753:
African musicians' ways of proceeding. ... Then, too, there appears to be no trace of an additive conception in the discourses of musicians, whether directly or indirectly. … It would seem, then, that whereas structural analysis (based on
European metalanguage) endorses an additive conception of the standard pattern, cultural analysis (originating in African musicians' thinking) denies it, ... no dancer thinks in cycles of 12 when interpreting the standard pattern. The evidence of the rate at which the dance feet move is that 4, not 12, is the reckoning that most closely approximates the regulative beat. ... what can be said for sure is that the cycle of four beats is felt and thus relied upon. This is cultural knowledge that players and especially dancers possess; without such knowledge, it is difficult to perform accurately.
557:
402:
155:
333:
744:
core of rhythmic traditions within which the composer conveys his ideas is the technique of cross-rhythm. The technique of cross-rhythm is a simultaneous use of contrasting rhythmic patterns within the 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 interplay of the two elements that produces the cross-rhythmic texture.
884:
prefer the divisive format. Those who imagine the addition of three, then three, then two sixteenth notes will treat the well-formedness of 3 + 3 + 2 as fortuitous, a product of grouping rather than of metrical structure. They will be tempted to deny that
African music has a bona fide metrical structure because of its frequent departures from normative grouping structure.
564:"I know of no music before or since…. which so felicitously exploits accentual and metrical variation and irregularity, and no more subtle rhythmic construction of any kind than that which is set in motion at the beginning of the 'Laudate Pueri,’ if, that is, the music is sung according to the verbal accents instead of... the editor's bar-lines".
854:
752:
Do
African musicians think additively? The evidence so far is that they do not. Writing in 1972 about the Yoruba version of the standard pattern, Kubik stated. 'There is no evidence that the musicians themselves think it as additive.' I have argued elsewhere that additive thinking is foreign to many
782:
the beats. From a metrical perspective then, the two ways of perceiving tresillo constitute two different rhythms. On the other hand, from the perspective of simply the pattern of attack-points, tresillo is a shared element of traditional folk music from the northwest tip of Africa to southeast tip
743:
In the development of cross rhythm, there are some selected rhythmic materials or beat schemes that are customarily used. These beat schemes, in their generic forms, are simple divisions of the same musical period in equal units, producing varying rhythmic densities or motions. At the center of a
883:
Although the difference between the two ways of notating this rhythm may seem small, they stem from fundamentally different conceptions. Those who wish to convey a sense of the rhythm's background , and who understand the surface morphology in relation to a regular subsurface articulation, will
247:
n discussions of rhythmic notation, practice or style, few terms are as confusing or used as confusedly as 'additive' and 'divisive'. … These confusions stem from two misapprehensions. The first is a failure to distinguish between systems of notation (which may have both additive and divisive
758:
The
African rhythmic structure which generates the standard pattern is a divisive structure and not an additive one … the standard pattern represents a series of attack points that outline the onbeat three-against-two / offbeat three-against-two sequence, not a series of durational
816:
301:
consists of one measure (whole note: 1) divided into a stronger first beat and slightly less strong second beat (half notes: 1, 3), which are in turn divided, by two weaker beats (quarter notes: 1, 2, 3, 4), and again divided into still weaker beats (eighth notes:
340:
Additive rhythm features nonidentical or irregular durational groups following one another at two levels, within the bar and between bars or groups of bars. This type of rhythm is also referred to in musicological literature by the
Turkish word
871:
African-based music has a divisive rhythm structure. Tresillo is generated through cross-rhythm: 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,
376:
307:
739:
is the basis for most Sub-Saharan
African music traditions. Rhythmic patterns are generated by simultaneously dividing a span of musical time by a triple-beat scheme and a duple-beat scheme.
489:, on the other hand, while also having eight quavers in a bar, divides them into three beats, the first three quavers long, the second three quavers long, and the last just two quavers long.
849:, a Spanish word meaning 'triplet' (three equal beats in the same time as two main beats). However, in the vernacular of Cuban popular music, the term refers to the figure shown below.
668:
made extensive use of additive rhythmic patterns, much of it stemming from his close study of the rhythms of Indian music. His "Danse de la fureur, pour les sept trompettes" from
658:
on the bridge". "The special effect of running even eighth notes accented as if triplets against the grain of the underlying backbeat is carried to a point more reminiscent of
825:
236:. The relationship between additive and divisive rhythms is complex, and the terms are often used in imprecise ways. In his article on rhythm in the second edition of the
377:
308:
1287:
162:
For example, 4 may be evenly divided by 2 or reached by adding 2 + 2. In contrast, 5 is only evenly divisible by 5 and 1 and may be reached by adding 2 or 3. Thus,
238:
1467:
690:
No. 13, "L'escalier du diable" features patterns involving quavers grouped in twos and threes. The rhythm at the start of the study follows the pattern
824:
879:
Because of its irregular pattern of attack-points, "tresillo" in
African and African-based musics has been mistaken for a form of additive rhythm.
248:
aspects) and the music notated under such a system. The second involves a failure to understand the divisive and additive aspects of meter itself.
553:, where the music follows the natural accentuation of the Latin words to create metrical groupings of twos, threes and fours at the very start:
676:
674:
is a bracing example. A gentler exploration of additive patterns can be found in "Le Regard de la Vierge" from the same composer's piano cycle
726:
263:
533:
for Wind
Instruments "ends with a jazzy 3+3+2 = 8 swung coda". Stravinsky himself found a kinship with additive rhythms in music of the
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musics may be considered as primarily additive. However, many pieces of music cannot be clearly labeled divisive or additive.
1642:
1460:
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time signature "serves only as a guideline, the actual meter consists of 36 quavers (three 'bars'), divided assymetrically".
336:
Divisive Rhythm. 1 whole note = 2 half notes = 4 quarter notes = 8 eighth notes = 16 sixteenth notes
857:
730:
669:
378:
309:
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in which the upper numeral is not divisible by two or three without a fraction, the result may alternatively be called
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581:. They may also occur in passing in pieces which are on the whole in conventional meters. In jazz,
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on various levels rather than through attempts to represent the organization with a single term".
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Fracile, Nice (2003). "The 'Aksak' Rhythm, a
Distinctive Feature of the Balkan Folklore".
838:
596:
550:
1323:
The Three
Against Two Relationship as the Foundation of Timelines in West African Musics
1213:
Moving Notation: A Handbook of Musical Rhythm and Elementary Labanotation for the Dancer
1050:"Monteverdi: Vespro della Beata Vergine, SV 206 – IV. Laudate, pueri Dominum a 8 (Live)"
1667:
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800:
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271:
267:
811:. In Middle Eastern and Asian music, the figure is generated through additive rhythm.
807:. This pattern may have migrated east from North Africa to Asia through the spread of
86:(joining end to end) a series of units into larger units of unequal length, such as a
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can be traced back to slaves brought north across the Sahara Desert from present-day
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or, conversely, some integer unit is regularly multiplied into larger, equal units.
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which have a regular pattern of beats of uneven length. For example, the
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time. 1 whole note = 8 eighth notes = 3 + 3 + 2.
1432:, edited by Gary Wittlich, Englewood Cliffs, New Jersey: Prentice-Hall.
1572:
1332:
The Clave Matrix; Afro-Cuban Rhythm: Its Principles and African Origins
1053:
792:
791:"Tresillo" is also found within a wide geographic belt stretching from
538:
1672:
1476:
1215:. Performing Arts Studies 6. Amsterdam: Harwood Academic Publishers.
463:
302:
1 & 2 & 3 & 4 &).
68:
44:
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meter, and the groupings into twos and threes are sometimes called
1657:
1194:
Representing African Music: Postcolonial Notes, Queries, Positions
1039:
Stravinsky, I. (1972, p120) Themes and Conclusions. London, Faber.
808:
748:"the entire African rhythmic structure... is divisive in nature".
555:
400:
373:
343:
331:
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contradict the beats. In additive form, the strokes of tresillo
428:
is also often used to refer to what are also incorrectly called
228:
was introduced for the former concept at about the same time by
1449:
1428:
Winold, Allen (1975). "Rhythm in Twentieth-Century Music". In
575:, most noticeably the "one-two-one-two-three" chorus parts in
474:(that is, two quavers) long. The asymmetric time signature
912:
910:
859:
Audio playback is not supported in your browser. You can
589:" features bars of nine quavers grouped into patterns of
71:
in which a larger period of time is divided into smaller
951:
949:
1066:
1374:
Reprinted 1988, New York: Columbia University Press.
1306:
All the Songs: The Story Behind Every Beatles Release
82:, in which larger periods of time are constructed by
1304:
Margotin, Philippe, and Jean-Michel Guesdon (2013).
1247:
Studia Musicologica Academiae Scientiarum Hungaricae
1003:
492:These kinds of rhythms are used, for example, by
347:, which means "limping". In the special case of
1363:, second edition. Boston: Allyn and Bacon, Inc.
1288:The New Grove Dictionary of Music and Musicians
837:The most basic duple-pulse figure found in the
764:Tresillo: divisive and additive interpretations
756:
750:
256:is best described through detailed analysis of
245:
1236:Brăiloiu, Constantin. 1951. "Le rythme Aksak"
567:Additive patterns also occur in some music of
1461:
232:, in agreement with the Turkish musicologist
101:meter produced by the regular alternation of
8:
1361:Music Notation: A Manual of Modern Practice
1325:. Urbana, Illinois: University of Illinois.
1260:Foundation Course in African Dance-Drumming
541:periods. For example, he marvelled at the
496:, who was influenced by similar rhythms in
239:New Grove Dictionary of Music and Musicians
1468:
1454:
1446:
1370:Rhythm and Tempo: A Study in Music History
876:2. Tresillo is a cross-rhythmic fragment.
613:features a rhythm "which switches between
43:are used to distinguish two types of both
143:are sometimes used as the equivalents of
1162:
1150:
1138:
1114:
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991:
702:. According to the composer's note, the
153:
1240:33, nos. 99 and 100 (December): 71–108.
1078:
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1211:Beck, Jill, and Joseph Reiser (1998).
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1308:. New York: Black Dog and Leventhal.
1174:
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1027:
1015:
979:
940:
799:in South Asia. Use of the pattern in
7:
928:
872:8 ÷ 3 = 2,
727:Sub-Saharan African music traditions
560:Monteverdi opening of Laudate Pueri
1430:Aspects of Twentieth-Century Music
1271:. Vol. Book 2. Mainz: Schott.
1262:(webpage, accessed 24 April 2010).
135:When applied to meters, the terms
25:
1401:. BBC Music Guides. London: BBC.
1334:. Redway, California: Bembe Inc.
1285:London, Justin (2001). "Rhythm".
774:In divisive form, the strokes of
500:. The third movement of Bartók's
218:originate with Curt Sachs's book
821:
677:Vingt regards sur l'enfant-Jésus
1351:" (retrieved 14 February 2012).
1299:. London: Macmillan Publishers.
671:The Quartet for the End of Time
1372:. New York City: W. W. Norton.
1:
1349:Notes on 'Here Comes the Sun'
158:Additive and divisive meters.
1321:Novotney, Eugene D. (1998).
1291:, second edition, edited by
856:
845:is a figure the Cubans call
731:Rhythm in Sub-Saharan Africa
78:This can be contrasted with
1192:Agawu, Victor Kofi (2003).
1067:Margotin & Guesdon 2013
243:Justin London states that:
1710:
1256:"The Myth of Cross-Rhythm"
767:
724:
721:Sub-Saharan African rhythm
1487:
1249:44, nos. 1 and 2:197–210.
264:Sub-Saharan African music
252:Winold recommends that, "
1598:Non-retrogradable rhythm
1330:Peñalosa, David (2009).
1254:Ladzekpo, C. K. (1995).
268:European (Western) music
1421:The Music of Stravinsky
1347:Pollack, Alan (n.d.). "
1267:Ligeti, György (1994).
1196:. New York: Routledge.
861:download the audio file
222:(1953), while the term
1004:Beck & Reiser 1998
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662:than of the Beatles".
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1492:Additive and divisive
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578:Einstein on the Beach
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1618:Prolation and tempus
1423:. London: Routledge.
1399:Bartók Chamber Music
1368:Sachs, Curt (1953).
1275:Ligeti: Étude No. 13
1238:Revue de Musicologie
587:Blue Rondo à la Turk
502:String Quartet No. 5
498:Bulgarian Folk Music
192:) is divisive while
177:(or, more commonly,
1006:, pp. 181–182.
795:in North Africa to
735:A divisive form of
504:, a scherzo marked
466:long, and has four
382:Additive rhythm in
313:Divisive rhythm in
270:is divisive, while
230:Constantin Brăiloiu
833:Divisive structure
787:Additive structure
601:Here Comes the Sun
562:
430:asymmetric rhythms
422:
399:
338:
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234:Ahmet Adnan Saygun
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59:(or, alternately,
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1680:
1593:Metric modulation
1269:Études pour Piano
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841:and music of the
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770:Tresillo (rhythm)
523:rhythm (4+2+3)".
434:irregular rhythms
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16:(Redirected from
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1440:. pp. 208-269.
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1319:
1315:
1314:9781579129521
1311:
1307:
1302:
1298:
1294:
1293:Stanley Sadie
1290:
1289:
1283:
1281:
1277:
1270:
1265:
1261:
1257:
1252:
1248:
1243:
1239:
1234:
1230:
1229:90-5702-179-X
1226:
1222:
1221:90-5702-178-1
1218:
1214:
1209:
1205:
1203:0-415-94390-6
1199:
1195:
1190:
1189:
1187:
1186:
1177:, p. 87.
1176:
1171:
1168:
1164:
1163:Novotney 1998
1159:
1156:
1152:
1151:Peñalosa 2009
1147:
1144:
1140:
1139:Novotney 1998
1135:
1132:
1129:, p. 94.
1128:
1123:
1120:
1116:
1115:Novotney 1998
1111:
1108:
1104:
1103:Ladzekpo 1995
1099:
1096:
1092:
1087:
1084:
1080:
1075:
1072:
1068:
1063:
1060:
1055:
1051:
1045:
1042:
1036:
1033:
1029:
1024:
1021:
1018:, p. 66.
1017:
1012:
1009:
1005:
1000:
997:
993:
992:Brăiloiu 1951
988:
985:
982:, p. 86.
981:
976:
973:
969:
964:
961:
957:
952:
950:
946:
942:
937:
934:
930:
925:
922:
918:
913:
911:
907:
900:
896:
893:
892:
888:
885:
880:
877:
875:
862:
852:
851:
850:
848:
844:
840:
832:
830:
814:
813:
812:
810:
806:
802:
798:
794:
786:
784:
781:
777:
771:
763:
760:
754:
749:
745:
740:
738:
732:
728:
720:
718:
711:
700:
694:
689:
685:
684:György Ligeti
681:
679:
678:
673:
672:
667:
663:
661:
652:
637:
622:
612:
611:
606:
602:
598:
593:
588:
584:
580:
579:
574:
570:
565:
558:
554:
552:
548:
544:
543:Laudate Pueri
540:
536:
532:
531:
526:
517:
507:
503:
499:
495:
490:
483:
473:
469:
465:
461:
452:
443:
439:
435:
431:
427:
414:
403:
391:
372:
370:
366:
362:
358:
354:
350:
346:
345:
334:
322:
303:
295:
286:For example:
281:
279:
277:
273:
269:
265:
261:
259:
255:
249:
244:
242:
240:
235:
231:
227:
226:
221:
217:
213:
208:
207:is additive.
201:
186:
171:
156:
152:
150:
146:
142:
138:
125:
110:
95:
85:
84:concatenating
81:
77:
74:
70:
66:
62:
58:
54:
53:
52:
50:
46:
42:
41:
36:
35:
30:
19:
1550:
1491:
1429:
1420:
1398:
1369:
1360:
1331:
1322:
1305:
1297:John Tyrrell
1286:
1268:
1259:
1246:
1237:
1212:
1193:
1184:
1183:
1170:
1158:
1146:
1134:
1122:
1110:
1098:
1086:
1074:
1062:
1052:– via
1044:
1035:
1023:
1011:
999:
987:
975:
963:
956:Fracile 2003
936:
924:
882:
878:
870:
846:
836:
820:
790:
779:
773:
757:
751:
747:
742:
737:cross-rhythm
734:
709:
698:
692:
682:
675:
670:
664:
650:
635:
620:
608:
591:
583:Dave Brubeck
576:
571:, and other
569:Philip Glass
566:
563:
542:
529:
515:
508:features a "
505:
491:
481:
450:
433:
429:
425:
423:
412:
389:
368:
364:
360:
356:
352:
342:
339:
320:
293:
285:
262:
251:
246:
237:
225:aksak rhythm
223:
219:
215:
211:
209:
199:
184:
169:
161:
148:
144:
140:
136:
134:
123:
108:
93:
79:
64:
60:
56:
39:
38:
33:
32:
31:, the terms
26:
1648:Syncopation
1093:, p. .
1091:Ligeti 1994
1079:Pollack n.d
968:Winold 1975
917:London 2001
605:The Beatles
573:minimalists
535:renaissance
494:Béla Bartók
436:– that is,
369:short beats
1663:Time point
1613:Polyrhythm
1608:Note value
1578:Homorhythm
1544:Note value
1534:Cross-beat
1175:Agawu 2003
1127:Agawu 2003
1028:Walsh 1988
1016:Walsh 1982
980:Agawu 2003
941:Sachs 1953
901:References
660:Stravinsky
610:Abbey Road
547:Monteverdi
525:Stravinsky
365:long beats
274:and other
210:The terms
1638:Stop-time
1588:Isorhythm
1563:Half-time
1527:Count off
1497:Anacrusis
1382:(cloth);
1223:(cloth);
929:Read 1969
797:Indonesia
783:of Asia.
599:'s song "
585:'s song "
470:, each a
462:is eight
432:and even
424:The term
357:imperfect
353:irregular
266:and most
141:imperfect
1688:Category
1539:Duration
1522:Counting
1517:Colotomy
1419:(1988).
1397:(1982).
1359:(1969).
919:, § I.8.
889:See also
847:tresillo
776:tresillo
759:values".
607:' album
472:crotchet
216:divisive
212:additive
149:additive
145:divisive
57:divisive
40:divisive
34:additive
1623:Prosody
1573:Hemiola
1280:YouTube
1185:Sources
1054:YouTube
793:Morocco
699:2+2+2+3
696:, then
592:2+2+2+3
539:baroque
464:quavers
137:perfect
1673:Tuplet
1558:Groove
1477:Rhythm
1436:
1405:
1390:(pbk).
1386:
1378:
1338:
1312:
1231:(pbk).
1227:
1219:
1200:
438:meters
361:uneven
272:Indian
69:rhythm
65:rhythm
45:rhythm
1658:Tempo
1643:Swing
1628:Pulse
1552:Gatra
1481:meter
809:Islam
693:2+2+3
688:Étude
603:" on
545:from
530:Octet
468:beats
359:, or
344:aksak
276:Asian
67:is a
49:meter
29:music
1653:Tala
1583:Iqa'
1507:Beat
1479:and
1434:ISBN
1403:ISBN
1384:ISBN
1376:ISBN
1336:ISBN
1310:ISBN
1295:and
1225:ISBN
1217:ISBN
1198:ISBN
805:Mali
729:and
643:and
537:and
397:time
367:and
328:time
214:and
147:and
139:and
116:and
47:and
37:and
1502:Bar
1278:on
780:are
686:'s
549:'s
527:'s
460:bar
27:In
1690::
1258:,
948:^
909:^
680:.
628:,
371:.
355:,
63:)
55:A
51::
1469:e
1462:t
1455:v
1411:.
1342:.
1316:.
1206:.
1105:.
1081:.
1056:.
994:.
943:.
874:r
863:.
710:8
651:8
636:4
621:8
516:8
482:8
451:4
413:8
390:8
321:4
294:4
241:,
200:8
185:4
170:8
131:.
124:8
109:8
94:8
20:)
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