Last update: March 1, 2026.

1 Biography

Francisco Gómez became Full Professor at the Technical University of Madrid in 1994. He started doing research on computational geometry, computer graphics and facility location. In fact, he was one of the founders of the Madrid Computational Geometry Group. In 2003 he switched to Music Information Retrieval and Computational Music Theory and has been doing research in this field since then.

Francisco Gómez received a Ph.D. in Computer Science from the Technical University of Madrid under the supervision of Godfried Toussaint (McGill University). He obtained an M.Sc. in Mathematics from Universidad Autónoma de Madrid.

He teaches courses on Computer Graphics, Computational Geometry, Statistics, Algebra, Discrete Mathematics, and Pattern Recognition, among others.

 

2 Academic Degrees

• M.Sc. in Mathematics from Universidad Autónoma de Madrid (major in Topology and Statistics).
• Ph.D. in Computer Science from the Technical University of Madrid under the supervision of Godfried Toussaint (McGill University).

 

3 Positions

1. Department of Mathematics and Statistics, Georgia State University. Visiting Professor (Jan–Jun 2016; Aug–Dec 2017).
2. School of Computer Science and CIRMMT, McGill University. Visiting Professor (Jun–Aug 2010).
3. School of Computer Science and CIRMMT, McGill University. Visiting Professor (Mar–Aug 2009).
4. Affiliate member, Centre for Interdisciplinary Research in Music Media and Technology, McGill University (since April 2009).
5. Technical University of Madrid. Full Professor (since 2008).
6. McGill University. Visiting Professor (Sep 2006–Aug 2007).
7. Technical University of Madrid. Assistant Professor (1991–1994), Full Professor (since 1994).
8. Technical University of Madrid, Industrial Engineering. Associate Professor (1989–1991).
9. Accenture (Arthur Andersen Consulting). Programmer and system analyst (1988–1989).

 

4 Teaching

• He has developed his own method, Integrated Active Learning (A2I), based on inquiry-based learning and integrating emotional and moral dimensions of learning. It combines elements of the Moore method (collaborative version), Mazur method, writing-based learning, and problem-based learning. Students explain theory to each other, work in carefully designed groups, and are not allowed to use external material in class.
• He teaches Discrete Mathematics in the Mathematics degree at UPM. Between 2022 and 2024 he taught Discrete Mathematics. In 2026–27 he taught Foundations of Mathematics.
• He has also taught in the Data Science and Artificial Intelligence degree at UPM (Discrete Mathematics and Calculus).
• In Computer Science degrees (ETSISI) he has taught Discrete Mathematics, Mathematical Analysis, Statistics, Algebra, Operations Research, Digital Signal Processing, Coding Theory, and Cryptography.
• During the pandemic he created a YouTube channel with lectures on Logic and Discrete Mathematics: link

5 Research Interests

Francisco Gómez initially worked in computational geometry and later shifted to computational music theory and music technology.

His main research interests are:

• Mathematical theory of scales, especially multi-octave scales;
• Computational models of the operatic voice;
• Algebraic models of tonality and harmony;
• Similarity measures, including rhythmic and melodic similarity;
• Phylogenetic analysis of music;
• Mathematical measures of rhythmic complexity and syncopation;
• Transformations of rhythm and melody;
• Automatic analysis of traditional music, especially flamenco, Afro-Cuban, Brazilian, and African music;
• Mathematical theory of rhythm;
• Mathematical and computational modeling of musical phenomena (grouping, phrasing, tension, etc.);
• Teaching mathematics through art;
• Active learning methods, including the Moore method, Mazur method, writing-based learning, and emotional classroom management.

Francisco Gómez has three recognized research periods (sexenios).

 

6 Research Projects

• TEIMUS. A multidisciplinary project involving musicians, musicologists, ethnomusicologists, mathematicians, and computer scientists. It studies musical patterns, corpora, and cognition. Funded by UNIR.
• Computational Analysis of Flamenco Music. Junta de Andalucía (P12-TIC-1362).
• Genesis and Evolution of Flamenco Music: An Interdisciplinary Computational Study. Junta de Andalucía (TIC-4840).
• Computational Analysis of Flamenco Melody. Junta de Andalucía.
• Computational Analysis of Flamenco Musical Structure. Junta de Andalucía.
• Geometric Optimization for Classification Problems. Ministerio de Ciencia y Tecnología.
• Perception of Rhythmic Similarity in Flamenco Music. CIRMMT, McGill University.
• European Research Network on Processing Open Cultural Heritage. European Commission.
• Foundations and Applications of Discrete Mathematics to Geometry. CYCIT.
• Combinatorial Structures in Geometry. CYCIT.

 

7 Peer-reviewed Publications

1. Pascual-Crowley, Emmet; Gómez-Martín, F. (2025). Non-octave-repeating as a form of tonal organization. Per Musi. link
2. Pascual-Crowley, Emmet; Gómez-Martín, F. (2023). Structural properties of multi-octave scales. Journal of Mathematics and Music. doi
3. Gómez-Martín, F.; Tizón, M.; Arronte Alvarez, A.; Padilla, V. (2023). Rhetorical Pattern Finding. International Journal of Interactive Multimedia and Artificial Intelligence. doi
4. Gómez-Martín, F. (2022). A review of Godfried Toussaint's The Geometry of Musical Rhythm. Journal of Mathematics and Music.
5. Arronte Álvarez, A.; Gómez, F. (2021). Motivic Pattern Classification of Music Audio Signals Combining Residual and LSTM Networks. International Journal of Interactive Multimedia and Artificial Intelligence. doi
6. Tizón Díaz, M.; Gómez Martín, F. (2020). La influencia del estilo musical en la emoción percibida. Revista Electrónica Complutense de Investigación en Educación Musical (RECIEM). doi
7. Gómez, F. (2018). Matherhythm: Lessons on divisibility and rhythm. En Theoretical and practical pedagogy of mathematical music theory. World Scientific.
8. Gómez, F. (2018). Flamenco music and its computational study. En Mathematical Music Theory. World Scientific.
9. Oramas, S.; Espinosa-Anke, L.; Gómez, F.; Serra, X. (2018). Natural Language Processing for Music Knowledge Discovery. Journal of New Music Research. doi
10. Kroher, N.; Gómez, E.; Chaachoo, A.; Sordo, M.; Gómez, F.; Mora, J.; Díaz-Báñez, J.M. (2018). Computational Ethnomusicology: A Study of Flamenco and Arab-Andalusian Vocal Music. En Handbook of Systematic Musicology. Springer.
11. Mora, J.; Gómez, F.; Gómez, E.; Díaz-Báñez, J.M. (2016). Melodic Contour and Mid-Level Global Features Applied to the Analysis of Flamenco Cantes. Journal of New Music Research. doi
12. Montiel, M.; Gómez, F. (2014). Music in the pedagogy of mathematics. Journal of Mathematics and Music.
13. Gómez, F.; Talaskian, P.; Toussaint, G.T. (2009). Interlocking and Euclidean Rhythms. Journal of Mathematics and Music.
14. Gómez, F.; Talaskian, P.; Toussaint, G.T. (2009). Structural Properties of Euclidean Rhythms. Journal of Mathematics and Music.
15. Guastavino, C.; Gómez, F.; Toussaint, G.; Marandola, F.; Gómez, E. (2009). Measuring Similarity between Flamenco Rhythmic Patterns. Journal of New Music Research.
16. Demaine, E.; Gómez, F.; Meijer, H.; Rappaport, D.; Taslakian, P.; Toussaint, G.T.; Winograd, T.; Wood, D.R. (2009). The Distance Geometry of Music. Computational Geometry: Theory and Application.
17. Colannino, J.; Gómez, F.; Toussaint, G.T. (2009). Analysis of Emergent Beat-Class Sets in Steve Reich’s Clapping Music and the Yoruba Bell Timeline. Perspectives of New Music.
18. Díaz-Báñez, J.M.; Gómez, J.M.; Farigu, G.; Gómez, F.; Rappaport, D.; Toussaint, G.T. (2005). Similaridad y evolución en la rítmica del flamenco. La Gaceta de la RSME.
19. Díaz-Báñez, J.M.; Gómez, F.; Ventura, I. (2006). The anchored Voronoi diagram. International Journal of Computational Geometry and Applications.
20. Gómez, P.; Hurtado, F.; Ramaswami, S.; Sacristán, V.; Toussaint, G. (2002). Implicit Convex Polygons. Journal of Mathematical Modelling and Algorithms.
21. Aloupis, G.; Cortes, C.; Gómez, F.; Soss, M.; Toussaint, G. (2002). Lower bounds for computing statistical depth. Computational Statistics and Data Analysis.
22. Gómez, P.; Ramaswami, S.; Toussaint, G. (2002). General position views of data. Journal of Visual Communication and Image Representation.
23. Gómez, P.; Hurtado, F.; Sellares, T.; Toussaint, G. (2001). Degeneracies removable by perspective projections. International Journal of Mathematical Algorithms.
24. Gómez, P.; Hurtado, F.; Sellares, J.A.; Toussaint, G. (2001). Nice perspective projections. Journal of Visual Communication and Image Representation.
25. Díaz-Báñez, J.M.; Gómez, P.; Hurtado, F. (2000). Approximation of point sets. INFORMS Journal of Computing.
26. Bose, P.; Gómez, P.; Ramos, P.; Toussaint, G. (1999). Drawing nice projections. Journal of Visual Communication and Image Representation.

 

8 Conference Papers

1. Crowley, E.; Gómez Martín, F. (2026). Diatonic chromaticism: Chords-scale relationship in non-octave-repeating scales applied in jazz improvisation. Music Theory and Education through the Ages, Real Conservatorio de La Haya.
2. Spector, J.; Mannone, M.; Montiel, M.; Gómez, F. (2024). Voice and Math: The Art of Singing in Light of Mathematical Music Theory. MCM 2024, LNCS, Springer. doi
3. Del Pozo, I.; Gómez-Martín, F. (2022). Mathematical models of tonal function (II): modulation. MCM 2022, LNCS.
4. Del Pozo, I.; Gómez-Martín, F. (2022). Mathematical models of tonal function (I): voice leadings. MCM 2022, LNCS.
5. Arronte Álvarez, A.; Gómez-Martín, P. (2019). An Attentional Neural Network Architecture for Folk Song Classification. International Computer Music Conference.
6. Arronte-Álvarez, A.; Gómez, F. (2019). Distributed vector representations of folksong motifs. MCM 2019, LNCS.
7. Del Pozo, D. I.; Gómez, F. (2019). Formalization of voice-leadings and the nabla algorithm. MCM 2019, LNCS.
8. Padilla, V.; Tizón, M.; Gómez, F.; Espigares, M.; Alonso, E. (2018). Towards an Automatic Detection of Rhetorical Patterns in the Renaissance Polyphonic Music. MUME 2018.
9. Oramas, S.; Gómez, F.; Gómez, E.; Mora, J. (2015). FlaBase: Towards the creation of a flamenco music knowledge base. ISMIR 2015.
10. Kroher, N.; Gómez, E.; Guastavino, C.; Gómez, F.; Bonada, J. (2014). Computational models for perceived melodic similarity in a cappella flamenco cantes. ISMIR 2014.
11. Gómez, F.; Díaz-Báñez, J. M.; Gómez, E.; Mora, J. (2014). Flamenco music and its computational study. BRIDGES 2014.
12. Tizón, M.; Gómez, F.; Oramas, S. (2014). Does always the Phrygian mode elicit responses of negative valence?. Folk Music Analysis Workshop.
13. Kroher, N.; Gómez, E.; Sordo, M.; Gómez-Martín, F.; Díaz-Báñez, J.M.; Mora, J. (2014). Computational ethnomusicology: a study of flamenco and Arab-Andalusian vocal music. Folk Music Analysis Workshop.
14. Tizón, M.; Gómez, F.; Oramas, S. (2013). Perceived emotion in Phrygian mode in musically trained children. ICME.
15. Pikrakis, A.; Gómez, F.; Oramas, S.; Gómez, E.; Mora, J.; Díaz-Báñez, J. M.; Escobar, F.; Salamon, J. (2012). Tracking melodic patterns in flamenco singing. ISMIR 2012.
16. Gómez, E.; Guastavino, C.; Gómez, F.; Bonada, J. (2012). Analyzing melodic similarity judgements in flamenco a cappella singing. ICMPC.
17. Gómez, F.; Pikrakis, A.; Mora, J.; Díaz-Báñez, J. M.; Gómez, E.; Escobar, F.; Oramas, S.; Salamon, J. (2012). Automatic detection of melodic patterns in flamenco singing. Folk Music Analysis Workshop.
18. Mora, J.; Gómez, F.; Gómez, E.; Escobar, F.; Díaz-Báñez, J. M. (2011). An integrated analysis of flamenco music. Folk Music Analysis Workshop.
19. Mora, J.; Gómez, F.; Gómez, E.; Escobar, F.; Díaz-Báñez, J. M. (2010). Characterization and melodic similarity of a cappella flamenco cantes. ISMIR 2010.
20. Gerofsky, S.; Gómez, F.; Rappaport, D.; Toussaint, G. (2009). Spirograph patterns and circular representations of rhythm. BRIDGES 2009.
21. Ballinger, B.; Benbernou, N.; Gómez, F.; O’Rourke, J.; Toussaint, G. (2009). The continuous hexachordal theorem. MCM 2009.
22. Gómez, F.; Taslakian, P.; Toussaint, G. (2008). Convergence of the shadow sequence of inscribed polygons. Fall Workshop on Computational Geometry.
23. Guastavino, C.; Gómez, F.; Toussaint, G.; Marandola, F.; Gómez, E. (2008). Perception of rhythmic similarity in Flamenco music. CIM.
24. Escobar-Borrego, F.; Díaz-Báñez, J. M.; Gómez, E.; Gómez, F.; Mora, J.; Cabrera, J. J. (2008). Comparative melodic analysis of a cappella flamenco cantes. CIM.
25. Guastavino, C.; Marandola, F.; Toussaint, G.; Gómez, F.; Absar, R. (2008). Perception of rhythmic similarity in flamenco music: comparing musicians and non-musicians. CIM.
26. Gómez, F.; Taslakian, P.; Toussaint, G. (2008). Evenness preserving operations on musical rhythms. Canadian Conference on Computer Science.
27. Gómez, F. (2008). Análisis filogenético en la música. Forma y Simetría.
28. Gómez, F.; Thul, E.; Toussaint, G. (2007). An experimental comparison of formal measures of rhythmic syncopation. ICMC.
29. Gómez, F.; Talaskian, P.; Toussaint, G. (2007). Distance-geometric properties of Euclidean rhythms. Kyoto Conference.
30. Absar, R.; Gómez, F.; Guastavino, C.; Marandola, F.; Toussaint, G. (2007). Perception of meter similarity in flamenco music. Canadian Acoustical Association.
31. Gómez, F.; Khoury, I.; Toussaint, G. (2007). Perception-based rhythmic transformations. Canadian Acoustics.
32. Gómez, F.; Khoury, I.; Kienzle, J.; McLeish, E.; Melvin, A.; Pérez-Fernandez, R.; Rappaport, D.; Toussaint, G. (2007). Mathematical models for binarization and ternarization of musical rhythms. BRIDGES 2007.
33. Colannino, J.; Gómez, F.; Toussaint, G. (2006). Steve Reich’s Clapping Music and the Yoruba bell timeline. BRIDGES 2006.
34. Melvin, A.; Gómez, F.; Rappaport, D.; Toussaint, G. (2005). Mathematical measures of syncopation. BRIDGES 2005.
35. Díaz-Báñez, J. M.; Farigu, G.; Gómez, F.; Rappaport, D.; Toussaint, G. (2004). El compás flamenco: A phylogenetic analysis. BRIDGES 2004.
36. Díaz-Báñez, J. M.; Farigu, G.; Gómez, F.; Rappaport, D.; Toussaint, G. (2004). Análisis filogenético del compás flamenco. Congreso Internacional de Arte Flamenco.
37. Díaz-Báñez, J.M.; Gómez, F.; Ventura, I. (2003). The anchored Voronoi diagram. European Conference on Computational Geometry.
38. Gómez, P.; Hurtado, F.; Toussaint, G. (1997). On removing non-degeneracy assumptions in computational geometry. Italian Conference on Algorithms and Complexity.
39. Bose, P.; Gómez, P.; Ramos, P.; Toussaint, G. (1995). Drawing nice projections of objects in space. Graph Drawing ’95, LNCS.

 

9 Editorial and Reviewing Activity

• Member of the editorial board of the Journal of Mathematics and Music.
• Editor of the proceedings of Mathematics and Computation in Music (2019, 2022).
• Editor of the book Theoretical and Practical Pedagogy of Mathematical Music Theory (World Scientific, 2018).
• Associate editor of the special issue Computational Ethnomusicology in the Journal of New Music Research.
• Reviewer for conferences: BRIDGES, ISMIR, ICMC, SMC.
• Reviewer for the Journal of Mathematics and Music.
• Reviewer for INFLA (Flamenco research conferences).
• Reviewer in computational geometry conferences.

 

10 PhD Supervision

• Isaac del Pozo. Algebraic models of tonal function. PhD in Music Science and Technology (UPM). Defended July 2024.
• Emmet Crowley. Structural properties of multi-octave scales. PhD in Music Science and Technology (UPM). Defended June 2023.
• Aitor Arronte Álvarez. Deep learning methods for motivic pattern extraction and classification. PhD in Music Science and Technology (UPM). Defended April 2021.
• Manuel Tizón Díaz. The influence of musical style on perceived emotion. Universidad Rey Juan Carlos. Defended December 2015.
• Pablo Romero Luis. The good musician: a consensus-based definition in classical and flamenco traditions. Universidad Rey Juan Carlos. Defended July 2017.
• Currently supervising two PhD theses in the UPM doctoral program in Music Science and Technology (web): one on the impact of technology on the operatic voice (Juliana Spector), and another on computational models of squillo (Sara Sabag), both co-supervised with Mariana Montiel (GSU).

 

11 Teaching training received

He has completed teaching training courses at the Institute of Educational Sciences (UPM) on various topics, including: voice control in the classroom, design and development of escape rooms, gamification, what it means to be a good teacher, project-based learning, flipped classroom, methodological innovation in higher education, and university teaching competencies.

 

12 Teaching training delivered

Francisco Gómez has taught courses on his A2I method—Integrated Active Learning—at the Institute of Educational Sciences (UPM) in 2019 and 2022.

 

13 Media Coverage

1. Principio de incertidumbre, interview conducted on the popular science radio program of Radio Extremadura on November 3, 2012.
2. Rhythms revealed by numbers, article in The Irish Times about the show Matherhythm, created together with Gutxi Céspedes and Giovanna Farigu, and presented at Maths Week Ireland 2011, a mathematics outreach event. The newspaper also recorded the performance and uploaded highlights to YouTube.
3. Interview conducted on December 14, 2009 about the article El ritmo musical y el algoritmo de Euclides están emparejados on the radio program La gran manzana de la ciencia of the COPE network.
4. Article El ritmo musical y el algoritmo de Euclides están emparejados published on the websites MadrI+D, SINC (FECyT), and the official website of the Technical University of Madrid.
5. Redes — Spanish science television program hosted by Eduardo Punset. Interview aired on January 26, 2009.
6. Alicia R. Mediavilla. Flamenco y Matemáticas. Article published in the magazine A fondo, August 2005.
7. Francisco Dancausa Ruiz. El Flamenco visto por las Matemáticas. Digital newspaper Noticias.com, August 8, 2005.
8. CanalSocial Noticias (digital newspaper). Un estudio revela la relación matemática entre los principales estilos del flamenco, August 11, 2005.
9. El País, September 7, 2005. link
10. El Mundo. La genética del flamenco, August 16, 2005.
11. Science portal Genciencia. Las Matemáticas con el flamenco, January 24, 2006.

 

14 Books

• Romé, Pablo; Gómez, Paco. The Path of the Good Musician. Self-published (Amazon KDP), 2026.
• Montiel, M.; Gómez, F. (eds.). Theoretical and Practical Pedagogy of Mathematical Music Theory. World Scientific (2018).
• Gómez, F. Exact String Pattern Recognition. OpenCourseWare (2010).
• Blanco, G. et al. Discrete Mathematics. UPM Publications (1996).

 

15 Outreach and Public Engagement

• Monthly outreach articles in DivulgaMat for 10 years (114 articles until 2022).
• Collaborations with FUNDAPROMAT.
• Participation in Maths Week Ireland (multiple years).
• Member of Contrasteatro, a science outreach theatre group.
• Participation in outreach events such as Street Alicante Science.

 

16 Prizes

• Third place in the Competition of popular science and technological articles (UPM Science and Technology Outreach Competition) for the article Si Euclides lo supiese... se sentiría orgulloso (If Euclid knew... he would be proud of himself). Awarded December 21, 2009.

 

17 Editor

• Dr. Gómez was in charge of the section Música y matemáticas in DivulgaMat, a digital magazine devoted to the popularization of mathematics and its cultural implications, sponsored by the Real Sociedad Matemática Española (Spanish Royal Mathematical Society). It was a monthly publication. The following articles were published in that section (in Spanish): El teorema del hexacordo I, El teorema del hexacordo II, El teorema del hexacordo III, Las matemáticas en la música de Xenakis I, Las matemáticas en la música de Xenakis II, Las matemáticas en la música de Xenakis III, De feraces relaciones, Similitud en el flamenco, Distancia y similitud musical I, Distancia y similitud musical II, Distancia y similitud musical III, La liga de los compositores automáticos, Medidas matemáticas de síncopa, Minimalismo y matemáticas: Clapping Music, Polígonos regulares y percusión, Rotación de ritmos, Matemáticas y música en los niños pequeños, Estadística en la Musicología I, Alcance y extralimitaciones de las matemáticas y la computación en la música, Enseñanza de la música por vía de las matemáticas, El aprendizaje por indagación, Transformaciones rítmicas: de binarizaciones y ternarizaciones, Similitud melódica como transformación de cadenas, La música flamenca y su estudio computacional, Teoría generativa de la música, Paradojas musicales y matemáticas, ¿Influye la formación musical en el aprendizaje de las matemáticas?, Otras armonías son posibles, Fractales en la percusión, Música y probabilidad, Consenso entre expertos en música: un enfoque matemático, Cadenas de Markov con restricciones aplicadas a modelos cognitivos en la improvisación del jazz, Composición algorítmica, Música fractal, Aritmética modular, transposiciones e inversiones en las fugas de Bach, Medidas de complejidad rítmica, Ritmos euclídeos y ritmos equilibrados, Más sobre medidas de síncopas, La geometría de la música.
• The current board of the RSME discontinued the DivulgaMat website service, and the articles are currently unavailable. They will be published on the author’s website during the first months of 2026.

 

18 Conference Organization

• Organizer of Mathematics and Computation in Music 2019 (Madrid). web
• Organizer of outreach conferences by Conciencia Musical.
• Organizer of INFLA-III (2012).
• Organizer of Folk Music Analysis Workshop (2012).
• Organizer of SITEMU (2010).
• Co-founder of International Workshops on Computational Music Theory.
• Organizer of flamenco computational analysis workshops.
• Organizer of Computational Geometry Meetings (Madrid, 1997).

 

19 Administrative Duties

• Member of the PhD Committee of the UPM doctoral program in Music Science and Technology (web).
• Member of the committee for the Mathematics degree at UPM.
• Vice-Dean for Outreach (1998–2000).
• Member of the School Board (various periods).

 

20 Languages

• Spanish: native.
• English: fluent (written and spoken).
• French: advanced. Score 835/990 in TFI. Compétence avancée en français.
• Spanish Sign Language: basic.

21 Other Activities

• Music: percussion, piano, and recorder (main instrument). Has performed in recorder consorts and percussion groups.
• Theatre: member of Contrasteatro.
• Sports: ice hockey, chess, basketball, table tennis. Certified hockey coach.
• Amateur interest in mathematical magic.