Legibilidad musical y aprendizaje computacional: comparación de ordenamientos de dificultad en música escrita para los niveles de estudios en flauta transversa

Patricio F. Calatayud; Pablo Padilla-Longoria; María del Mar Galera-Núñez; Gabriela Pérez-Acosta

doi:10.22201/fesa.26832917e.2026.7.2.463

Authors

Patricio F. Calatayud National Autonomous University of Mexico (MX) https://orcid.org/0000-0001-7693-7666
Pablo Padilla-Longoria National Autonomous University of Mexico. Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (MX) https://orcid.org/0000-0003-3457-6289
María del Mar Galera-Núñez University of Seville (ES) https://orcid.org/0000-0003-3693-1694
Gabriela Pérez-Acosta National Autonomous University of Mexico (MX) https://orcid.org/0000-0002-5371-5128

DOI:

https://doi.org/10.22201/fesa.26832917e.2026.7.2.463

Keywords:

Musical readability, musical complexity, musical sheet, computational learning, transverse flute

Abstract

Readability is a subjective assessment of the difficulty of reading texts. In the musical field, these decisions can be optimized through the systematization of quantifiable elements. The Musical Readability Index (ÍLeMus) is a tool developed in the Postgraduate Program in Musical Cognition at UNAM (Universidad Nacional Autónoma de México) that, based on cognitive experimentation on musical reading, analyzes various factors: the length of a fragment, the amount of ink, the average number of accidentals in the clefs, entropy, the similarity between events and their relationship to the tempo, as well as the metronome marking. This text reports an experiment with two interventions, whose objective is to evaluate the ÍLeMus's ability to generate difficulty rankings in musical sheets for flute. To this end, the ranking of scores from the International Music Score Library Project (IMSLP) was used as a reference and compared with a new ranking constructed based on the ÍLeMus indicators. To evaluate the index's effectiveness in this task, another complexity model, derived from computational learning (CL), was employed: the regression tree, used to organize the scores of a specific corpus according to their level of difficulty. This strategy provides quantitative information on the aforementioned indicators and a suggested readability ranking, useful for teachers, researchers, or composers who wish to more rigorously justify their subjective decisions.

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Author Biographies

Patricio F. Calatayud, National Autonomous University of Mexico

Musical composer with honorable mention from Universidad Nacional Autónoma de México for a research on the concept of intention in composition. He holds a Master's degree in Music Technology with honorable mention from Universidad Nacional Autónoma de México (UNAM), where his research focused on new forms of computer-based musical notation. He is currently pursuing a doctorate in Music Cognition at UNAM's graduate program. He is a tenured professor in the Music Department at Facultad de Música, specializing in LIMME area, and has also taught courses at INBA, CENART, and TEC de Monterrey. His research interests center on dynamic music notation, musical cognition, and mathematics in music. His work has been presented in museums, galleries, and numerous experimental sound spaces throughout Latin America. His most recent compositions are dedicated to the interpretation of dynamic music notation.
Pablo Padilla-Longoria, National Autonomous University of Mexico. Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas

He earned bachelor's degrees in Mathematics (receiving the Gabino Barreda Medal) and Physics from Universidad Nacional Autónoma de México (UNAM) and studied Piano at Conservatorio Nacional de Música. He obtained a Master of Science (M.Sc.) and a Ph.D. from the Courant Institute of Mathematical Sciences at New York University, as well as a diploma in piano from Mannes College of Music, where he also studied harpsichord, composition, and improvisation. He held a postdoctoral position at the Swiss Federal Institute of Technology in Zurich (ETH) and continued his harpsichord studies at the Zurich University of the Arts with Carmen Schibli. He has been a visiting professor at various universities, including the University of Oxford, the School for Advanced Studies in the Social Sciences (EHESS, Paris), and the University of Cambridge. He has lectured at several institutions, including Universidad Complutense de Madrid, Universidad de Granada, the Korea Institute for Advanced Studies (KIAS), the Tunis School of Engineering (ENIT), the Universities of Rome, Chile, and Keio (Japan), the Lisbon Higher Technical Institute, Harvard University, the Isaac Newton Institute in Cambridge, etc. He is currently a Full Professor (Category C) in the Department of Mathematics and Mechanics at Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (IIMAS) of UNAM and teaches at Facultad de Ciencias and Facultad de Música, also at UNAM.
María del Mar Galera-Núñez, University of Seville

Doctor of Education, holds advanced degrees in Piano, Chamber Music, and Solfège and Music Theory; Bachelor of Arts in Art History from Universidad de Sevilla; Expert in Methods and Resources of Music Education from the University of La Laguna. She is a member of the Didactic Research Group (GID).

Her main lines of research are related to artistic languages in education, music technology, and the musical training of early childhood teachers. She has participated as director and researcher in various research projects related to music education and has been a member of the scientific committee of several educational conferences, as well as a reviewer for journals related to music and arts education: LEEME, Educación XX1, Pedagogía Social, Electronic Journal of Research in Educational Psychology, among others. She has nearly one hundred published works, including presentations, journal articles, book chapters, and books related to
Gabriela Pérez-Acosta, National Autonomous University of Mexico

Pianist and Master in Musical Cognition. A graduate from the Bachelor of Music program in Piano from Facultad de Música at the Universidad Nacional Autónoma de México (UNAM).

She continued her performance studies at the Alfred Cortot School of Music in Paris. In August 2008, she earned a Master of Music degree specializing in Musical Cognition. She has presented her research at numerous national and international conferences in Mexico, Italy, Brazil, Argentina, Austria, Finland, Greece, Israel, and England.

She is a full-time professor at Facultad de Música UNAM and served as Academic Secretary there from 2011 to 2014.

Since 2012, she has also been a member of the faculty of tutors and visiting professors for the Postgraduate Program in Cognitive Sciences at Universidad Autónoma del Estado de Morelos, and since January 2015, she has been a researcher at Centro Nacional de Investigación, Documentación e Información Musical “Carlos Chavez”. Currently, she is pursuing doctoral studies in Musical Cognition in the Postgraduate Program in Music at UNAM, and during the first semester of 2017 she completed a research stay with the Music, Mind & Brain group at Goldsmiths University in London, England.

References

ABSM. 2025. Homepage ABRSM. https://www.abrsm.org/en-mx

Abdallah, Samer y Mark Plumbley. 2009. “Information Dynamics: Patterns of Expectation and Surprise in the Perception of Music”. Connection Science 21, no. 2–3: 89–117. https://doi.org/10.1080/09540090902733756. DOI: https://doi.org/10.1080/09540090902733756

Angeler, David. 2020. “Biodiversity in Music Scores”. Challenges 11, no. 1: 7. https://doi.org/10.3390/challe11010007. DOI: https://doi.org/10.3390/challe11010007

Aurnhammer, Christoph, y Stefan Frank. 2019. “Evaluating Information-Theoretic Measures of Word Prediction in Naturalistic Sentence Reading”. Neuropsychologia 134 (November): 107198. https://doi.org/10.1016/j.neuropsychologia.2019.107198. DOI: https://doi.org/10.1016/j.neuropsychologia.2019.107198

Baddeley, Alan David. 2003. “Working Memory: Looking Back and Looking Forward”. Nature Reviews Neuroscience 4, no. 10: 829–839. DOI: https://doi.org/10.1038/nrn1201

Bailin, Alan, y Ann Grafstein. 2016. Readability: Text and Context. England: Springer. DOI: https://doi.org/10.1057/9781137388773

Bressan, Glaucia., De Azevedo, Beatriz., & Lizzi, Elisangela. (2017). “A Decision Tree Approach for the Musical Genres Classification.” Applied Mathematics & Information Sciences 11, no. 6: 1703-1713. https://doi.org/10.18576/amis/110617 DOI: https://doi.org/10.18576/amis/110617

Calatayud, Patricio Federico. 2024. El ÍleMus (Índice de Legibilidad Musical): Un nuevo modelo cognitivo matemático para la medición de la legibilidad en música escrita. Tesis doctoral, Universidad Nacional Autónoma de México. https://tesiunam.dgb.unam.mx/F/ETSSVY2CKLLUFADI52AQF9PL46F972LM1ANH2D711KTTL3GSAU-18903?func=find-b&local_base=TES01&request=%C3%8DLeMus&find_code=WRD&adjacent=N&filter_code_2=WYR&filter_request_2=&filter_code_3=WYR&filter_request_3=

Chase, Ivan. 2006. “Music Notation: A New Method for Visualizing Social Interaction in Animals and Humans”. Frontiers in Zoology 3, no. 1: 18. https://doi.org/10.1186/1742-9994-3-18. DOI: https://doi.org/10.1186/1742-9994-3-18

Chang, Ting-Yun, y Isabel Gauthier. 2021. “Domain-Specific and Domain-General Contributions to Reading Musical Notation”. Attention, Perception, & Psychophysics, advance online publication, 83 (January 2):2983-2994.https://doi.org/10.3758/s13414-021-02349-3. DOI: https://doi.org/10.3758/s13414-021-02349-3

Drai-Zerbib, Véronique y Thierry Baccino. 2014. “The effect of expertise in music reading: Cross-modal competence”. Journal of Eye Movement Research 6, no. 5 (January): 1-10. https://doi.org/10.16910/jemr.6.5.5 DOI: https://doi.org/10.16910/jemr.6.5.5

Eden Ünlü, Seda, y Ahmet Serkan Ece. 2019. “Reading notation with Gestalt perception principles: Gestalt algı ilkeleri ile notasyon okuma”. Journal of Human Sciences 16, no. 4: 4. https://www.j-humansciences.com/ojs/index.php/IJHS/article/view/5822/3325 DOI: https://doi.org/10.14687/jhs.v16i4.5822

Endestad, Tor, Rolf Inge Godøy, Markus Handal Sneve, Thomas Hagen, Agata Bochynska, y Bruno Laeng. 2020. “Mental Effort When Playing, Listening, and Imagining Music in One Pianist’s Eyes and Brain”. Frontiers in Human Neuroscience 14 (October):1-23. https://doi.org/10.3389/fnhum.2020.576888. DOI: https://doi.org/10.3389/fnhum.2020.576888

Flute pieces by level. IMSLP. (s.f.). Recuperado el 1 de enero de 2023, desde https://imslp.org/wiki/Special:DiffPage/DiffMain/4

Flesch, Rudolph. 1948. “A New Readability Yardstick.” Journal of Applied Psychology 32, no. 3: 221-233. https://psycnet.apa.org/record/1949-01274-001?doi=1 DOI: https://doi.org/10.1037/h0057532

Friston, Karl. 2010. “The Free-Energy Principle: A Unified Brain Theory?” Nature Reviews Neuroscience 11, no. 2: 127–138. https://doi.org/10.1038/nrn2787. DOI: https://doi.org/10.1038/nrn2787

Gao, Hong, Zijian Lu, Vera Demberg, y Enkelejda Kasneki. 2021. “The Index of Cognitive Activity Predicts Cognitive Processing Load in Linguistic Task”. En Proceedings of the EMICS workshop at CHI’21.

Goldsmiths, Universidad de Londres. “Learn to play:computational Assessment of Musical Playability for Users´Practice”. Revisado el 9 de noviembre, 2025. https://gtr.ukri.org/projects?ref=AH%2FP013287%2F1.

Guo, E. W., y Project Petrucci. 2006. IMSLP: Free Sheet Music PDF Download”. Revisado el 9 de noviembre 2025, https://imslp.org/.

Hattie, John. 2010. Visible Learning: A Synthesis of over 800 Meta-Analyses Relating to Achievement. Reprinted. London: Routledge. https://inspirasifoundation.org/wp-content/uploads/2020/05/John-Hattie-Visible-Learning_-A-synthesis-of-over-800-meta-analyses-relating-to-achievement-2008.pdf.

IMSLP / Petrucci Music Library. 2025. “Free Sheet Music PDF Download.” IMSLP: https://imslp.org/

IMSLP / Petrucci Music Library. 2025. “Flaute Pieces by Level.” IMSLP: https://imslp.org/wiki/Special:DiffPage/DiffMain/4

Janurik, Márta, Noémi Surján, y Krisztián Józsa. 2022. “The Relationship between Early Word Reading, Phonological Awareness, Early Music Reading and Musical Aptitude”. Journal of Intelligence 10, no. 3: 50. https://doi.org/10.3390/jintelligence10030050. DOI: https://doi.org/10.3390/jintelligence10030050

Loh, Wei‐Yin. 2011. “Classification and Regression Trees”. WIREs Data Mining and Knowledge Discovery 1, no. 1: 14-23. https://doi.org/10.1002/widm.8. DOI: https://doi.org/10.1002/widm.8

Malbrán, Silvia. 2007. El oído de la mente. Ciudad de México: Akal.

Marín, Cristina, Ma Puy Pérez Echeverría, & Susan Hallam. 2012. “Using the musical score to perform: A study with Spanish flute students.” British Journal of Music Education 29, no. 2: 193-212. https://doi.org/10.1017/S0265051712000046 DOI: https://doi.org/10.1017/S0265051712000046

Music Information Retrival (MIR). 2025. https://musicinformationretrieval.com/intro.html

New York State School Music Association (NYMSSA). 2025. NYSSMA - New Yor State School Music Association. https://www.nyssma.org/

Ogura, Hiroshi, Hiromi Amano, y Masato Kondo. 2013. “Gamma-Poisson Distribution Model for Text Categorization”. ISRN Artificial Intelligence 4, no. 6 (April): 1–17. https://doi.org/10.1155/2013/829630. DOI: https://doi.org/10.1155/2013/829630

Sancho Guinda, Carmen. 2002. “Punctuation as readability and textuality factor in technical discourse.” Ibérica, Revista de la Asociación Europea de Lenguas para Fines Específicos 4: 75–94. https://www.redalyc.org/articulo.oa?id=287026292005.

Sayood, Khalid. 2018. “Information Theory and Cognition: A Review”. Entropy 20, no. 9. https://doi.org/10.3390/e20090706. DOI: https://doi.org/10.3390/e20090706

Scot, Brian. 2025. “Learn About the Flesch Reading Ease Formula.” ReadabilityFormulas.com. https://readabilityformulas.com/learn-about-the-flesch-reading-ease-formula/

Sheridan, Heather, y Abigail L Kleinsmith. 2021. “Music Reading Expertise Affects Visual Change Detection: Evidence from a Music-Related Flicker Paradigm”. Quarterly Journal of Experimental Psychology 75, no. 9 (November). DOI: https://doi.org/10.1177/17470218211056924

Shiffman, Daniel. 2024. The Nature of Code: Simulating Natural Systems with JavaScript. New York: No Starch Press.

Sprevak, Mark. 2020. “Two Kinds of Information Processing in Cognition”. Review of Philosophy and Psychology 11, no. 3: 591–611. https://doi.org/10.1007/s13164-019-00438-9. DOI: https://doi.org/10.1007/s13164-019-00438-9

Tiffin School Music Departament. 2025. GCSE Performing Difficulty Levels. https://sites.google.com/tiffin.kingston.sch.uk/music/curricular-music/gcse-music/gcse-performing/gcse-performing-difficulty-levels

W3C. 2021. The Element MusicXML 4.0. Última modificación en junio de 2021. https://www.w3.org/2021/06/musicxml40/musicxml-reference/elements/fifths/

Xenakis, Iannis. 1992. Formalized music: thought and mathematics in composition. Rev. ed. Harmonologia series, no. 6. Stuyvesant, NY: Pendragon Press.

Yang, Yi-Hsuan, Yu-Ching Lin, Ya-Fan Su, & Homer H. Chen. 2008. “A regression approach to music emotion recognition.” IEEE Transactions on Audio Speech and Language Processing 16, no. 2: 448–457. https://doi.org/10.1109/tasl.2007.911513 DOI: https://doi.org/10.1109/TASL.2007.911513