Abstract
This paper we propose a novel method, based on a fuzzy approach, for assessing the compatibility of a set of experimentally measured notes with any theoretical tuning system. Through the exposition of three illustrative experiments, we demonstrate the potential of this method, where we calculate the average tuning distance between the music performance and the theoretical values, revealing insights into the suitability of different tuning systems for specific musical contexts, as well as the nuanced adjustments made by the musicians in response to varying musical scenarios.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Barbour, J. M.: Tuning and Temperament: A Historical Survey. Courier Corporation (2004)
Rahkonen, C.: How Equal Temperament Ruined Harmony (and Why You Should Care) (2008)
Halewood, M.: On equal temperament: tuning, modernity and compromise. Hist. Hum. Sci. 28(3), 3–21 (2015)
Milne, A., Sethares, W., Plamondon, J.: Tuning continua and keyboard layouts. J. Math. Music 2(1), 1–19 (2008)
Slevc, L.R., Davey, N.S., Buschkuehl, M., Jaeggi, S.M.: Tuning the mind: exploring the connections between musical ability and executive functions. Cognition 152, 199–211 (2016)
Sloboda, J.A. : The acquisition of musical performance expertise: deconstructing the talent account of individual differences in musical expressivity. In: The Road to Excellence, pp. 107–126 (2014)
Geringer, J., Witt, A.: An investigation of tuning performance and perception of string instrumentalists. Bull. Counc. Res. Music. Educ. 85, 90–101 (1985)
Sundberg, J.: How can music be expressive? Speech Commun. 13(1), 239–253 (1993)
Heister, H.W.: Music and Fuzzy Logic: The Dialectics of Idea and Realizations in the Artwork Process. Springer, Heidelberg (2021). https://doi.org/10.1007/978-3-662-62907-9
Liern, V.: Fuzzy tuning systems: the mathematics of musicians. Fuzzy Sets Syst. 150(1), 35–52 (2005)
León, T., Liern, V.: A fuzzy framework to explain musical tuning in practice. Fuzzy Sets Syst. 214, 51–64 (2013)
Wood, A.: The Physics of Music. Davies Press, London (2008)
André, H., Khelf, I., Leclere, Q.: Harmonic product spectrum revisited and adapted for rotating machine monitoring based on IAS. In: Proceedings of the 9th International Conference Surveillance, Fes, Morocco. Institut International des Sciences Appliquées (2017)
Noll, A.M.: Pitch determination of human speech by the harmonic product spectrum, the harmonic sum spectrum, and a maximum likelihood estimate. In: Proceedings of Symposium on Computer Processing in Communication, vol. 19, pp. 779–797. University of Brooklyn Press, New York (1970)
Martínez, B., Liern, V.: A fuzzy-clustering based approach for measuring similarity between melodies. In: Agustín-Aquino, O.A., Lluis-Puebla, E., Montiel, M. (eds.) MCM 2017. LNCS (LNAI), vol. 10527, pp. 279–290. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-71827-9_21
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
A Appendix
A Appendix
Calculations based on Definition 2 for several tuning systems used on this research (Tables 6, 7 and 8).
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Martínez-Rodríguez, B., Liern, V. (2024). Assessing the Compatibility Between Musical Performance and Tuning System. In: Noll, T., Montiel, M., Gómez, F., Hamido, O.C., Besada, J.L., Martins, J.O. (eds) Mathematics and Computation in Music. MCM 2024. Lecture Notes in Computer Science, vol 14639. Springer, Cham. https://doi.org/10.1007/978-3-031-60638-0_28
Download citation
DOI: https://doi.org/10.1007/978-3-031-60638-0_28
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-60637-3
Online ISBN: 978-3-031-60638-0
eBook Packages: Computer ScienceComputer Science (R0)