a rítmica study

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Tuplets

This article is about the note groupings. For mathematical grouping, seetuple.

Irrational rhythm triplet above second beat features three rather than the usual two equal divisions of the beat, while the four sixteenth notes (semiquavers) above the third beat are

rational, four being a multiple of two

Inmusica tuplet(also irrational rhythmor groupings, artificial divisionor groupings, abnormal divisions,irregular rhythm, gruppetto, extra-

metric groupings, or, rarely, contrametric rhythm) is "anyrhythmthat involves dividing thebeatinto a different number of equal subdivisionsfrom that

usually permitted by thetime-signature(e.g., triplets, duplets, etc.)" (Humphries 2002, 266). This is indicated by a number (or sometimes two), i ndicating

the fraction involved. The notes involved are also often grouped with a bracket or (in older notation) a slur. The most common type is the "triplet".

Terminology

Sextuplet)), or six notes. As the extra brackets show: six notes in the time of four = three notes in the time of two X 2

The modern term 'tuplet' comes from a mistaken splitting of the suffixes of words like quintu(s)-(u)plet and sextu(s)-(u)plet, and from related mathematicalterms such as "tuple", "-uplet" and "-plet", which are used to form terms denotingmultiplets(Oxford English Dictionary, entries "multiplet", "-plet, comb.

form", "-let, suffix", and "et, suffix1"). An alternative modern term, "irrational rhythm", was originally borrowed from Greekprosodywhere it referred to "a

syllable having a metrical value not corresponding to its actual time-value, or ... a metrical foot containing such a syllable" (Oxford English Dictionary,

entry "irrational"). The term would be incorrect if used in the mathematical sense (because the note-values are rational fractions) or i n the more general

sense of "unreasonable, utterly illogical, absurd".

"True sextuplet": in order to contrast with the above "false sextuplet", the 1st, 3rd, and 5th notes of a sextuplet must be stressed rather than the 1st and 4th (Baker, Slonimsky, and

Kuhn 1995,208).

Alternative terms found occasionally are "artificial division"(Jones 1974, 19), "abnormal divisions" (Donato 1963, 34), "irregular rhythm" (Read 1964,

181), and "irregular rhythmic groupings" (Kennedy 1994). The term "polyrhythm"(or "polymeter"), sometimes incorrectly used of "tuplets", actually refers

to the simultaneous use of opposing time signatures (Read 1964, 167).

Besides "triplet", the terms "duplet", "quadruplet", "quintuplet", "sextuplet", "septuplet", and "octuplet" are used frequently. The terms "nonuplet",

"decuplet", "undecuplet", "dodecuplet", and "tredecuplet" had been suggested but up until 1925 had not caught on (Dunstan 1925,[page needed]). By 1964 the

terms "nonuplet" and "decuplet" were usual, while subdivisions by greater numbers were more commonly described as "group of eleven notes", "group of

twelve notes", and so on (Read 1964,189).
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Triplets

The most common tuplet (Schonbrun 2007,8) is the triplet(Ger.Triole, Fr.triolet,It.terzinaor tripletta,Sp.tresillo), shown at right.

Tuplet: a standard triplet; a triplet denoted without a bracket; a tuplet denoted as a ratio

Whereas normally twoquarter notes(crotchets) are the samedurationas ahalf note(minim), three triplet quarter notes total that same duration, so the

duration of a triplet quarter note is 2/3 thedurationof a standard quarter note. Similarly, three triplet eighth notes(quavers) are equal in duration to one

quarter note. If several note values appear under the triplet bracket, they are all affected the same way, reduced to 2/3 their original duration. The triplet

indication may also apply to notes of different values, for example a quarter note followed by one eighth note, in which case the quarter note may be

regarded as two triplet eighths tied together(Gherkens 1921,19).

Tuplet notation

If the notes of the tuplet arebeamedtogether, the bracket (or slur) may be omitted and the number written next to the beam, as shown in the second

illustration.

Septuplet rhythm: seven against four (more frequent) and seven against eight (sometimes found) ( Play(helpinfo)).

For other tuplets, the number indicates aratioto the next lower normal value in the prevailing meter. So

a quintuplet(quintoletor pentuplet(Cunningham 2007, 111)) indicated with the numeral 5 means that five of the indicated note value total

thedurationnormally occupied by four (or, as a division of a dotted note in compound time, three), equivalent to the secondhigher note value; for

example, five quintuplet eighth notes total the same duration as a half note (or, in 3/8 or compound meters such as 6/8, 9/8, etc. time, a dotted quarter

note). Some numbers are used inconsistently: for example septuplets(septoletsor septimoles) usually indicate 7 notes in thedurationof 4or in

compound meter 7 for 6but may sometimes be used to mean 7 notes in the duration of 8 (Read 1964, 18384). Thus, a septuplet lasting a whole note

can be written with either quarter notes (7:4) or eighth notes (7:8). To avoid ambiguity, composers sometimes write the ratio explicitly instead of just a

single number, as shown in the third illustration; this is also done for cases like 7:11, where the validity of this practice is established by the complexity of

the figure. A French alternative is to write pour("for") or de("of") in place of the colon, or above the bracketed "irregular" number (Read 1964,21921).

This reflects the French usage of, for example, "six-pour-quatre" as an alternative name for the sextolet(Damour, Burnett, and Elwart 1838,79; Hubbard

1924,480).

There are disagreements about the sextuplet(pronounced with stress on the first syllable, according toBaker 1895,177)which is also

called sestole, sestolet, sextole, orsextolet(Baker 1895,177;Cooper 1973, 32; Latham 2002;Shedlock 1876,62, 68, 87, 93;Stainer and Barrett 1876,

395;Taylor 187989;Taylor 2001). This six-part division may be regarded either as a tri plet with each note divided in half (2 + 2 + 2)therefore with an

accent on the first, third, and fifth notesor else as an ordinary duple pattern with each note subdivided into triplets (3 + 3) and accented on both the first

and fourth notes. Some authorities treat both groupings as equally valid forms (Damour, Burnett, and Elwart 1838,80; Khler 1858,2:5253; Latham

2002; Marx 1853, 114; Read 1964,215), while others dispute this, holding the first type to be the "true" (or "real") sextuplet, and the second type to be

properly a "double triplet", which should always be written and named as such (Kastner 1838,94; Riemann 1884,13435;Taylor 187989,3:478). Some

go so far as to call the latter, when written with a numeral 6, a "false" sextuplet (Baker 1895, 177; Lobe 1881,36; Shedlock 1876,62). Still others, on the

contrary, define the sextuplet precisely and solely as the double triplet (Stainer and Barrett 1876,395;Sembos 2006,86), and a few more, while

accepting the distinction, contend that the true sextuplet has no internal subdivisionsonly the first note of the group should be accented (Riemann 1884,

134;Taylor 187989,3:478; Taylor 2001).

Duplet and quadruplet notated in 6/8 Play(helpinfo). Two duplets or four quadruplets equal three regular eighth notes or a dotted quarter note.

Incompound meter, even-numbered tuplets can indicate that a note value is changed in relation to thedottedversion of the next highernote value.Thus,

two dupleteighth notes(most often used in 6/8meter)take the time normally totaled by three eighth notes, equal to a dotted quarter note.

Four quadruplet(or quartole) eighth notes would also equal a dotted quarter note. The duplet eighth note is thus exactly the same duration as a dotted
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eighth note, but the duplet notation is far more common in compound meters (Jones 1974,20). A duplet in compound time is more often written as 2:3 (a

dotted quarter note split into two duplet eighth notes) than 2:1.5 (a dotted quarter note split into two duplet quarter notes), even though the former is

inconsistent with a quadruplet also being written as 4:3 (a dotted quarter note split into two quadruplet eighth notes) (Anon. 19972000).

"Quadruplet" with each note on a different drum in a kitused as a fill(Peckman 2007,129). play(helpinfo)

Indrumming, "quadruplet" refers to one group of three sixteenth-note triplets "with an extra [ non-tuplet eighth] note added on to the end", thus filling one

beat in 4/4 time (Peckman 2007, 12728), with four notes of unequal value.

Usage and purpose

Tuplets can produce rhythms such as thehemiola,or may be used aspolyrhythmswhen played against the regular duration. They

areextrametricrhythmic units.

Sextuplet in quintuple time: six against five ( Play(helpinfo)).

Traditional music notationfavors duple divisions of a steadybeator time unit. A wholenote(semibreve) divides into two half notes, a half note into two

quarters, etc. and other notes are made by tying these together.

An irrational rhythm (by definition) is one that uses exact time points or durations that lie outside the scope of the duple system.

The n-tuplet notation shows the proportional increase or decrease of tempo needed for the bracketed notes, relative to the prevailing tempo. For example,

a bracket labeled "5:4" (read five in the space of four) could group together durations (notes or rests) with a total of five sixteenth notes. A tempo 5/4

faster than usual then compresses these events into the space of four sixteenth notes.

The actual duration can be found by dividing the notated duration by the indicated tempo increase ((5/16)/(5/4) = 1/4, in thi s example).

Normally, the total duration of the bracketed notes is chosen to be exactly equal to the duration of one of the duple divisions. For the example of a 5:4

bracket, this is possible if the total bracketed duration has a 5 in it s numerator, 5/16 in the example.

Sometimes though that requirement is dropped to create total durations not exactly expressible in the duple system. For example, one might have only

three of the usual five sixteenth notes grouped by a bracket marked "3 of 5:4".

Counting

Tuplets may becounted,most often at extremely slow tempos, using thelowest common multiple(LCM) between the original and tuplet divisions. For

example, with a 3-against-2 tuplet (triplets) the LCM is 6. Since 6/2 = 3 and 6/3 = 2 the quarter notes fall every three counts (overlined) and the triplets

every two (underlined):

1 2 3 4 5 6

This is fairly easily brought up to tempo, and depending on the music may be counted in tempo, while 7-against-4, having an LCM of 28, may be counted

at extremely slow tempos but must be played intuitively ("felt out") at tempo:
http://en.wikipedia.org/wiki/Tuplet#CITEREFJones1974http://en.wikipedia.org/wiki/Tuplet#CITEREFJones1974http://en.wikipedia.org/wiki/Tuplet#CITEREFJones1974http://en.wikipedia.org/wiki/Tuplet#CITEREFAnon.1997.E2.80.932000http://en.wikipedia.org/wiki/Tuplet#CITEREFAnon.1997.E2.80.932000http://en.wikipedia.org/wiki/Tuplet#CITEREFAnon.1997.E2.80.932000http://en.wikipedia.org/wiki/Tuplet#CITEREFAnon.1997.E2.80.932000http://en.wikipedia.org/wiki/Tuplet#CITEREFAnon.1997.E2.80.932000http://en.wikipedia.org/wiki/Drum_kithttp://en.wikipedia.org/wiki/Drum_kithttp://en.wikipedia.org/wiki/Drum_kithttp://en.wikipedia.org/wiki/Fill_(music)http://en.wikipedia.org/wiki/Fill_(music)http://en.wikipedia.org/wiki/Tuplet#CITEREFPeckman2007http://en.wikipedia.org/wiki/Tuplet#CITEREFPeckman2007http://en.wikipedia.org/wiki/Tuplet#CITEREFPeckman2007http://upload.wikimedia.org/wikipedia/commons/f/fb/Quadruplet.midhttp://upload.wikimedia.org/wikipedia/commons/f/fb/Quadruplet.midhttp://en.wikipedia.org/wiki/Wikipedia:Media_helphttp://en.wikipedia.org/wiki/Wikipedia:Media_helphttp://en.wikipedia.org/wiki/File:Quadruplet.midhttp://en.wikipedia.org/wiki/File:Quadruplet.midhttp://en.wikipedia.org/wiki/File:Quadruplet.midhttp://en.wikipedia.org/wiki/Drumshttp://en.wikipedia.org/wiki/Drumshttp://en.wikipedia.org/wiki/Drumshttp://en.wikipedia.org/wiki/Tuplet#CITEREFPeckman2007http://en.wikipedia.org/wiki/Tuplet#CITEREFPeckman2007http://en.wikipedia.org/wiki/Tuplet#CITEREFPeckman2007http://en.wikipedia.org/wiki/Hemiolahttp://en.wikipedia.org/wiki/Hemiolahttp://en.wikipedia.org/wiki/Hemiolahttp://en.wikipedia.org/wiki/Polyrhythmhttp://en.wikipedia.org/wiki/Polyrhythmhttp://en.wikipedia.org/wiki/Polyrhythmhttp://en.wikipedia.org/wiki/Extrametrichttp://en.wikipedia.org/wiki/Extrametrichttp://en.wikipedia.org/wiki/Rhythmic_unithttp://en.wikipedia.org/wiki/Rhythmic_unithttp://en.wikipedia.org/wiki/Rhythmic_unithttp://upload.wikimedia.org/wikipedia/commons/c/cc/Sextuplet_against_five_rhythm.midhttp://upload.wikimedia.org/wikipedia/commons/c/cc/Sextuplet_against_five_rhythm.midhttp://upload.wikimedia.org/wikipedia/commons/c/cc/Sextuplet_against_five_rhythm.midhttp://en.wikipedia.org/wiki/Wikipedia:Media_helphttp://en.wikipedia.org/wiki/Wikipedia:Media_helphttp://en.wikipedia.org/wiki/File:Sextuplet_against_five_rhythm.midhttp://en.wikipedia.org/wiki/File:Sextuplet_against_five_rhythm.midhttp://en.wikipedia.org/wiki/File:Sextuplet_against_five_rhythm.midhttp://en.wikipedia.org/wiki/Music_notationhttp://en.wikipedia.org/wiki/Music_notationhttp://en.wikipedia.org/wiki/Music_notationhttp://en.wikipedia.org/wiki/Beat_(music)http://en.wikipedia.org/wiki/Beat_(music)http://en.wikipedia.org/wiki/Beat_(music)http://en.wikipedia.org/wiki/Notehttp://en.wikipedia.org/wiki/Notehttp://en.wikipedia.org/wiki/Notehttp://en.wikipedia.org/wiki/Counting_(music)http://en.wikipedia.org/wiki/Counting_(music)http://en.wikipedia.org/wiki/Counting_(music)http://en.wikipedia.org/wiki/Lowest_common_multiplehttp://en.wikipedia.org/wiki/Lowest_common_multiplehttp://en.wikipedia.org/wiki/Lowest_common_multiplehttp://en.wikipedia.org/wiki/File:Sextuplet_against_five_rhythm.midhttp://en.wikipedia.org/wiki/File:Sextuplet_against_five_rhythm.pnghttp://en.wikipedia.org/wiki/File:Quadruplet.midhttp://en.wikipedia.org/wiki/File:Quadruplet.pnghttp://en.wikipedia.org/wiki/File:Sextuplet_against_five_rhythm.midhttp://en.wikipedia.org/wiki/File:Sextuplet_against_five_rhythm.pnghttp://en.wikipedia.org/wiki/File:Quadruplet.midhttp://en.wikipedia.org/wiki/File:Quadruplet.pnghttp://en.wikipedia.org/wiki/File:Sextuplet_against_five_rhythm.midhttp://en.wikipedia.org/wiki/File:Sextuplet_against_five_rhythm.pnghttp://en.wikipedia.org/wiki/File:Quadruplet.midhttp://en.wikipedia.org/wiki/File:Quadruplet.pnghttp://en.wikipedia.org/wiki/File:Sextuplet_against_five_rhythm.midhttp://en.wikipedia.org/wiki/File:Sextuplet_against_five_rhythm.pnghttp://en.wikipedia.org/wiki/File:Quadruplet.midhttp://en.wikipedia.org/wiki/File:Quadruplet.pnghttp://en.wikipedia.org/wiki/Lowest_common_multiplehttp://en.wikipedia.org/wiki/Counting_(music)http://en.wikipedia.org/wiki/Notehttp://en.wikipedia.org/wiki/Beat_(music)http://en.wikipedia.org/wiki/Music_notationhttp://en.wikipedia.org/wiki/File:Sextuplet_against_five_rhythm.midhttp://en.wikipedia.org/wiki/Wikipedia:Media_helphttp://upload.wikimedia.org/wikipedia/commons/c/cc/Sextuplet_against_five_rhythm.midhttp://en.wikipedia.org/wiki/Rhythmic_unithttp://en.wikipedia.org/wiki/Extrametrichttp://en.wikipedia.org/wiki/Polyrhythmhttp://en.wikipedia.org/wiki/Hemiolahttp://en.wikipedia.org/wiki/Tuplet#CITEREFPeckman2007http://en.wikipedia.org/wiki/Drumshttp://en.wikipedia.org/wiki/File:Quadruplet.midhttp://en.wikipedia.org/wiki/Wikipedia:Media_helphttp://upload.wikimedia.org/wikipedia/commons/f/fb/Quadruplet.midhttp://en.wikipedia.org/wiki/Tuplet#CITEREFPeckman2007http://en.wikipedia.org/wiki/Fill_(music)http://en.wikipedia.org/wiki/Drum_kithttp://en.wikipedia.org/wiki/Tuplet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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

25 26 27 28

Four eighth-note triplets = one half-note triplet.

To play a half-note (minim)triplet accurately in abarof 4/4, count eighth-note triplets and tie them together in groups of four. With a stress on each

targetnote, one would count:

1-2-3 / 1-2-3 / 1-2-3/ 1-2-3

The same principle can be applied to quintuplets, septuplets, and so on.
http://en.wikipedia.org/wiki/Minim_(music)http://en.wikipedia.org/wiki/Minim_(music)http://en.wikipedia.org/wiki/Minim_(music)http://en.wikipedia.org/wiki/Bar_(music)http://en.wikipedia.org/wiki/Bar_(music)http://en.wikipedia.org/wiki/Bar_(music)http://en.wikipedia.org/wiki/Notehttp://en.wikipedia.org/wiki/Notehttp://en.wikipedia.org/wiki/Notehttp://en.wikipedia.org/wiki/File:Tuplet_counting_subdivide.pnghttp://en.wikipedia.org/wiki/Notehttp://en.wikipedia.org/wiki/Bar_(music)http://en.wikipedia.org/wiki/Minim_(music)


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Desplazamiento RtmicoLick 1: On the Beat To begin, lets take a classic-sounding jazz lick you can learn starting on beat 1 of the bar, then well start to vary this lick in the next two examples.

In order to make sure you can quickly grasp those variations, make sure you memorize this lick and get it comfortable under your fingers and in your earsbefore moving to the next two sections of this l esson.

Lick 2: AnticipatedThe first variation well look at is taking the exact same lick, but starting it on the "and" of 4 on the bar before the progression starts.

This creates a sense of anticipation in your line, and gives you a quick and relatively easy variation for the original lick that you can use in your solos

without sounding repetitive or monotonous with the same lick.

Lick 3: Delayed

As well as starting the lick an 8th-note early when playing it over a ii V I progression, you also can start it an 8th note later to add a sense of delayedresolution to your lines.

Once you have worked this lick out on the "and" of 4, 1 and the "and" of 1, you can move it around to start on any beat in the bar in order to take it furtherin the practice room and out on the bandstand.

Now that you have practiced playing the lick starting on three different beats within the bar, you can try moving it around to other beats to see how itsounds when you start on beat 2, the "and" of 2, 3, etc.

By working a lick around the bar like this, you are learning eight different variations for the same li ck, by starting on the eight 8th-notes in the bar,providing you a ton of improvisational material from just one classic jazz line.

Do you have a question or comment about this lick transposition technique? Share your thoughts in the COMMENTS section below.


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Rhythmic displacement

Perhaps the most common method of variation in popular music is rhythmic displacement, where the motif is moved to different beats in a bar, keeping the motifs rhythmic structure

intact.

Example 31

If the motif is moved by a quaver, the accented and unaccented beats will shift, and the motifs rhythmic character will change to the extent that it will be difficult to recognize the

original motif.

Example 32

Now practice rhythmic displacement by singing rhythms with a metronome. First write down a motif and sing it; then sing the same motif shifted forward by a crotchet. Next, sing the

original motif and then the same motif shifted by two crotchets, and so on.


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Example 33

Printer-friendly version of the examples on this page

When you get more skilled, produce motifs of your own. Use your imagination. Dont forget to move the original motif to diffe rent beats in a bar. You can work with different motifs and

then go back to the first one.
http://www3.siba.fi/afroimpro/sites/siba.fi.afroimpro/files/rhythmic_displacement_en.pdfhttp://www3.siba.fi/afroimpro/sites/siba.fi.afroimpro/files/rhythmic_displacement_en.pdfhttp://www3.siba.fi/afroimpro/sites/siba.fi.afroimpro/files/rhythmic_displacement_en.pdf


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Cross-beatThis article is about music. For horology, seeEscapement#Cross-beat escapement.For cross-beat tonguing, seetonguing.For the Christian media organization, seeCross Rhythms.

Inmusic,a cross-beator cross-rhythmis a specific form ofpolyrhythm.The term crossrhythmwas introduced in 1934 by themusicologistArthur Morris Jones(18891980).

Cross-rhythm. A rhythm in which the regular pattern of accents of the prevailing meter iscontradicted by a conflicting pattern and not merely a momentary displacement that leaves theprevailing meter fundamentally unchallengedNew Harvard Dictionary of Music(1986: 216).[1]

Contents

[hide]

1 African musico 1.1 One main systemo 1.2 An embodiment of the people

2 Cross-rhythmic ratioso 2.1 3:2o 2.2 6:4o 2.3 3:4o 2.4 1.5:4 (or 3:8)o 2.5 4:3

3 Duple-pulse correlative of 3:2

4 Cross-rhythm, not polymeter

5 Adaptive instruments

6 Jazzo 6.1 3:2 (or 6:4)o 6.2 3:4o 6.3 2:3o 6.4 Duple-pulse correlative of 3:2

7 Sources

African musicOne main system

Niger-Congo linguistic group (yellow and yellow-green).
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African cross-rhythm is most prevalent within the greater Niger-Congo linguistic group, whichdominates the continent south of the Sahara Desert.[2]Cross-rhythm was first identified as thebasis of sub-Saharan rhythm by A.M. Jones. Later, the concept was more fully explained in thelectures ofEwemaster drummer and scholar C.K. Ladzekpo, and in the writings of DavidLocke.[3]Jones observes that the shared rhythmic principles of Sub-Saharan African musictraditions constitute one main system.[4]Similarly, Ladzekpo affirms theprofound

homogeneityof sub-Saharan African rhythmic principles.[5]

InSub-Saharan African musictraditions(and manyDiasporamusics) cross-rhythm is the generating principle; the meter is ina permanent state of contradiction.

An embodiment of the people

At the center of a core of rhythmic traditions and composition is the technique of cross-rhythm.The technique of cross-rhythm is a simultaneous use of contrasting rhythmic patterns withinthe same scheme of accents or meter. . . By the very nature of the desired resultant rhythm,the main beat scheme cannot be separated from the secondary beat scheme. It is the interplayof the two elements that produces the cross-rhythmic textureLadzekpo (1995).[6]

From the philosophical perspective of the African musician, cross-beats can symbolize thechallenging moments or emotional stress we all encounter. Playing cross-beats while fully

grounded in the main beats, prepares one for maintaining a life-purpose while dealing withlifes challenges. Many sub-Saharan languages do not have a word for rhythm, or even music.From the African viewpoint, the rhythms represent the very fabric of life itself; they are anembodiment of the people, symbolizing interdependence in human relationshipsPealosa(2009: 21).[7]

Cross-rhythmic ratios3:2[edit]

The cross-rhythmicratiothree-over-two(3:2) or verticalhemiola,is the most significantrhythmiccellfound in sub-Saharan rhythms. The following measure is evenly divided by threebeats and two beats. The twocyclesdo not share equal status though. The two bottom notes

are the primary beats, the ground, the main temporal referent. The three notes above are thesecondary beats. Typically, the dancer's feet mark the primary beats, while the secondarybeats are accented musically.

Polyrhythm 3:2
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Three-over-two cross-rhythm.

[Watch: Stepping to the main beats within 3:2 cross-rhythm. Afro-Cuban Obatal dance (MartaRuiz).]The example below shows the African 3:2 cross-rhythm within its proper metricstructure.

Three-over-two cross-rhythm.

We have to grasp the fact that if from childhood you are brought up to regard beating 3 against2 as being just as normal as beating in synchrony, then you develop a two dimensional attitudeto rhythm This bi-podal conception is part of the African's natureJones (1959: 102)[8]

Novotney observes: "The 3:2 relationship (and [its] permutations) is the foundation of most

typical polyrhythmic textures found in West African musics."[9]

3:2 is the generativeortheoreticformof sub-Saharan rhythmic principles.Agawusuccinctly states: "[The] resultant [3:2] rhythmholds the key to understanding . . . there is no independence here, because 2 and 3 belong toa single Gestalt."[10]

AfricanXylophonessuch as thebalafonandgyilplay cross-rhythms, which are often thebasis ofostinatomelodies. In the following example, a Ghanaiangyilsounds the three-against-two cross-rhythm. The left hand (lower notes) sounds the two main beats, while the right hand(upper notes) sounds the three cross-beats.[11]

Ghanaian gyil

Ghanaian gyil sounds 3:2 cross-rhythm.

6:4

The primary cycle of four beats
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Polyrhythm 6:4

A great deal of African music is built upon acycleof four main beats. This basicmusicalperiodhas abipartitestructure; it is made up of twocells,consisting of two beats each.Ladzekpo states: "The first most useful measure scheme consists of four main beats with eachmain beat measuring off three equal pulsations [12/8] as its distinctive feature . . . The next

most useful measure scheme consists of four main beats with each main beat flavored bymeasuring off four equal pulsations [4/4]" (1996: Web).[12]The four-beat cycle is a shorter periodthan what is normally heard in European music. This accounts for the stereotype of Africanmusic as "repetitive."[13]A cycle of only two main beats, as in the case of 3:2, does not constitutea complete primary cycle.[14]Within the primary cycle there are two cells of 3:2, or, a single cycleof six-against-four (6:4). The six cross-beats are represented below as quarter-notes for visualemphasis.

Six-against-four cross-rhythm (note that this is identical to the three-over-two cross-rhythm above, played twice).

Interacting the four recurrent triple structure main beat schemes (four beat scheme)simultaneously with the six recurrent two pulse beat schemes (six beat scheme) produces thefirst most useful cross rhythmic texture in the development ofAnlo-Ewedance-drumming

Ladzekpo (1995: web).[15]

The following notated example is from thekushaurapart of the traditional mbira piece "NhemaMussasa." The left hand plays theostinato"bass line," built upon the four main beats, while theright hand plays the upper melody, consisting of six cross-beats. The composite melody is anembellishment of the 6:4 cross-rhythm.[16]

Holding an mbira dzavadzimu.

Kushaura mbira part for "Nhema Mussasa." Play(helpinfo)
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3:4

Polyrhythm 3:4

If every other cross-beat is sounded, the three-against-four (3:4) cross-rhythm is generated.The "slow" cycle of three beats is more metrically destabilizing and dynamic than the six beats.The Afro-Cuban rhythmabaku(Havana-style) is based on the 3:4 cross-rhythm.[17]The three-beat cycle is represented as half-notes in the following example for visual emphasis.

Three-against-four cross-rhythm.

In contrast to the four main beat scheme, the rhythmic motion of the three beat scheme isslower. A simultaneous interaction of these two beat schemes with contrasting rhythmicmotions produces the next most useful cross rhythmic texture in the development of sub-Saharan dance-drumming. The composite texture of the three-against-four cross rhythmproduces a motif covering a length of themusical period.The motif begins with the component

beat schemes coinciding and continues with the beat schemes in alternate motions thusshowing a progression from a "static" beginning to a "dynamic" continuationLadzekpo (1995:web).[18]

The following pattern is an embellishment of the three-beat cycle, commonly heard in Africanmusic. It consists of three sets of three strokes each.

Embellishment of 3:4 cross-rhythm
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1.5:4 (or 3:8)

Polyrhythm 4:1.5

Even more metrically destabilizing and dynamic than 3:4, is the one and a half beat-against-four(1.5:4) cross-rhythm. Another way to think of it is as three "very slow" cross-beatsspanning two main beatcycles(of four beats each), or three beats overtwoperiods(measures), a type of macro "hemiola." In terms of the beat scheme comprising the

complete 24-pulse cross-rhythm, theratiois 3:8. The three cross-beats are shown as wholenotes below for visual emphasis.

1.5:4 or 3:8. Play(helpinfo)

The 1.5:4 cross-rhythm is the basis for the open tone pattern of the en (largebatdrum head)for theAfro-Cubanrhythm chang (Shango).[19]It is the same pattern as the previous figure, butthe strokes occur at half the rate.

Drum pattern based on 1.5:4 cross-rhythm.

Ewegankoquibell

The followingbell patternis used in theEwerhythm kadodo.[20]The pattern consists of threemodulestwo pairs of strokes, and a single stroke. The three single stroke are muted. Thepattern is another embellishment of the 1.5:4 cross-rhythm.
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kadodo bell pattern

4:3[edit]

When duple pulses (4/4) are grouped in sets of three, the four-against-three (4:3) cross-rhythmis generated. The four cross-beats cycle every three main beats. In terms of cross-rhythm only,

this is the same as having duple cross-beats in a triple beat scheme, such as 3/4 or 6/4. Thepulses on the top line are grouped in threes for visual emphasis.

4:3 cross-rhythm in modular form.

However, this 4:3 is within a duple beat scheme, with duple (quadruple) subdivisions of thebeats. Since themusical periodis acycleof four main beats, the 4:3 cross-rhythm significantlycontradicts the period by cycling every three main beats. The complete cross-beat cycle is

shown below in relation to thekey patternknown in Afro-Cuban music asclave.[21]

Thesubdivisions are grouped (beamed) in sets of four to reflect the proper metric structure. Thecomplete cross-beat cycle is three claves in length. Within the context of the complete cross-rhythm, there is a macro 4:3four 4:3 modules-against-three claves. Continuous duple-pulsecross-beats are often sounded by thequinto,the lead drum in the Cubanrhythmsrumbaandconga de comparsa.[22][23][24]

Quinto drum

Complete cycle of 4:3 cross-rhythm shown in relation to clave.

While 3:2 pervades ternary music, quaternary music seldom uses tuplets; instead, a set ofdotted notes may temporarily make 2:3 and 4:3 temporal structuresLocke (2011: 56).[25]
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Duple-pulse correlative of 3:2[edit]

In sub-Saharan rhythm the four main beats are typically divided into three or four pulses,creating a 12-pulse (12/8), or 16-pulse ( 4/4)cycle.[26]Every triple-pulse pattern has its duple-pulse correlative; the two pulse structures are two sides of the same coin. Cross-beats aregenerated by grouping pulses contrary to their given structure, for example: groups of two or

four in 12/8 or groups of three or six in 4/4.[27]

The duple-pulse correlative of the three cross-beats of thehemiola,is a figure known in Afro-Cuban music astresillo.Tresillo isaSpanishword meaning tripletthree equal notes within the same time span normallyoccupied by two notes. As used in Cuban popular music, tresillo refers to the most basic duple-pulse rhythmiccell.[28]The pulse names of tresillo and the three cross-beats of the hemiola areidentical: one, one-ah, two-and.

Top: "tresillo" over two; bottom: three-over-two (3:2).

The composite pattern of tresillo and the main beats is commonly known asthehabanera,[29]congo,[30]tango-congo,[31]or tango.[32]The habanera rhythm is the duple-pulsecorrelative of the verticalhemiola(above). The three cross-beats of the hemiola are generatedby grouping triple pulses in twos: 6 pulses 2 = 3 cross-beats. Tresillo is generated bygrouping duple pulses in threes: 8 pulses 3 = 2 cross-beats (consisting of three pulses each),with a remainder of a partial cross-beat (spanning two pulses). In other words, 8 3 = 2, r2.Tresillo is a cross-rhythmic fragment. It contains the first three cross-beats of 4:3.[33]

Tresilloover two Video
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Tresillo consists of the first three cross-beats of 4:3.

Cross-rhythm, not polymeter[edit]

Early ethnomusicological analysis often perceived African music aspolymetric.Pioneers suchasA.M. Jonesand Anthony King identified the prevailing rhythmic emphasis as metricalaccents (main beats), instead of the contrametrical accents (cross-beats) they in fact are.Some of their music examples are polymetric, with multiple and conflicting main beat cycles,each requiring its own separate time signature. King shows twoYorubadundun pressure drum("talking drum") phrases in relation to the five-strokestandard pattern,or "clave," played on thekagano dundun (top line).[34]The standard pattern is written in a polymetric 7/8 + 5/8 timesignature. One dundun phrase is based on a grouping of three pulses written in 3/8, and theother, a grouping of four pulses written in 4/8. Complicating the transcription further, onepolymetric measure is offset from the other two.

Dundun drum ensemble represented as polymeter.

African music is often characterized as polymetric, because, in contrast to most Westernmusic, African music cannot be notated without assigning different meters to the differentinstruments of an ensembleChernoff (1979: 45).[35]

More recent writings represent African music as cross-rhythmic, within a single meter.

Of the many reasons why the notion of polymeter must be rejected, I will mention three. First, ifpolymeter were a genuine feature of African music, we would expect to find some indication of
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its pertinence in the discourses and pedagogical schemes of African musicians, carriers of thetradition. As far as I know, no such data is avail-ableSecond, because practically all theensemble music in which polymeter is said to be operative in dance music, and given thegrounding demanded by choreography, it is more likely that these musics unfold withinpolyrhythmic matrices in single meters rather than inmixed metersThird, decisions abouthow to represent drum ensemble music founder on the assumption, made most dramatically by

Jones, that accents are metrical rather than phenomenalphenomenal accents play a moreimportant role in African music than metrical accents. Because meter and grouping are distinct,postulating a single meter in accordance with the dance allows phenomenal or contrametricaccents to emerge against a steady background. Polymeter fails to convey the true accentualstructure of African music insofar as it creates the essential tension between a firm and stablebackground and a fluid foregroundAgawu (2003: 84, 85).[36]

[The] term polymetric is only applicable to a very special kind of phenomenon. If we takemetre in its primary sense of metrum (the metre being the temporal reference unit),polymetric would describe the simultaneous un-folding of several parts in a single work atdifferent tempos so as not to be reducible to a single metrum. This happens in some modernmusic, such as some ofCharles Ives'works,Elliott Carters Symphony,B.A. Zimmermannsopera "Die Soldaten," andPierre Boulezs "Rituel." Being polymetric in the strict sense, these

works can only be performed with several simultaneous conductorsArom (1991: 205).[37]

When written within a single meter, we see that the dundun in the second line sounds the mainbeats, and the subdivision immediately preceding it. The firstcell(halfmeasure)of the top lineis ahemiola.The two dunduns shown in the second and third lines sound an embellishment ofthe three-over-four (3:4) cross-rhythmexpressed as three pairs of strokes against four pairsof strokes.[38]

Dundun drum ensemble represented as cross-rhythm within a single meter.

Adaptive instruments[edit]

Sub-Saharan instruments are constructed in a variety of ways to generate cross-rhythmicmelodies. Some instruments organize the pitches in a uniquely divided alternate array not inthe straight linearbasstotreblestructure that is so common to many western instruments suchas thepiano,harp,marimba,etc...

Lamellophonesincludingmbira,mbila, mbira huru, mbira njari, mbira nyunga, marimba,karimba,kalimba,likembe, and okeme. These instruments are found in several formsindigenous to different regions of Africa and most often have equal tonal ranges for right andleft hands. Thekalimbais a modern version of these instruments originated by the pioneer
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ethnomusicologistHugh Traceyin the early 20th century which has over the years gainedworld-wide popularity.

Hugh Tracey Treble Kalimba

Signature SeriesGravikord

Chordophones,such as the West Africankora,and Doussn'gouni, part of theharp-lutefamilyof instruments, also have this African separated double tonal array structure. Anotherinstrument, theMarovanyfrom Madagascar is a double sided box zither which also employsthis divided tonal structure. TheGravikordis a new American instrument closely related to boththe African kora and the kalimba. It was created to exploit this adaptive principle in a modernelectro-acoustic instrument.[39]

On these instruments one hand of the musician is not primarily in the bass nor the otherprimarily in the treble, but both hands can play freely across the entire tonal range of theinstrument. Also the fingers of each hand can play separate independent rhythmic patterns andthese can easily cross over each other from treble to bass and back, either smoothly or withvarying amounts ofsyncopation.This can all be done within the same tight tonal range, withoutthe left and right hand fingers ever physically encountering each other. These simple rhythmswill interact musically to produce complex cross rhythms including repeating on beat/offbeatpattern shifts that would be very difficult to create by any other means. Thischaracteristically African structure allows often simple playing techniques to combine with eachother and produce cross-rhythmic music of great beauty and complexity.

Jazz[edit]

The New Harvard Dictionary of Musiccallsswing"an intangible rhythmic momentum in jazz,"adding that "swing defies analysis; claims to its presence may inspire arguments." The only

specific description offered is the statement that "triplet subdivisions contrast with duplesubdivisions."[40]The argument could be made that by nature of its simultaneous triple and duplesubdivisions, swing is fundamentally a form of polyrhythm. However, the use of true systematiccross-rhythm injazzdid not occur until the second half of the twentieth century.

3:2 (or 6:4)[edit]

In 1959Mongo Santamariarecorded "Afro Blue," the first jazz standard built upon a typicalAfrican 3:2 cross-rhythm.[41]The song begins with the bass repeatedly playing 3 cross-beats pereach measure of 6/8 (3:2), or 6 cross-beats per 12/8 measure (6:4). The following exampleshows the originalostinato"Afro Blue" bass line. The slashed noteheads are not bass notes,but are shown to indicate the mainbeats,where you would normally tap your foot to "keeptime."

"Afro Blue" bass line, with main beats indicated by slashed noteheads.
http://en.wikipedia.org/wiki/Hugh_Traceyhttp://en.wikipedia.org/wiki/Hugh_Traceyhttp://en.wikipedia.org/wiki/Hugh_Traceyhttp://en.wikipedia.org/wiki/Kalimbahttp://en.wikipedia.org/wiki/Kalimbahttp://en.wikipedia.org/wiki/Kalimbahttp://en.wikipedia.org/wiki/Gravikordhttp://en.wikipedia.org/wiki/Gravikordhttp://en.wikipedia.org/wiki/Gravikordhttp://en.wikipedia.org/wiki/Chordophonehttp://en.wikipedia.org/wiki/Chordophonehttp://en.wikipedia.org/wiki/Kora_(instrument)http://en.wikipedia.org/wiki/Kora_(instrument)http://en.wikipedia.org/wiki/Kora_(instrument)http://en.wikipedia.org/wiki/Harp-lutehttp://en.wikipedia.org/wiki/Harp-lutehttp://en.wikipedia.org/wiki/Harp-lutehttp://en.wikipedia.org/wiki/Marovanyhttp://en.wikipedia.org/wiki/Marovanyhttp://en.wikipedia.org/wiki/Marovanyhttp://en.wikipedia.org/wiki/Gravikordhttp://en.wikipedia.org/wiki/Gravikordhttp://en.wikipedia.org/wiki/Gravikordhttp://en.wikipedia.org/wiki/Cross-beat#cite_note-39http://en.wikipedia.org/wiki/Cross-beat#cite_note-39http://en.wikipedia.org/wiki/Cross-beat#cite_note-39http://en.wikipedia.org/wiki/Syncopationhttp://en.wikipedia.org/wiki/Syncopationhttp://en.wikipedia.org/wiki/Syncopationhttp://en.wikipedia.org/wiki/Off-beat_(music)http://en.wikipedia.org/wiki/Off-beat_(music)http://en.wikipedia.org/wiki/Off-beat_(music)http://en.wikipedia.org/wiki/Off-beat_(music)http://en.wikipedia.org/w/index.php?title=Cross-beat&action=edit&section=13http://en.wikipedia.org/w/index.php?title=Cross-beat&action=edit&section=13http://en.wikipedia.org/w/index.php?title=Cross-beat&action=edit&section=13http://en.wikipedia.org/wiki/Swing_(jazz_performance_style)http://en.wikipedia.org/wiki/Swing_(jazz_performance_style)http://en.wikipedia.org/wiki/Swing_(jazz_performance_style)http://en.wikipedia.org/wiki/Cross-beat#cite_note-40http://en.wikipedia.org/wiki/Cross-beat#cite_note-40http://en.wikipedia.org/wiki/Cross-beat#cite_note-40http://en.wikipedia.org/wiki/Jazzhttp://en.wikipedia.org/wiki/Jazzhttp://en.wikipedia.org/wiki/Jazzhttp://en.wikipedia.org/w/index.php?title=Cross-beat&action=edit&section=14http://en.wikipedia.org/w/index.php?title=Cross-beat&action=edit&section=14http://en.wikipedia.org/w/index.php?title=Cross-beat&action=edit&section=14http://en.wikipedia.org/wiki/Mongo_Santamariahttp://en.wikipedia.org/wiki/Mongo_Santamariahttp://en.wikipedia.org/wiki/Mongo_Santamariahttp://en.wikipedia.org/wiki/Afro_Bluehttp://en.wikipedia.org/wiki/Afro_Bluehttp://en.wikipedia.org/wiki/Afro_Bluehttp://en.wikipedia.org/wiki/Cross-beat#cite_note-41http://en.wikipedia.org/wiki/Cross-beat#cite_note-41http://en.wikipedia.org/wiki/Cross-beat#cite_note-41http://en.wikipedia.org/wiki/Ostinatohttp://en.wikipedia.org/wiki/

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