TIMELINE SPACES
A THEORY OF TEMPORAL PROCESS IN AFRICAN DRUM/DANCE MUSIC
Chris Stover
The New School
[email protected]
American Musicological Society—Society for Music Theory Annual Conference
Vancouver, 4 November 2016
How Timelines Have Been Defined
“a constant point of reference by which the phrase structure of a song as well as the linear metrical
organization of phrases are guided” (Nketia 1963)
“a regulative element in many kinds of African music”; one of the basic “principles of timing” (Kubik
1994)
“the structural core of a musical piece, something like a condensed and extremely concentrated
expression of the motional possibilities open to the participants” (Kubik 1994)
“short, distinct, and often memorable rhythmic figure(s) of modest duration…[that serve as] point(s)
of temporal reference” (Agawu 2003)
“a distinctly shaped and often memorable rhythmic figure of modest duration that is played as an
ostinato throughout a given dance composition” (Agawu 2006)
“a phrasing referent, not a structural referent in African musical thought and ensemble composition”
(Nzewi 1997)
How Timelines Have Been Defined
“a constant point of reference by which the phrase structure of a song as well as the linear metrical
organization of phrases are guided” (Nketia 1963)
“a regulative element in many kinds of African music”; one of the basic “principles of timing” (Kubik
1994)
“the structural core of a musical piece, something like a condensed and extremely concentrated
expression of the motional possibilities open to the participants” (Kubik 1994)
“short, distinct, and often memorable rhythmic figure(s) of modest duration…[that serve as] point(s)
of temporal reference” (Agawu 2003)
“a distinctly shaped and often memorable rhythmic figure of modest duration that is played as an
ostinato throughout a given dance composition” (Agawu 2006)
“a phrasing referent, not a structural referent in African musical thought and ensemble composition”
(Nzewi 1997)
How Timelines Have Been Defined
“a constant point of reference by which the phrase structure of a song as well as the linear metrical
organization of phrases are guided” (Nketia 1963)
“a regulative element in many kinds of African music”; one of the basic “principles of timing” (Kubik
1994)
“the structural core of a musical piece, something like a condensed and extremely concentrated
expression of the motional possibilities open to the participants” (Kubik 1994)
“short, distinct, and often memorable rhythmic figure(s) of modest duration…[that serve as] point(s)
of temporal reference” (Agawu 2003)
“a distinctly shaped and often memorable rhythmic figure of modest duration that is played as an
ostinato throughout a given dance composition” (Agawu 2006)
“a phrasing referent, not a structural referent in African musical thought and ensemble composition”
(Nzewi 1997)
How Timelines Have Been Defined
“a constant point of reference by which the phrase structure of a song as well as the linear metrical
organization of phrases are guided” (Nketia 1963)
“a regulative element in many kinds of African music”; one of the basic “principles of timing” (Kubik
1994)
“the structural core of a musical piece, something like a condensed and extremely concentrated
expression of the motional possibilities open to the participants” (Kubik 1994)
“short, distinct, and often memorable rhythmic figure(s) of modest duration…[that serve as] point(s)
of temporal reference” (Agawu 2003)
“a distinctly shaped and often memorable rhythmic figure of modest duration that is played as an
ostinato throughout a given dance composition” (Agawu 2006)
“a phrasing referent, not a structural referent in African musical thought and ensemble composition”
(Nzewi 1997)
How Timelines Have Been Defined
“a constant point of reference by which the phrase structure of a song as well as the linear metrical
organization of phrases are guided” (Nketia 1963)
“a regulative element in many kinds of African music”; one of the basic “principles of timing” (Kubik
1994)
“the structural core of a musical piece, something like a condensed and extremely concentrated
expression of the motional possibilities open to the participants” (Kubik 1994)
“short, distinct, and often memorable rhythmic figure(s) of modest duration…[that serve as] point(s)
of temporal reference” (Agawu 2003)
“a distinctly shaped and often memorable rhythmic figure of modest duration that is played as an
ostinato throughout a given dance composition” (Agawu 2006)
“a phrasing referent, not a structural referent in African musical thought and ensemble composition”
(Nzewi 1997)
How Timelines Have Been Defined
“a constant point of reference by which the phrase structure of a song as well as the linear metrical
organization of phrases are guided” (Nketia 1963)
“a regulative element in many kinds of African music”; one of the basic “principles of timing” (Kubik
1994)
“the structural core of a musical piece, something like a condensed and extremely concentrated
expression of the motional possibilities open to the participants” (Kubik 1994)
“short, distinct, and often memorable rhythmic figure(s) of modest duration…[that serve as] point(s)
of temporal reference” (Agawu 2003)
“a distinctly shaped and often memorable rhythmic figure of modest duration that is played as an
ostinato throughout a given dance composition” (Agawu 2006)
“a phrasing referent, not a structural referent in African musical thought and ensemble composition”
(Nzewi 1997)
How Timelines Have Been Defined
“a constant point of reference by which the phrase structure of a song as well as the linear metrical
organization of phrases are guided” (Nketia 1963)
“a regulative element in many kinds of African music”; one of the basic “principles of timing” (Kubik
1994)
“the structural core of a musical piece, something like a condensed and extremely concentrated
expression of the motional possibilities open to the participants” (Kubik 1994)
“short, distinct, and often memorable rhythmic figure(s) of modest duration…[that serve as] point(s)
of temporal reference” (Agawu 2003)
“a distinctly shaped and often memorable rhythmic figure of modest duration that is played as an
ostinato throughout a given dance composition” (Agawu 2006)
“a phrasing referent, not a structural referent in African musical thought and ensemble composition”
(Nzewi 1997)
How Timelines Have Been Defined
“a constant point of reference by which the phrase structure of a song as well as the linear metrical
organization of phrases are guided” (Nketia 1963)
“a regulative element in many kinds of African music”; one of the basic “principles of timing”
(Kubik 1994)
“the structural core of a musical piece, something like a condensed and extremely concentrated
expression of the motional possibilities open to the participants” (Kubik 1994)
“short, distinct, and often memorable rhythmic figure(s) of modest duration…[that serve as] point(s)
of temporal reference” (Agawu 2003)
“a distinctly shaped and often memorable rhythmic figure of modest duration that is played as an
ostinato throughout a given dance composition” (Agawu 2006)
“a phrasing referent, not a structural referent in African musical thought and ensemble
composition” (Nzewi 1997)
What Gets to Count as a Timeline
What Gets to Count as a Timeline
(a very partial list of lists)
Kofi Agawu. 2016. The African Imagination in Music. Oxford University Press, 175.
Bertram Lehmann. 2000. “Timelines: A Qualitative Survey of Cyclical Phrasing Referents in Africa and the
Americas.” Unpublished MS.
Jeff Pressing. 1983. “Cognitive Isomorphisms Between Pitch and Rhythm in World Musics: West Africa, the
Balkans and Western Tonality.” Studies in Music 17: 57–61.
Jay Rahn. 1987. “Asymmetrical Ostinatos in Sub-Saharan Music: Time, Pitch, and Cycles Reconsidered.” In
Theory Only 9(7): 27–28.
Godfried Toussaint. 2003. “Classification and Phylogenetic Analysis of African Ternary Rhythm Timelines.”
Proceedings of BRIDGES: Mathematical Connections in Art, Music and Science, University of Granada, Spain, 23–26
July: 27–32.
_____. 2015. “Quantifying Musical Meter: How Similar are African and Western Rhythm?” Analytical
Approaches to World Music 4(2): 30.
Three (or Six) Timelines I’m Concerned With Today
Morphological Characteristics of Timelines
African music scholarship (Agawu 2003, 2006; Jones 1959; Kubik
2010b; Locke 1992; Nketia 1974); Cuban music scholarship (Alén
Rodriguez 1986; Crook 1982; Moore 2006; Peñalosa 2009; Spiro
2006); in terms of mathematical or geometric properties (Clough
and Douthett 1991; Pressing 1983; Rahn 1987; Toussaint 2003,
2009, 2015); phenomenologically (Stover 2009); from perception
and cognition studies perspectives (London [2004] 2012; Magill and
Pressing 1997; Pressing 1983, 2002; Temperley 2000).
Morphological Characteristics of Timelines
(a very partial bibliography)
Kofi Agawu. 2003. Representing African Music: Postcolonial Notes, Queries, Positions. Routledge.
_____. 2006. “Structural Analysis or Cultural Analysis? Competing Perspectives on the ‘Standard Pattern’ of West African Rhythm.” Journal of the American
Musicological Society 59(1): 1–46.
Olavo Alén Rodriguez. 1986. La Música de las Sociedades de Tumba Francesa. Casa de las Americas.
_____. 1995. “Rhythm as Duration of Sounds in Tumba Francesa.” Ethnomusicology 39(1): 55–74.
John Clough and Jack Douthett. 1991. “Maximally Even Sets.” Journal of Music Theory 35(1–2): 93–173.
Larry Crook. 1982. “A Musical Analysis of the Cuban Rumba.” Latin American Music Review 3(1): 92–123.
A.M. Jones. 1959. Studies in African Music. Oxford University Press.
Gerhard Kubik. 2010. Theory of African Music—Vol. II. University of Chicago Press.
David Locke. 1992. Kpegisu: A War Drum of the Ewe. White Cliffs Media Company.
Justin London. [2004] 2012. Hearing in Time: Psychological Aspects of Musical Meter. Second Revised Edition. Oxford University Press.
Jonathan M. Magill and Jeff Pressing. 1997. “Asymmetric Cognitive Clock Structures in West African Rhythms.” Music Perception 15(2): 189–222.
Kevin Moore. 2006. Timba: Understanding Cuban Rhythms. Online Book. www.timba.com/bookpre/index.asp.
J.H. Kwabena Nketia. 1974. The Music of Africa. W.W. Norton.
Eugene Novotny. 1998. The 3:2 Relationship as the Foundation of Timelines in West African Musics. DMA Dissertation, University of Illinois, Urbana-Champaign.
David Peñalosa. 2009. The Clave Matrix. Afro-Cuban Rhythm: Its Principles and African Origins. Edited by Peter Greenwood. Bembe Books.
Jeff Pressing. 1983. “Cognitive Isomorphisms Between Pitch and Rhythm in World Musics: West Africa, the Balkans and Western Tonality.” Studies in Music 17: 57–61.
_____. 2002. “Black Atlantic Rhythm: Its Computational and Transcultural Foundations.” Music Perception 19/3: 285-310.
Jay Rahn. 1987. “Asymmetrical Ostinatos in Sub-Saharan Music: Time, Pitch, and Cycles Reconsidered.” In Theory Only 9(7): 27–28.
Michael Spiro. 2006. The Conga Drummer’s Guidebook. Sher Music Co.
Chris Stover. 2009. A Theory of Flexible Rhythmic Spaces for Diasporic African Music. PhD Dissertation, University of Washington.
David Temperley. 2000. “Meter and Grouping in African Music: A View from Music Theory.” Ethnomusicology 44: 65–95.
Godfried Toussaint. 2003. “Classification and Phylogenetic Analysis of African Ternary Rhythm Timelines.” Proceedings of BRIDGES: Mathematical Connections in
Art, Music and Science, University of Granada, Spain, 23–26 July: 25–36.
_____. 2015. “Quantifying Musical Meter: How Similar are African and Western Rhythm?” Analytical Approaches to World Music 4(2): 30.
Morphological Characteristics of Timelines
(a very partial bibliography)
Kofi Agawu. 2003. Representing African Music: Postcolonial Notes, Queries, Positions. Routledge.
_____. 2006. “Structural Analysis or Cultural Analysis? Competing Perspectives on the ‘Standard Pattern’ of West African Rhythm.” Journal of the American
Musicological Society 59(1): 1–46.
Olavo Alén Rodriguez. 1986. La Música de las Sociedades de Tumba Francesa. Casa de las Americas.
_____. 1995. “Rhythm as Duration of Sounds in Tumba Francesa.” Ethnomusicology 39(1): 55–74.
John Clough and Jack Douthett. 1991. “Maximally Even Sets.” Journal of Music Theory 35(1–2): 93–173.
Larry Crook. 1982. “A Musical Analysis of the Cuban Rumba.” Latin American Music Review 3(1): 92–123.
A.M. Jones. 1959. Studies in African Music. Oxford University Press.
Gerhard Kubik. 2010. Theory of African Music—Vol. II. University of Chicago Press.
David Locke. 1992. Kpegisu: A War Drum of the Ewe. White Cliffs Media Company.
Justin London. [2004] 2012. Hearing in Time: Psychological Aspects of Musical Meter. Second Revised Edition. Oxford University Press.
Jonathan M. Magill and Jeff Pressing. 1997. “Asymmetric Cognitive Clock Structures in West African Rhythms.” Music Perception 15(2): 189–222.
Kevin Moore. 2006. Timba: Understanding Cuban Rhythms. Online Book. www.timba.com/bookpre/index.asp.
J.H. Kwabena Nketia. 1974. The Music of Africa. W.W. Norton.
Eugene Novotny. 1998. The 3:2 Relationship as the Foundation of Timelines in West African Musics. DMA Dissertation, University of Illinois, Urbana-Champaign.
David Peñalosa. 2009. The Clave Matrix. Afro-Cuban Rhythm: Its Principles and African Origins. Edited by Peter Greenwood. Bembe Books.
Jeff Pressing. 1983. “Cognitive Isomorphisms Between Pitch and Rhythm in World Musics: West Africa, the Balkans and Western Tonality.” Studies in Music 17: 57–61.
_____. 2002. “Black Atlantic Rhythm: Its Computational and Transcultural Foundations.” Music Perception 19/3: 285-310.
Jay Rahn. 1987. “Asymmetrical Ostinatos in Sub-Saharan Music: Time, Pitch, and Cycles Reconsidered.” In Theory Only 9(7): 27–28.
Michael Spiro. 2006. The Conga Drummer’s Guidebook. Sher Music Co.
Chris Stover. 2009. A Theory of Flexible Rhythmic Spaces for Diasporic African Music. PhD Dissertation, University of Washington.
David Temperley. 2000. “Meter and Grouping in African Music: A View from Music Theory.” Ethnomusicology 44: 65–95.
Godfried Toussaint. 2003. “Classification and Phylogenetic Analysis of African Ternary Rhythm Timelines.” Proceedings of BRIDGES: Mathematical Connections in
Art, Music and Science, University of Granada, Spain, 23–26 July: 25–36.
_____. 2015. “Quantifying Musical Meter: How Similar are African and Western Rhythm?” Analytical Approaches to World Music 4(2): 30.
Morphological Characteristics of Timelines
(a very partial bibliography)
Kofi Agawu. 2003. Representing African Music: Postcolonial Notes, Queries, Positions. Routledge.
_____. 2006. “Structural Analysis or Cultural Analysis? Competing Perspectives on the ‘Standard Pattern’ of West African Rhythm.” Journal of the American
Musicological Society 59(1): 1–46.
Olavo Alén Rodriguez. 1986. La Música de las Sociedades de Tumba Francesa. Casa de las Americas.
_____. 1995. “Rhythm as Duration of Sounds in Tumba Francesa.” Ethnomusicology 39(1): 55–74.
John Clough and Jack Douthett. 1991. “Maximally Even Sets.” Journal of Music Theory 35(1–2): 93–173.
Larry Crook. 1982. “A Musical Analysis of the Cuban Rumba.” Latin American Music Review 3(1): 92–123.
A.M. Jones. 1959. Studies in African Music. Oxford University Press.
Gerhard Kubik. 2010. Theory of African Music—Vol. II. University of Chicago Press.
David Locke. 1992. Kpegisu: A War Drum of the Ewe. White Cliffs Media Company.
Justin London. [2004] 2012. Hearing in Time: Psychological Aspects of Musical Meter. Second Revised Edition. Oxford University Press.
Jonathan M. Magill and Jeff Pressing. 1997. “Asymmetric Cognitive Clock Structures in West African Rhythms.” Music Perception 15(2): 189–222.
Kevin Moore. 2006. Timba: Understanding Cuban Rhythms. Online Book. www.timba.com/bookpre/index.asp.
J.H. Kwabena Nketia. 1974. The Music of Africa. W.W. Norton.
Eugene Novotny. 1998. The 3:2 Relationship as the Foundation of Timelines in West African Musics. DMA Dissertation, University of Illinois, Urbana-Champaign.
David Peñalosa. 2009. The Clave Matrix. Afro-Cuban Rhythm: Its Principles and African Origins. Edited by Peter Greenwood. Bembe Books.
Jeff Pressing. 1983. “Cognitive Isomorphisms Between Pitch and Rhythm in World Musics: West Africa, the Balkans and Western Tonality.” Studies in Music 17: 57–61.
_____. 2002. “Black Atlantic Rhythm: Its Computational and Transcultural Foundations.” Music Perception 19/3: 285-310.
Jay Rahn. 1987. “Asymmetrical Ostinatos in Sub-Saharan Music: Time, Pitch, and Cycles Reconsidered.” In Theory Only 9(7): 27–28.
Michael Spiro. 2006. The Conga Drummer’s Guidebook. Sher Music Co.
Chris Stover. 2009. A Theory of Flexible Rhythmic Spaces for Diasporic African Music. PhD Dissertation, University of Washington.
David Temperley. 2000. “Meter and Grouping in African Music: A View from Music Theory.” Ethnomusicology 44: 65–95.
Godfried Toussaint. 2003. “Classification and Phylogenetic Analysis of African Ternary Rhythm Timelines.” Proceedings of BRIDGES: Mathematical Connections in
Art, Music and Science, University of Granada, Spain, 23–26 July: 25–36.
_____. 2015. “Quantifying Musical Meter: How Similar are African and Western Rhythm?” Analytical Approaches to World Music 4(2): 30.
Morphological Characteristics of Timelines
(a very partial bibliography)
Kofi Agawu. 2003. Representing African Music: Postcolonial Notes, Queries, Positions. Routledge.
_____. 2006. “Structural Analysis or Cultural Analysis? Competing Perspectives on the ‘Standard Pattern’ of West African Rhythm.” Journal of the American
Musicological Society 59(1): 1–46.
Olavo Alén Rodriguez. 1986. La Música de las Sociedades de Tumba Francesa. Casa de las Americas.
_____. 1995. “Rhythm as Duration of Sounds in Tumba Francesa.” Ethnomusicology 39(1): 55–74.
John Clough and Jack Douthett. 1991. “Maximally Even Sets.” Journal of Music Theory 35(1–2): 93–173.
Larry Crook. 1982. “A Musical Analysis of the Cuban Rumba.” Latin American Music Review 3(1): 92–123.
A.M. Jones. 1959. Studies in African Music. Oxford University Press.
Gerhard Kubik. 2010. Theory of African Music—Vol. II. University of Chicago Press.
David Locke. 1992. Kpegisu: A War Drum of the Ewe. White Cliffs Media Company.
Justin London. [2004] 2012. Hearing in Time: Psychological Aspects of Musical Meter. Second Revised Edition. Oxford University Press.
Jonathan M. Magill and Jeff Pressing. 1997. “Asymmetric Cognitive Clock Structures in West African Rhythms.” Music Perception 15(2): 189–222.
Kevin Moore. 2006. Timba: Understanding Cuban Rhythms. Online Book. www.timba.com/bookpre/index.asp.
J.H. Kwabena Nketia. 1974. The Music of Africa. W.W. Norton.
Eugene Novotny. 1998. The 3:2 Relationship as the Foundation of Timelines in West African Musics. DMA Dissertation, University of Illinois, Urbana-Champaign.
David Peñalosa. 2009. The Clave Matrix. Afro-Cuban Rhythm: Its Principles and African Origins. Edited by Peter Greenwood. Bembe Books.
Jeff Pressing. 1983. “Cognitive Isomorphisms Between Pitch and Rhythm in World Musics: West Africa, the Balkans and Western Tonality.” Studies in Music 17: 57–61.
_____. 2002. “Black Atlantic Rhythm: Its Computational and Transcultural Foundations.” Music Perception 19/3: 285-310.
Jay Rahn. 1987. “Asymmetrical Ostinatos in Sub-Saharan Music: Time, Pitch, and Cycles Reconsidered.” In Theory Only 9(7): 27–28.
Michael Spiro. 2006. The Conga Drummer’s Guidebook. Sher Music Co.
Chris Stover. 2009. A Theory of Flexible Rhythmic Spaces for Diasporic African Music. PhD Dissertation, University of Washington.
David Temperley. 2000. “Meter and Grouping in African Music: A View from Music Theory.” Ethnomusicology 44: 65–95.
Godfried Toussaint. 2003. “Classification and Phylogenetic Analysis of African Ternary Rhythm Timelines.” Proceedings of BRIDGES: Mathematical Connections in
Art, Music and Science, University of Granada, Spain, 23–26 July: 25–36.
_____. 2015. “Quantifying Musical Meter: How Similar are African and Western Rhythm?” Analytical Approaches to World Music 4(2): 30.
Morphological Characteristics of Timelines
(a very partial bibliography)
Kofi Agawu. 2003. Representing African Music: Postcolonial Notes, Queries, Positions. Routledge.
_____. 2006. “Structural Analysis or Cultural Analysis? Competing Perspectives on the ‘Standard Pattern’ of West African Rhythm.” Journal of the American
Musicological Society 59(1): 1–46.
Olavo Alén Rodriguez. 1986. La Música de las Sociedades de Tumba Francesa. Casa de las Americas.
_____. 1995. “Rhythm as Duration of Sounds in Tumba Francesa.” Ethnomusicology 39(1): 55–74.
John Clough and Jack Douthett. 1991. “Maximally Even Sets.” Journal of Music Theory 35(1–2): 93–173.
Larry Crook. 1982. “A Musical Analysis of the Cuban Rumba.” Latin American Music Review 3(1): 92–123.
A.M. Jones. 1959. Studies in African Music. Oxford University Press.
Gerhard Kubik. 2010. Theory of African Music—Vol. II. University of Chicago Press.
David Locke. 1992. Kpegisu: A War Drum of the Ewe. White Cliffs Media Company.
Justin London. [2004] 2012. Hearing in Time: Psychological Aspects of Musical Meter. Second Revised Edition. Oxford University Press.
Jonathan M. Magill and Jeff Pressing. 1997. “Asymmetric Cognitive Clock Structures in West African Rhythms.” Music Perception 15(2): 189–222.
Kevin Moore. 2006. Timba: Understanding Cuban Rhythms. Online Book. www.timba.com/bookpre/index.asp.
J.H. Kwabena Nketia. 1974. The Music of Africa. W.W. Norton.
Eugene Novotny. 1998. The 3:2 Relationship as the Foundation of Timelines in West African Musics. DMA Dissertation, University of Illinois, Urbana-Champaign.
David Peñalosa. 2009. The Clave Matrix. Afro-Cuban Rhythm: Its Principles and African Origins. Edited by Peter Greenwood. Bembe Books.
Jeff Pressing. 1983. “Cognitive Isomorphisms Between Pitch and Rhythm in World Musics: West Africa, the Balkans and Western Tonality.” Studies in Music 17: 57–61.
_____. 2002. “Black Atlantic Rhythm: Its Computational and Transcultural Foundations.” Music Perception 19/3: 285-310.
Jay Rahn. 1987. “Asymmetrical Ostinatos in Sub-Saharan Music: Time, Pitch, and Cycles Reconsidered.” In Theory Only 9(7): 27–28.
Michael Spiro. 2006. The Conga Drummer’s Guidebook. Sher Music Co.
Chris Stover. 2009. A Theory of Flexible Rhythmic Spaces for Diasporic African Music. PhD Dissertation, University of Washington.
David Temperley. 2000. “Meter and Grouping in African Music: A View from Music Theory.” Ethnomusicology 44: 65–95.
Godfried Toussaint. 2003. “Classification and Phylogenetic Analysis of African Ternary Rhythm Timelines.” Proceedings of BRIDGES: Mathematical Connections in
Art, Music and Science, University of Granada, Spain, 23–26 July: 25–36.
_____. 2015. “Quantifying Musical Meter: How Similar are African and Western Rhythm?” Analytical Approaches to World Music 4(2): 30.
“Alvorada” (Cartola) excerpt; partial transcription
Circular reading of Zuckerkandl’s metric ebb and flow (modifying Zuckerkandl 1959)
away-from
Circular reading of Zuckerkandl’s metric ebb and flow (modifying Zuckerkandl 1959)
away-from
back-to
“Alvorada” (Cartola) excerpt; partial transcription
“Alvorada” (Cartola) excerpt; partial transcription
“Alvorada” (Cartola) excerpt; partial transcription
(
)
(
)
( )
“Alvorada” (Cartola) excerpt; partial transcription
(
)
(
)
( )
“Alvorada” (Cartola) excerpt; partial transcription
(
<0
)
1
(
2
3>
)
( )
“Alvorada” (Cartola) excerpt; partial transcription
(
)
(
)
<0
1
(
)
(
2
3>
)
( )
“Alvorada” (Cartola) excerpt; partial transcription
(
)
(
)
(
)
(
( )
)
<2>
fade
“Alvorada” (Cartola) excerpt; partial transcription
“Alvorada” (Cartola) excerpt; partial transcription
“Alvorada” (Cartola) excerpt; partial transcription
“Alvorada” (Cartola) excerpt; partial transcription
“Alvorada” (Cartola) excerpt; partial transcription
(muted) (open)
“Alvorada” (Cartola) excerpt; partial transcription
(muted) (open)
“Alvorada” (Cartola) excerpt; partial transcription
8-cycle:
4-cycle:
“short” cycle:
(muted) (open)
“long” cycle;
harm. rhythm:
“long” cycle;
vocal phrasing:
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
5) Timelines need not be audibly articulated to function as such.
Three (or Six) Timelines I’m Concerned With Today
Three (or Six) Timelines I’m Concerned With Today
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
5) Timelines need not be audibly articulated to function as such.
6) Timeline spaces unfold as malleable, de-hierarchized strata.
7) Call and response plays a legislative role in constituting timeline spaces.
8) Timeline spaces evoke circularity in a non-trivial way.
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
5) Timelines need not be audibly articulated to function as such.
6) Timeline spaces unfold as malleable, de-hierarchized strata.
7) Call and response plays a legislative role in constituting timeline spaces.
8) Timeline spaces evoke circularity in a non-trivial way.
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
5) Timelines need not be audibly articulated to function as such.
6) Timeline spaces unfold as malleable, de-hierarchized strata.
7) Call and response plays a legislative role in constituting timeline spaces.
8) Timeline spaces evoke circularity in a non-trivial way.
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
5) Timelines need not be audibly articulated to function as such.
6) Timeline spaces unfold as malleable, de-hierarchized strata.
7) Call and response plays a legislative role in constituting timeline spaces.
8) Timeline spaces evoke circularity in a non-trivial way.
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
5) Timelines need not be audibly articulated to function as such.
6) Timeline spaces unfold as malleable, de-hierarchized strata.
7) Call and response plays a legislative role in constituting timeline spaces.
8) Timeline spaces evoke circularity in a non-trivial way.
3-cycle and 4-cycle partitions of (or superimpositions upon) the 12-cycle
3-cycle:
12-cycle:
4-cycle:
3:2 cross-rhythm as foundation of metric structure (after Novotney 1998)
3:2 cross-rhythm as foundation of metric structure (after Novotney 1998)
12-cycle
16-cycle
“tresillo”
Multiply-directed syncopations in son clave
Multiply-directed syncopations in son clave
one tresillo onset
syncopates with 8-cycle
Multiply-directed syncopations in son clave
two tresillo onsets
syncopate with 4-cycle
Multiply-directed syncopations in son clave
two clave onsets
syncopate with tresillo
Multiply-directed syncopations in son clave
three tresillo onsets
syncopate with clave
Multiply-directed syncopations in son clave
one 4-cycle onset
syncopates with
tresillo and clave
one 4-cycle onset
syncopates with
clave only
one 4-cycle onset
syncopates with
tresillo only
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
5) Timelines need not be audibly articulated to function as such.
6) Timeline spaces unfold as malleable, de-hierarchized strata.
7) Call and response plays a legislative role in constituting timeline spaces.
8) Timeline spaces evoke circularity in a non-trivial way.
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
5) Timelines need not be audibly articulated to function as such.
6) Timeline spaces unfold as malleable, de-hierarchized strata.
7) Call and response plays a legislative role in constituting timeline spaces.
8) Timeline spaces evoke circularity in a non-trivial way.
Timeline Spaces: Some Preliminary Definitions
1) Timelines occupy and define a liminal space between meter and rhythm.
2) Timelines are dependent on meter for their identity and function.
3) But they also partially constitute meter; that is, they partially determine how meter
behaves in the music and music-dance contexts within which timelines operate.
4) Timelines only exist within their ecological contexts; when extracted or relocated into
other contexts they lose their identity as timelines.
5) Timelines need not be audibly articulated to function as such.
6) Timeline spaces unfold as malleable, de-hierarchized strata.
7) Call and response plays a legislative role in constituting timeline spaces.
8) Timeline spaces evoke circularity in a non-trivial way.
Paradoxical spaces as a “primordial” axiom?
Paradoxical spaces as a “primordial” axiom?
Paradoxical spaces as a “primordial” axiom?
“He dances…. His movements are generally in small, quick, and irregular patterns. He is
perceived as a divine but mischievous child, or a wise, secretive elder, and so his body
is low to the ground and his gestures shift and change abruptly. His floor pattern
often traces the four cardinal directions or the crossroads. He runs and jumps,
animating all possible space. He powerfully governs opportunities and chances; he opens
doors and closes them. He is both the beginning and the end and is often painted red or
white on one side of his body with the other side revealing his skin to mark his unity
of oppositions. His different…names…are for different paths or aspects of his life
history. Elegba and Elegbara are for his opening dimension; his Echu or Exu name is his
closing dimension; and Ena is his duality. All names signify his activating, energetic
energy. He is Vital Force with any of his names and stimulates movement throughout
his environment.” (Daniel 2005, 138, emph. added)
“Kiriboto” opening (transcription by Chris Stover)
“Kiriboto” opening (transcription by Chris Stover)
slight gap
in phrasing
$
’
’
’
#
grouping
hints at
4-cycle
articulation
(and parallel
8-cycle
stream)
Emerging standard pattern timeline, projecting continuation-implication
q
|
S
q e q q q e q
\
|
S’
“Kiriboto” opening (transcription by Chris Stover)
’
g g
g
’
’
(articulating 2-cycle or 3:2 relation)
g
g
g
g
The timeline space of “Kiriboto”
1) The omele abo timeline partially determines metric impulses and has rhythmic implications in
its performed iteration.
2) It depends on meter through its interactions with (multiple strata of) isochronous pulses,
which interpret the timeline’s variously directed motions.
3) It partially constitutes meter by helping orient us to cycle beginning-points.
4) It is inextricable from the performative environment with which it forms an assemblage.
5) It need not be audibly articulated; viz. we can back-form a sense of timeline space in the
first cycle, before the articulated timeline enters.
6) The various temporal layers are non-hierarchical: all rely ontologically on one another.
7) Call-response behaviors animate the ongoing, emergent context of any given timeline
spaces.
8) This all evinces a sense of circularity.
The timeline space of “Kiriboto”
1) The omele abo timeline partially determines metric impulses and has rhythmic implications in
its performed iteration.
2) It depends on meter through its interactions with (multiple strata of) isochronous pulses,
which interpret the timeline’s variously directed motions.
3) It partially constitutes meter by helping orient us to cycle beginning-points.
4) It is inextricable from the performative environment with which it forms an assemblage.
5) It need not be audibly articulated; viz. we can back-form a sense of timeline space in the
first cycle, before the articulated timeline enters.
6) The various temporal layers are non-hierarchical: all rely ontologically on one another.
7) Call-response behaviors animate the ongoing, emergent context of any given timeline
spaces.
8) This all evinces a sense of circularity.
The timeline space of “Kiriboto”
1) The omele abo timeline partially determines metric impulses and has rhythmic implications in
its performed iteration.
2) It depends on meter through its interactions with (multiple strata of) isochronous pulses,
which interpret the timeline’s variously directed motions.
3) It partially constitutes meter by helping orient us to cycle beginning-points.
4) It is inextricable from the performative environment with which it forms an assemblage.
5) It need not be audibly articulated; viz. we can back-form a sense of timeline space in the
first cycle, before the articulated timeline enters.
6) The various temporal layers are non-hierarchical: all rely ontologically on one another.
7) Call-response behaviors animate the ongoing, emergent context of any given timeline
spaces.
8) This all evinces a sense of circularity.
The timeline space of “Kiriboto”
1) The omele abo timeline partially determines metric impulses and has rhythmic implications in
its performed iteration.
2) It depends on meter through its interactions with (multiple strata of) isochronous pulses,
which interpret the timeline’s variously directed motions.
3) It partially constitutes meter by helping orient us to cycle beginning-points.
4) It is inextricable from the performative environment with which it forms an assemblage.
5) It need not be audibly articulated; viz. we can back-form a sense of timeline space in the
first cycle, before the articulated timeline enters.
6) The various temporal layers are non-hierarchical: all rely ontologically on one another.
7) Call-response behaviors animate the ongoing, emergent context of any given timeline
spaces.
8) This all evinces a sense of circularity.
The timeline space of “Kiriboto”
1) The omele abo timeline partially determines metric impulses and has rhythmic implications in
its performed iteration.
2) It depends on meter through its interactions with (multiple strata of) isochronous pulses,
which interpret the timeline’s variously directed motions.
3) It partially constitutes meter by helping orient us to cycle beginning-points.
4) It is inextricable from the performative environment with which it forms an assemblage.
5) It need not be audibly articulated; viz. we can back-form a sense of timeline space in the
first cycle, before the articulated timeline enters.
6) The various temporal layers are non-hierarchical: all rely ontologically on one another.
7) Call-response behaviors animate the ongoing, emergent context of any given timeline
spaces.
8) This all evinces a sense of circularity.
The timeline space of “Kiriboto”
1) The omele abo timeline partially determines metric impulses and has rhythmic implications in
its performed iteration.
2) It depends on meter through its interactions with (multiple strata of) isochronous pulses,
which interpret the timeline’s variously directed motions.
3) It partially constitutes meter by helping orient us to cycle beginning-points.
4) It is inextricable from the performative environment with which it forms an assemblage.
5) It need not be audibly articulated; viz. we can back-form a sense of timeline space in the
first cycle, before the articulated timeline enters.
6) The various temporal layers are non-hierarchical: all rely ontologically on one another.
7) Call-response behaviors animate the ongoing, emergent context of any given timeline
spaces.
8) This all evinces a sense of circularity.
The timeline space of “Kiriboto”
1) The omele abo timeline partially determines metric impulses and has rhythmic implications in
its performed iteration.
2) It depends on meter through its interactions with (multiple strata of) isochronous pulses,
which interpret the timeline’s variously directed motions.
3) It partially constitutes meter by helping orient us to cycle beginning-points.
4) It is inextricable from the performative environment with which it forms an assemblage.
5) It need not be audibly articulated; viz. we can back-form a sense of timeline space in the
first cycle, before the articulated timeline enters.
6) The various temporal layers are non-hierarchical: all rely ontologically on one another.
7) Call-response behaviors animate the ongoing, emergent context of any given timeline
spaces.
8) This all evinces a sense of circularity.
The timeline space of “Kiriboto”
1) The omele abo timeline partially determines metric impulses and has rhythmic implications in
its performed iteration.
2) It depends on meter through its interactions with (multiple strata of) isochronous pulses,
which interpret the timeline’s variously directed motions.
3) It partially constitutes meter by helping orient us to cycle beginning-points.
4) It is inextricable from the performative environment with which it forms an assemblage.
5) It need not be audibly articulated; viz. we can back-form a sense of timeline space in the
first cycle, before the articulated timeline enters.
6) The various temporal layers are non-hierarchical: all rely ontologically on one another.
7) Call-response behaviors animate the ongoing, emergent context of any given timeline
spaces.
8) This all evinces a sense of circularity.
Thanks for listening!
And a few more references:
Marcos Branda–Lacerda. 1988. Kultische Trommelmusik der Yoruba in der Volksrepublik Benin: Bata-Sango und Bata-Egungun in den
Städten Pobè und Sakété. Verlag der Musikalienhandlung Karl Dieter Wagner.
Barbara Browning. 1995. Samba: Resistance in Motion. Indiana University Press.
Stefania Capone. 2010. Searching for Africa in Brazil: Power and Tradition in Candomblé. Translated by Lucy Lyall Grant. Duke
University Press.
Yvonne Daniel. 1995. Rumba: Dance and Social Change in Contemporary Cuba. Indiana University Press.
Christopher Hasty. 1997. Meter as Rhythm. Oxford University Press.
Fred Lerdahl and Ray Jackendoff. 1983. A Generative Theory of Tonal Music. The MIT Press.
Glaura Lucas. 2002. Os sons do rosário: o congado mineiro dos Arturos e Jatobá. Ed. UFMG.
Dafnis Prieto. 2016. A World of Rhythmic Possibilities. Dafnison Music.
Chris Stover. 2016. “Circularidade: Theorizing Temporality in Afro-Brazilian Popular Song.” Unpublished MS presented at the
New England Conference of Music Theory.
Maury Yeston. 1976. The Stratification of Musical Rhythm. Yale University Press.
Victor Zuckerkandl. 1959. The Sense of Music. Princeton: Princeton University Press.