An indicator for assessing Intrinsic Complexity in Common Practice music notation
DOI:
https://doi.org/10.24215/18530494e081Keywords:
music notation, literary review, Music Education, entropy, complexityAbstract
This experimental study emerges from the need to have quantitative values that distinguish the complexity of learning and execution of the different elements of musical notation. Although the relationship between music and complexity is vast, there is not much information about complexity models and musical notation. Still, we managed to design a model that distinguishes Intrinsic Complexity in a group of Common Practice music notation elements. A first experiment, performed on a corpus of music education books (N = 64), allows us to build a basic set of music notation items, filtered from their huge set. This selection was organized by two variables: Ordinality and Preference, which is statistically significant to be included in a complexity measurement (Pearson correlation of -0.88; p < 0.001). With the help of a decision risk measurement calculus, we conducted a second experiment, where we constructed a new indicator based on the above variables. This, which we call the Relevance Indicator, assigns a different intrinsic complexity value for each musical notation element. Finally, it is important to emphasize that the relationship between statistics and music theory is far from having rigorous results, this text reports an approach from the simplest statistics and aims to be part of the integration between this and music theory.
References
Angeler, D. G. (2020). Biodiversity in Music Scores. Challenges, 11(1), 7. https://doi.org/10.3390/challe11010007
Aurnhammer, C. y Frank, S. L. (2019). Evaluating information-theoretic measures of word prediction in naturalistic sentence reading. Neuropsychologia, 134, 107198. https://doi.org/10.1016/j.neuropsychologia.2019.107198
Bernstein, S. (2021). Music Theory: The Complete Guide to Read, Write and Understand Music from Beginner to Expert. F. Johnson.
Chase, I. D. (2006). Music notation: A new method for visualizing social interaction in animals and humans. Frontiers in Zoology, 3, 18. https://doi.org/10.1186/1742-9994-3-18
Checchi, E. J. (2008). La sintaxis de la Práctica Común. Educa.
Chignell, M., Tong, T., Mizobuchi, S. y Walmsley, W. (2014). Combining speed and accuracy into a global measure of performance. Proceedings of the Human Factors and Ergonomics Society Annual Meeting, 58(1), 1442-1446. https://doi.org/10.1177/1541931214581301
Endestad, T., Godøy, R. I., Sneve, M. H., Hagen, T., Bochynska, A. y Laeng, B. (2020). Mental Effort When Playing, Listening, and Imagining Music in One Pianist’s Eyes and Brain. Frontiers in Human Neuroscience, 14, 576888 https://doi.org/10.3389/fnhum.2020.576888
Estrada-García, J. M. (2002). Entropía. Asignación de pesos no subjetivos, para la valuación [Tesis de maestría no publicada]. Instituto Tecnológico de la Construcción.
Galera Núñez, M. D. M. (2010). Efectos de diferentes variables en la lectura musical cantada [Tesis de doctorado no publicada]. Universidad de Sevilla.
Gehrkens, K. W. (2006). Music Notation and Terminology. The Project Gutenberg. (Trabajo original publicado en 1914).
Gomberg, D. A. (1977). A computer-oriented system for music printing. Computers and the Humanities, 11(2), 63-80. https://doi.org/10.1007/bf02404004
Grier, J. (2021). Musical notation in the West. Cambridge University Press.
Gudmundsdottir, H. R. (2010). Advances in music-reading research. Music Education Research, 12(4), 331-338. https://doi.org/10.1080/14613808.2010.504809
Hattie, J. (2008). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge.
Hilgard, E. R. y Bower, G. H. (1966). Theories of learning. Appleton-Century-Crofts.
Holder, E. (s. f.). Musiplectics (Musical Complexity Scoring). Ethan Holder. Recuperado el 11 de septiembre de 2025 de http://ethanholder.com/html/MusicScoring.html
Holder, E., Tilevich, E. y Gillick, A. (2015). Musiplectics: Computational assessment of the complexity of music scores. En 2015 ACM International Symposium on New Ideas, New Paradigms, and Reflections on Programming and Software (Onward!) (pp. 107-120). Association for Computing Machinery. https://doi.org/10.1145/2814228.2814243
Kurkela, K. (1989). Score, vision, action. Contemporary Music Review, 4(1), 417-435. https://doi.org/10.1080/07494468900640461
Laskowska, B. y Kamola, M. (2020). Grouping compositions based on similarity of music themes. PLOS ONE, 15(10), e0240443. https://doi.org/10.1371/journal.pone.0240443
Lassfolk, K. (2004). Music notation as objects. University of Helsinki Press.
Lepper, M., Oehler, M., Kinzler, H. y Trancón y Widemann, B. (2019). Diminuendo al bottom—Clarifying the semantics of music notation by re-modeling. PLOS ONE, 14(11), e0224688. https://doi.org/10.1371/journal.pone.0224688
Lopes, A. M. y Tenreiro Machado, J. A. (2019). On the Complexity Analysis and Visualization of Musical Information. Entropy, 21(7), 669. https://doi.org/10.3390/e21070669
Pease, A., Mahmoodi, K. y West, B. J. (2018). Complexity measures of music. Chaos, Solitons & Fractals, 108, 82-86. https://doi.org/10.1016/j.chaos.2018.01.021
Posner, R. (1988). Balance of complexity and hierarchy of precision: Two principles of economy in the notation of language and music. En M. Herzfeld y L. Melazzo (Eds.), Semiotic Theory and Practice (pp. 909-920). De Gruyter Mouton. https://doi.org/https://doi.org/10.1515/9783110868883-093
Prince, J. B., Thompson, W. F. y Schmuckler, M. A. (2009). Pitch and time, tonality and meter: How do musical dimensions combine? Journal of Experimental Psychology: Human Perception and Performance, 35(5), 1598-1627. https://doi.org/10.1037/a0016456
Read, G. (1972). Music notation: A manual of modern practice. Crescendo Publishers.
Roemer, C. (1985). The art of music copying: The preparation of music for performance. Roerick Music Co.
Sayood, K. (2018). Information theory and cognition: A review. Entropy, 20(9), 706. https://doi.org/10.3390/e20090706
Schultz, M. (1998). La notación musical desde la perspectiva semiótica. Arte e Investigación, 2(2), 44-47.
Treitler, L. (1982). The Early History of Music Writing in the West. Journal of the American Musicological Society, 35(2), 237-279. https://doi.org/10.2307/831146
Trías, E. (2010). La imaginación sonora. Argumentos musicales. Galaxia Gutenberg.
Williams, C. F. A. (1903). The Story of Notation. Walter Scott Publishing Company.
Wong, Y. K. y Gauthier, I. (2010). Holistic processing of musical notation: Dissociating failures of selective attention in experts and novices. Cognitive, Affective, & Behavioral Neuroscience, 10(4), 541-551. https://doi.org/10.3758/cabn.10.4.541
Xenakis, I. (1992). Formalized music: Thought and mathematics in composition. (Ed. revisada). Pendragon Press.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Patricio Federico Calatayud, Pablo Padilla Longoria, María del Mar Galera-Núñez, Gabriela Pérez Acosta
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Politica vigente desde octubre de 2019
La aceptación del manuscrito por parte de la revista implica la cesión no exclusiva de los derechos patrimoniales de los/as autores/as en favor del editor, quien permite la reutilización, luego de su edición (postprint), bajo una Licencia Creative Commons Atribución-NoComercial-CompartirIgual 4.0 Internacional (CC BY-NC-SA 4.0)
Acorde a estos términos, el material se puede copiar y redistribuir en cualquier medio o formato siempre que a) se cite la autoría y la fuente original de su publicación (revista y URL de la obra), se brinde el acceso a la licencia y se indique si se realizaron cambios; b) no se utilice el material para fines comerciales.
La cesión de derechos no exclusivos implica que luego de su edición (postprint) en Epistemus los/as autores/as pueden publicar su trabajo en cualquier idioma, medio y formato; en tales casos, se solicita que se consigne que el material fue publicado originalmente en esta revista.
Tal cesión supone, también, la autorización de los/as autores/as para que el trabajo sea cosechado por SEDICI, el repositorio institucional de la Universidad Nacional de La Plata, y sea difundido en las bases de datos que el equipo editorial considere adecuadas para incrementar la visibilidad de la publicación y de sus autores/as.
Asimismo, la revista incentiva a los/as autores/as para que luego de su publicación en Epistemus depositen sus producciones en otros repositorios institucionales y temáticos, bajo el principio de que ofrecer a la sociedad la producción científica y académica sin restricciones contribuye a un mayor intercambio del conocimiento global.
