque]] dance rhythms.

Romanian [[musicologist]] [[Constantin Brăiloiu]] had a special interest in compound time signatures, developed while studying the [[Traditional music of Romania|traditional music]] of certain regions in his country. While investigating the origins of such unusual meters, he learned that they were even more characteristic of the traditional music of neighboring peoples (e.g., the [[Bulgarian Folk Music|Bulgarians]]). He suggested that such timings can be regarded as compounds of simple two-beat and three-beat meters, where an accent falls on every first beat, even though, for example in [[Bulgarian dances|Bulgarian music]], beat lengths of 1, 2, 3, 4 are used in the metric description. In addition, when focused only on stressed beats, simple time signatures can count as beats in a slower, compound time. However, there are two different-length beats in this resulting compound time, a one half-again longer than the short beat (or conversely, the short beat is {{frac|2|3}} the value of the long). This type of meter is called ''[[aksak]]'' (the Turkish word for "limping"), ''impeded'', ''jolting'', or ''shaking'', and is described as an ''irregular bichronic rhythm''. A certain amount of confusion for Western musicians is inevitable, since a measure they would likely regard as {{music|time|7|16}}, for example, is a three-beat measure in ''aksak'', with one long and two short beats (with subdivisions of {{serif|'''2+2+3'''}}, {{serif|'''2+3+2'''}}, or {{serif|'''3+2+2'''}}).<ref>Constantin Brăiloiu, ''Le rythme Aksak'', ''Revue de Musicologie'' 33, nos. 99 and 100 (December 1951): 71–108. Citation on pp. 75–76.</ref>

Folk music may make use of metric time bends, so that the proportions of the performed metric beat time lengths differ from the exact proportions indicated by the metric. Depending on playing style of the same meter, the time bend can vary from non-existent to considerable; in the latter case, some musicologists may want to assign a different meter. For example, the Bulgarian tune "[[Bulgarian dances|Eleno Mome]]" is written in one of three forms: (1) {{serif|'''7 {{=}} 2+2+1+2'''}}, (2) {{serif|'''13 {{=}} 4+4+2+3'''}}, or (3) {{serif|'''12 {{=}} 3+4+2+3'''}}, but an actual performance (e.g., "Eleno Mome"<ref>[https://folkways.si.edu/eleno-mome/world/music/track/smithsonian Audio: "Eleno Mome"] from ''The Dances of the World's Peoples, Vol. 1: Dances of the Balkans and Near East'', Smithsonian Folk Ways</ref>{{original research inline|date=June 2020}}) may be closer to {{serif|'''4+4+2+3'''}}.{{clarify|date=June 2020|reason=What does this even mean, just after 13 = 4+4+2+3 has been mentioned as one of the forms in which the music is written?}} The Macedonian {{serif|'''[[Leventikos|3+2+2+3+2]]'''}} meter is even more complicated, with heavier time bends, and use of quadruples on the threes. The metric beat time proportions may vary with the speed that the tune is played. The Swedish [[Polska (dance)|Boda Polska]] (Polska from the parish Boda) has a typical elongated second beat.

In Western classical music, metric time bend is used in the performance of the [[Viennese waltz]]. Most Western music uses metric ratios of 2:1, 3:1, or 4:1 (two-, three- or four-beat time signatures)—in other words, integer ratios that make all beats equal in time length. So, relative to that, 3:2 and 4:3 ratios correspond to very distinctive metric rhythm profiles. Complex accentuation occurs in Western music, but as [[syncopation]] rather than as part of the metric accentuation.{{Citation needed|date=January 2010}}

Brăiloiu borrowed a term from [[Music of Turkey|Turkish]] medieval music theory: ''aksak''. Such compound time signatures fall under the "aksak rhythm" category that he introduced along with a couple more that should describe the rhythm figures in traditional music.<ref name="Oprea">Gheorghe Oprea, ''Folclorul muzical românesc'' (Bucharest: Ed. Muzicala, 2002), {{Page needed|date=January 2010}} {{ISBN|973-42-0304-5}}</ref> The term Brăiloiu revived had moderate success worldwide, but in Eastern Europe it is still frequently used. However, aksak rhythm figures occur not only in a few European countries, but on all continents, featuring various combinations of the two and three sequences. The longest are in Bulgaria. The shortest aksak rhythm figures follow the five-beat timing, comprising a two and a three (or three and two).

'''Some video samples are shown below.'''

{| class="wikitable"
| [[File:Video-for-time-signature-3+2+3.theora.ogv|thumb|320 px|none| {{music|time|3+2+3|8}} at 120 [[BPM (music)|bpm]]]]
| [[File:Blue-Rondo-à-La-Turk.theora.ogv|thumb|320 px|none| The rhythm of [[Dave Brubeck]]'s "[[Blue Rondo à la Turk]]": It consists of three measures of {{serif|'''2+2+2+3'''}} followed by one measure of {{serif|'''3+3+3'''}} and the cycle then repeats. Taking the smallest time unit as eighth notes, the arrows on the tempo dial show the tempi for ♪, ♩, ♩. and the measure beat. Starts slow, speeds up to usual tempo]]
|}
A method to create meters of lengths of any length has been published in the Journal of Anaphoria Music Theory<ref>{{Cite web|url=http://anaphoria.com/journal.html|title = The Journal of Anaphorian Music Theory}}</ref> and Xenharmonikon 16<ref>{{Cite web|url=http://frogpeak.org/fpartists/fpchalmers.html|title=Frog Peak Artist: John Chalmers}}</ref> using both those based on the Horograms of [[Erv Wilson]] and Viggo Brun's algorithm written by  [[Kraig Grady]].