Appendix: References and Further Reading

The research and analysis in this guide draws on ethnomusicological scholarship, mathematical rhythm theory, and music production science. References are grouped by the chapter where they are first cited.

Nothing in this guide — including the Theory Deep Dives section — is original research. The guide summarises and re-organises the published work below, restated in Poly’s vocabulary for practical use; where a deep-dive page compresses ensemble practice into a rule of thumb that no single source states, the page’s Attribution note says so explicitly.

Chapter 1: Foundations

[1] Toussaint, G. T. (2005). “The Euclidean Algorithm Generates Traditional Musical Rhythms.” Proceedings of BRIDGES: Mathematical Connections in Art, Music, and Science. arXiv:0705.4085

[2] Goldberg, D. (2025). “Music Theory as an Instrument of Nationalism: Notation, Identity, and Systemization in Dobri Hristov’s Conception of Bulgarian Meter.” Music Theory Online, 31(2). MTO

Chapter 2: Sub-Saharan Africa

[4] “Rhythm in Sub-Saharan Africa.” Wikipedia. Link

[6] Jones, A. M. (1959). Studies in African Music. 2 vols. London: Oxford University Press. Review in Africa 30(3)

[7] “Musical Traditions of Sub-Saharan Africa.” Music in Global America. Scalar

[8] Addy, M. T. “Agbekor Dance.” Scribd

[9] Oluranti, S. O. “Polyrhythmic Structures in West African Drumming.” Dissertation, University of Pittsburgh. Link

Chapter 3: Afro-Cuban

[10] “The Clave Rhythm.” YouTube

[11] “Clave Explained.” YouTube

[12] “Piano Montunos: The Complete Guide.” Piano With Jonny. Link

[13] Mauleón, R. “Rhythmic Styles and Structures.” Sher Music. Sample pages

Chapter 4: Afrobeat

[14] “Fela Kuti: Afrobeat Creator.” YouTube

[15] “The Genius of Fela Kuti.” YouTube

[16] “Afro House Explained: Rhythm, Culture, and Production Techniques.” Samplesound. Link

[17] “Afro House Production Guide.” Lian Productions. Link

Chapter 5: Gamelan

[18] “Algorithmic Thinking and the Art of Javanese Gamelan.” Oxford Academic. Link

[19] “Ladrang Pangkur: Colotomic Structure in Javanese Gamelan.” Oxford University Press. Link

[20] Yudane. “Introduction to Balinese Gamelan.” Gamelan New Zealand. PDF

Chapter 6: Indian Classical

[21] “The Silent Language of Taal: Exploring Philosophical Underpinnings of Tala in Indian Classical Music.” Artium Academy. Link

[22] “Hindustani Music Theory.” National Institute of Open Schooling (NIOS). PDF

[23] Reindl, M. “Indian Rhythmic Systems in Comparative Perspective.” Journal of the International Folk Art and World Music Society. PDF

[24] “Konnakol: Algorithmic Pattern and Oral Composition.” Algorithmic Pattern. Link

[25] “Konnakol Mastery.” YouTube

Chapter 7: Balkan

[26] “Balkan Folk Music: Complex Rhythms and Vocal Techniques.” Fiveable. Link

[27] “Balkan Dance Rhythms.” Chromatone. Link

[28] Holzapfel, A. “Metrical Structure in Turkish Makam Music.” DiVA Portal. PDF

[29] Holzapfel, A. “Metrical Strength and Syncopation Distribution in Turkish Usul.” DiVA Portal. PDF

[30] “Structures of Rhythm in Mevlevi Music: A Cyclical Analysis Model.” Academia. Link

[31] Aji, I. “Arab Rhythmic Cycles (Iqa’at).” TNP / MTSNYS. Link

Chapter 8: Minimalism

[32] “Steve Reich.” Wikipedia. Link

[33] “The Story of Minimalism: A New Way of Listening.” All Classical Portland. Link

[34] Reich, S. “Music as a Gradual Process, Part II.” PDF

[35] Scherzinger, M. “Piano Phase in Global Perspective.” PDF

Chapter 9: Electronic

[36] “Roger Linn on Drum Machine Groove and J Dilla’s Off-Beat Sound.” Brettworks. Link

[37] “In Praise of the Akai MPC: A Hip-Hop Time Machine.” Noise Machines Studio. Link

[38] Hein, E. (2023). “Building the Amen Break.” Ethan Hein Blog. Link

[39] “Shaping Rhythm, Timing, and Sound in Five Groove-Based Genres.” Popular Music, Cambridge University Press. PDF

[40] “L’analyse des ensembles microrythmiques dans l’Intelligent Dance Music.” Revue musicale OICRM. Link

[41] “Rhythmic Ambiguity in Aphex Twin.” Érudit / Circuit: Musiques contemporaines. PDF

Chapter 10: Brazilian

[42] Schloss, A. “The Brazilian Groove: Ginga and Rhythmic Feel.” University of Victoria. PDF

[43] “Baião (music).” Wikipedia. Link

Chapter 14: Synthesis

[44] Gotham, M. (2013). “Review: Toussaint, The Geometry of Musical Rhythm.” Music Theory Online, 19(2). MTO

Chapter 15: Compositional Grammar

Chapter 1: Foundations (additional)

[46] Bjorklund, E. (2003). “The Theory of Rep-Rate Pattern Generation in the SNS Timing System.” Technical Note SNS-NOTE-CNTRL-100, Los Alamos National Laboratory. The original paper describing the pulse-distribution algorithm that Toussaint later identified with world rhythm. Semantic Scholar

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Further Reading

A curated bibliography beyond the numbered citations above, grouped by the chapter each source deepens. These are the works to consult for the music theory behind idiomatic counterpoint in each tradition.

Foundations and Cross-Cultural Rhythm Theory (Chapter 1)

• Toussaint, G. T. (2013). The Geometry of Musical Rhythm: What Makes a “Good” Rhythm Good? CRC Press.
• London, J. (2012). Hearing in Time: Psychological Aspects of Musical Meter, 2nd ed. Oxford University Press. — The theory of non-isochronous meters; the theoretical frame behind both aksak and tala.
• Pressing, J. (2002). “Black Atlantic Rhythm: Its Computational and Transcultural Foundations.” Music Perception, 19(3). — Why the shared timelines of the Black Atlantic have common cognitive properties.

Sub-Saharan Africa (Chapter 2)

• Arom, S. (1991). African Polyphony and Polyrhythm: Musical Structure and Methodology. Cambridge University Press.
• Locke, D. (1998). Drum Gahu: An Introduction to African Rhythm. White Cliffs Media.
• Locke, D. (1982). “Principles of Offbeat Timing and Cross-Rhythm in Southern Ewe Dance Drumming.” Ethnomusicology, 26(2). — How support parts are placed against the bell timeline.
• Chernoff, J. M. (1979). African Rhythm and African Sensibility. University of Chicago Press. — The ensemble-social logic behind timeline, support, and lead roles.
• Anku, W. (2000). “Circles and Time: A Theory of Structural Organization of Rhythm in African Music.” Music Theory Online, 6(1). — A circular, set-theoretic model of African rhythm close in spirit to Poly’s cycle model.
• Polak, R. (2010). “Rhythmic Feel as Meter: Non-Isochronous Beat Subdivision in Jembe Music from Mali.” Music Theory Online, 16(4). — Measured microtiming showing jembe subdivision is systematically uneven.
• Polak, R. & London, J. (2014). “Timing and Meter in Mande Drumming from Mali.” Music Theory Online, 20(1).
• Novotney, E. (1998). “The 3:2 Relationship as the Foundation of Timelines in West African Musics.” PhD dissertation, University of Illinois.
• Agawu, K. (2006). “Structural Analysis or Cultural Analysis? Competing Perspectives on the ‘Standard Pattern’ of West African Rhythm.” Journal of the American Musicological Society, 59(1).
• Charry, E. (2000). Mande Music: Traditional and Modern Music of the Maninka and Mandinka of Western Africa. University of Chicago Press. — Jembe drumming is one of its four surveyed spheres; cited for what Manding ensemble practice actually is, against the guide’s same-cycle simplification.
• Kubik, G. (1999). Africa and the Blues. University Press of Mississippi. — Traces African rhythmic retentions through the Western and Central Sudanic belt; cited for the thread running from Chapter 2 to Chapter 4.
• Agawu, K. (2003). Representing African Music: Postcolonial Notes, Queries, Positions. Routledge. — A critique of how African music is written about and by whom. Distinct from Agawu (2006) below, which argues a narrower methodological point about structural versus cultural analysis; cited where the guide frames the African–minimalist connection.

Afro-Cuban (Chapter 3)

• Acosta, L. (2003). Cubano Be, Cubano Bop: One Hundred Years of Jazz in Cuba. Smithsonian Books. — Covers the Cuban presence in New Orleans and the “Spanish tinge” in early jazz there; cited for the historical depth behind how clave practice travelled.
• Peñalosa, D. (2009). The Clave Matrix: Afro-Cuban Rhythm — Its Principles and African Origins. Bembe Books. — The definitive treatment of clave alignment rules.
• Mauleón, R. (1993). Salsa Guidebook for Piano and Ensemble. Sher Music.
• Uribe, E. (1996). The Essence of Afro-Cuban Percussion and Drum Set. Warner Bros. — Practical part-by-part idiom: cascara, tumbao, conga marcha.
• Washburne, C. (1997). “The Clave of Jazz: A Caribbean Contribution to the Rhythmic Foundation of an African-American Music.” Black Music Research Journal, 17(1).
• Lomax, A. (1950). Mister Jelly Roll: The Fortunes of Jelly Roll Morton, New Orleans Creole and “Inventor of Jazz”. Duell, Sloan and Pearce. — The Library of Congress interviews in which Morton describes the “Spanish tinge”.

Afrobeat (Chapter 4)

• Allen, T. with Veal, M. E. (2013). Tony Allen: An Autobiography of the Master Drummer of Afrobeat. Duke University Press.
• Veal, M. (2000). Fela: The Life and Times of an African Musical Icon. Temple University Press.

Gamelan (Chapter 5)

• Tenzer, M. (2000). Gamelan Gong Kebyar: The Art of Twentieth-Century Balinese Music. University of Chicago Press. — The authoritative analysis of kotekan varieties.
• Vitale, W. (1990). “Kotekan: The Technique of Interlocking Parts in Balinese Music.” Balungan, 4(2). — Short and practical; shows real kotekan is not a pure set complement.
• Sumarsam (1995). Gamelan: Cultural Interaction and Musical Development in Central Java. University of Chicago Press. — Colotomic structure and irama levels.

Indian Classical (Chapter 6)

• Powers, H. (1980). “India, subcontinent of”. The New Grove Dictionary of Music and Musicians, vol. 9, ed. S. Sadie. Macmillan. — The standard survey of Indian art-music theory across the subcontinent; cited for the wider frame this guide narrows from.
• Clayton, M. (2000). Time in Indian Music: Rhythm, Metre, and Form in North Indian Rāg Performance. Oxford University Press. — The scholarly standard on tala, laya, and sam.
• Nelson, D. (2008). Solkattu Manual. Wesleyan University Press. — Carnatic rhythmic construction, including the tihai/mora arithmetic.
• Kippen, J. (1988). The Tabla of Lucknow. Cambridge University Press. — Theka elaboration practice.

Balkan (Chapter 7)

• Silverman, C. (2007). “Bulgarian Wedding Music between Folk and Chalga: Politics, Markets and Current Directions”. Muzikologija. — Traces svatbarska muzika from its suppression under state socialism to its post-socialist decline against chalga; cited for the tradition’s history rather than its metrics.
• Peycheva, L. & Dimov, V. (2002). The Zurna Tradition in Southwest Bulgaria: Romani Musicians in Practice. Bŭlgarsko muzikoznanie. — Existence, authors, year, title and series confirmed from catalogue records; contents unverified, the work being in Bulgarian and no translation yet obtained. Listed because the scholarship on Romani professional practice in Bulgaria is relevant to Chapter 7’s subject; no claim in this guide currently rests on it.
• Brăiloiu, C. (1951). “Le rythme aksak.” Revue de Musicologie, 33. — The origin of the term and the two/three-cell theory of additive meter.
• Rice, T. (1994). May It Fill Your Soul: Experiencing Bulgarian Music. University of Chicago Press.
• Goldberg, D. (2015). “Timing Variations in Two Balkan Percussion Performances.” Empirical Musicology Review, 10(4). — Measured evidence that aksak “long” beats are not exactly 3:2.
• Holzapfel, A. (2015). “Metrical Structure in Turkish Makam Music.” DiVA Portal.

Minimalism (Chapter 8)

• Reich, S. (2002). Writings on Music, 1965–2000. Oxford University Press.
• Cohn, R. (1992). “Transpositional Combination of Beat-Class Sets in Steve Reich’s Phase-Shifting Music.” Perspectives of New Music, 30(2). — The formal theory of which phase relationships produce which composite rhythms; a design guide for Drift.
• Potter, K. (2000). Four Musical Minimalists. Cambridge University Press.
• Gann, K. (1995). The Music of Conlon Nancarrow. Cambridge University Press. — Tempo-ratio counterpoint, the model behind the per-lane tempo multiplier.
• Scherzinger, M. (2010). “Piano Phase in Global Perspective.” Proceedings of the ICTM.

Electronic and Drum & Bass (Chapters 9, 13)

• Harrison, N. (2025). “Reflections on the Amen Break: A Continued History, an Unsettled Ethics”. In The Routledge Companion to Remix Studies, 2nd ed., eds. E. Navas, O. Gallagher & x. burrough. Routledge. — By the maker of the 2004 work that first documented the break’s history; cited for that history and for the sampling ethics around it, not for a count of uses.
• Linn, R., interviewed in Attack Magazine (2020). “Roger Linn On Swing, Groove & The Magic Of The MPC’s Timing”. — Linn describing the LM-1 mechanism in his own words: quantise each beat to the nearest step, then delay the playback of every other step. Tier B as a professional publication interviewing the primary actor rather than scholarship; cited in preference to commentary quoting it second-hand.
• Butler, M. J. (2006). Unlocking the Groove: Rhythm, Meter, and Musical Design in Electronic Dance Music. Indiana University Press.
• Danielsen, A., ed. (2010). Musical Rhythm in the Age of Digital Reproduction. Ashgate. — Microrhythm in programmed music.
• Collins, N. (2001). “Algorithmic Composition Methods for Breakbeat Science.” Proceedings of Music Without Walls. — Generative breakbeat chopping.
• Reynolds, S. (1998). Energy Flash: A Journey Through Rave Music and Dance Culture. Picador.

Brazilian (Chapter 10)

• Crook, L. (2009). Focus: Music of Northeast Brazil, 2nd ed. Routledge. — Its Afro-Brazilian traditions chapter covers Candomblé, afoxé and maracatu; cited for the baque virado ensemble and its parts.
• Sandroni, C. (2001). Feitiço Decente: Transformações do Samba no Rio de Janeiro, 1917–1933. Jorge Zahar. — The canonical analysis of samba’s rhythmic paradigms (in Portuguese).
• Gerischer, C. (2006). “O Suingue Baiano: Rhythmic Feeling and Microrhythmic Phenomena in Brazilian Percussion.” Ethnomusicology, 50(1). — Measured samba microtiming.
• Naveda, L., Gouyon, F., Guedes, C. & Leman, M. (2011). “Microtiming Patterns and Interactions with Musical Properties in Samba Music.” Journal of New Music Research, 40(3). — Quantifies the long-short-short-long sixteenth-note profile of samba.
• Fryer, P. (2000). Rhythms of Resistance: African Musical Heritage in Brazil. Pluto Press.

Synthesis (Chapter 14)

• Born, G. & Hesmondhalgh, D., eds. (2000). Western Music and Its Others: Difference, Representation, and Appropriation in Music. University of California Press. — An edited collection on musical borrowing and on how music is used to represent difference; cited for the framing this chapter needs rather than for any single finding.

Funk, Soul, and Jazz (Chapters 11, 12)

• Danielsen, A. (2006). Presence and Pleasure: The Funk Grooves of James Brown and Parliament. Wesleyan University Press. — The book on the One, the pocket, and funk microrhythm.
• Stewart, A. (2000). “‘Funky Drummer’: New Orleans, James Brown and the Rhythmic Transformation of American Popular Music.” Popular Music, 19(3).
• Berliner, P. (1994). Thinking in Jazz: The Infinite Art of Improvisation. University of Chicago Press.
• Monson, I. (1996). Saying Something: Jazz Improvisation and Interaction. University of Chicago Press. — Comping as conversation, the model behind Mutation.
• Riley, J. (1994). The Art of Bop Drumming. Manhattan Music. — Practical comping vocabulary.
• Keil, C. (1987). “Participatory Discrepancies and the Power of Music.” Cultural Anthropology, 2(3). — The coinage and original theory of ensemble timing discrepancies as constitutive of groove.
• Friberg, A. & Sundström, A. (2002). “Swing Ratios and Ensemble Timing in Jazz Performance.” Music Perception, 19(3). — Swing ratio varies from roughly 3.5:1 at slow tempi toward 1:1 at 300 BPM.
• Benadon, F. (2006). “Slicing the Beat: Jazz Eighth-Notes as Expressive Microrhythm.” Ethnomusicology, 50(1).
• Prögler, J. A. (1995). “Searching for Swing: Participatory Discrepancies in the Jazz Rhythm Section.” Ethnomusicology, 39(1). — Bass/drums timing counterpoint.

Microtiming and Groove Science (cross-chapter)

• Iyer, V. (2002). “Embodied Mind, Situated Cognition, and Expressive Microtiming in African-American Music.” Music Perception, 19(3).
• Hennig, H. et al. (2011). “The Nature and Perception of Fluctuations in Human Musical Rhythms.” PLoS ONE, 6(10). — Human timing fluctuations are long-range correlated (1/f), not white noise; the case against naive humanization.