Appendix: References

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 is original research. The guide summarises and re-organises the published work below, restated in Poly’s vocabulary for practical use; where a chapter compresses ensemble practice into a rule of thumb that no single source states, it says so explicitly.

What this bibliography cites. The guide does not cite Wikipedia. It is reviewable and often a fair summary, but it summarises other sources, and a claim in this guide names the source itself. Nor does it cite a video: a video may be excellent and still has no text a reader can check against the claim it is cited for.

A source is judged by what it is rather than by its tier. The guide does not cite course material, a commercial or marketing page, or a blog; a practitioner’s own text may be cited, at Tier B, with the reason it stands recorded beside it.

Foundations and Cross-Cultural Rhythm Theory (Chapter 1)

• [1] Toussaint, G. T. (2005). “The Euclidean Algorithm Generates Traditional Musical Rhythms.” Proceedings of BRIDGES: Mathematical Connections in Art, Music, and Science, 47–56. PDF (Open access)
• [46] Bjorklund, E. (2003). “The Theory of Rep-Rate Pattern Generation in the SNS Timing System.” Technical Note SNS-NOTE-CNTRL-99, Los Alamos National Laboratory. The original paper describing the pulse-distribution algorithm that Toussaint later identified with world rhythm. Semantic Scholar (Free online)
• Toussaint, G. T. (2013). The Geometry of Musical Rhythm: What Makes a “Good” Rhythm Good? CRC Press. ISBN 9781466512023 (Borrowable)

Sub-Saharan Africa (Chapter 2)

• [6] Jones, A. M. (1959). Studies in African Music. 2 vols. London: Oxford University Press. Borrowable scan · Review of the book in Africa 30(3) (Borrowable)
• Locke, D. (1982). “Principles of Offbeat Timing and Cross-Rhythm in Southern Ewe Dance Drumming.” Ethnomusicology, 26(2), 217–246. JSTOR — How support parts are placed against the bell timeline. (Purchasable)
• 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. ISBN 9780226101637 (Purchasable)
• 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. ISBN 9781578061464 (Borrowable)
• 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. ISBN 9780415943901 (Purchasable)

Central Africa (Chapter 2b)

• Arom, S. (1991). African Polyphony and Polyrhythm: Musical Structure and Methodology. Cambridge University Press. ISBN 9780521616010 (Purchasable)

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. ISBN 9781588341471 (Purchasable)
• Peñalosa, D. (2009). The Clave Matrix: Afro-Cuban Rhythm — Its Principles and African Origins. Bembe Books. — The definitive treatment of clave alignment rules. ISBN 9781886502802 (Purchasable)
• Mauleón, R. (1993). Salsa Guidebook for Piano and Ensemble. Sher Music. ISBN 0961470194 (Purchasable)
• 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”. ISBN 9780520024021 (Borrowable)

Afrobeat (Chapter 4)

• Allen, T. with Veal, M. E. (2013). Tony Allen: An Autobiography of the Master Drummer of Afrobeat. Duke University Press. ISBN 9780822355915 (Purchasable)
• Veal, M. (2000). Fela: The Life and Times of an African Musical Icon. Temple University Press. ISBN 9780585366739 (Purchasable)

Gamelan (Chapter 5)

• [18] “Algorithmic Thinking and the Art of Javanese Gamelan.” Oxford Academic. Link (Purchasable)
• Tenzer, M. (2000). Gamelan Gong Kebyar: The Art of Twentieth-Century Balinese Music. University of Chicago Press. — The authoritative analysis of kotekan varieties. ISBN 9780226792811 (Borrowable)
• Vitale, W. (1990). “Kotekan: The Technique of Interlocking Parts in Balinese Music.” Balungan, 4(2). PDF — Short and practical; shows real kotekan is not a pure set complement. (Open access)

Indian Classical (Chapter 6)

• Qureshi, R., Powers, H. S., Katz, J., Widdess, R. et al. (2001). “India, subcontinent of”. Grove Music Online. Oxford University Press. DOI — The standard survey of Indian art-music theory across the subcontinent; cited for the wider frame this guide narrows from, and for its “Rhythm and tāla” section in particular. This is the 2001 second-edition rewrite of Powers’s 1980 New Grove article of the same title, which the anchor still names; the rewrite is the version a reader can reach. (Purchasable)
• 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. ISBN 9780198166863 (Borrowable)
• Nelson, D. (2008). Solkattu Manual. Wesleyan University Press. — Carnatic rhythmic construction, including the tihai/mora arithmetic. ISBN 9780819568717 (Purchasable)
• Kippen, J. (1988). The Tabla of Lucknow. Cambridge University Press. — Theka elaboration practice. ISBN 9780521335294 (Borrowable)

Balkan (Chapter 7)

• Silverman, C. (2007). “Bulgarian Wedding Music between Folk and Chalga: Politics, Markets and Current Directions”. Muzikologija, 7. — 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. Issue 7, from p. 69 (Open access)
• Brăiloiu, C. (1951). “Le rythme aksak.” Revue de Musicologie, 33(99/100), 71–108. JSTOR — The origin of the term and the two/three-cell theory of additive meter. (Purchasable)
• Rice, T. (1994). May It Fill Your Soul: Experiencing Bulgarian Music. University of Chicago Press. ISBN 9780226711225 (Purchasable)
• 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. DOI (Open access)

Minimalism (Chapter 8)

• [34] Schwarz, K. R. (1981–82). “Steve Reich: Music as a Gradual Process Part II.” Perspectives of New Music, 20(1/2), 225–286. JSTOR · PDF (Open access)
• [35] Scherzinger, M. “Piano Phase in Global Perspective.” PDF (Free online)
• Cohn, R. (1992). “Transpositional Combination of Beat-Class Sets in Steve Reich’s Phase-Shifting Music.” Perspectives of New Music, 30(2). ResearchGate · JSTOR — The formal theory of which phase relationships produce which composite rhythms; a design guide for Drift. (Free online)
• Potter, K. (2000). Four Musical Minimalists. Cambridge University Press. ISBN 9780521482509 (Borrowable)
• Scherzinger, M. (2018). “Steve Reich’s ‘Piano Phase’ in Global Perspective: Myths & Realities.” In J. P. Hiekel (Ed.), Clash! Generationen – Kulturen – Identitäten in der Gegenwartsmusik (pp. 144–163). Mainz: Schott. PDF (Free online)

Electronic and Drum & Bass (Chapters 9, 13)

• [39] “Shaping Rhythm, Timing, and Sound in Five Groove-Based Genres.” Popular Music, Cambridge University Press. PDF (Free online)
• 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. Book · Chapter DOI — 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. (Purchasable)
• Scarth, G., & Linn, R. (2013). “Roger Linn on Swing, Groove & the Magic of the MPC’s Timing.” Attack Magazine. Link — 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. (Open access)
• Butler, M. J. (2006). Unlocking the Groove: Rhythm, Meter, and Musical Design in Electronic Dance Music. Indiana University Press. ISBN 9780253346629 (Borrowable)

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. ISBN 9780415960656 (Purchasable)
• 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). ISBN 9788571106062 (Purchasable)
• Fryer, P. (2000). Rhythms of Resistance: African Musical Heritage in Brazil. Pluto Press. ISBN 9780745303833 (Borrowable)

Synthesis (Chapter 14)

• [44] Gotham, M. (2013). “Review: Toussaint, The Geometry of Musical Rhythm.” Music Theory Online, 19(2). MTO (Open access)
• 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. ISBN 9780520220843 (Purchasable)

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

• Monson, I. (1996). Saying Something: Jazz Improvisation and Interaction. University of Chicago Press. — Comping as conversation, the model behind Mutation. ISBN 9780226534787 (Borrowable)