Next Article in Journal
A SOM-Based Membrane Optimization Algorithm for Community Detection
Next Article in Special Issue
Discriminatory Target Learning: Mining Significant Dependence Relationships from Labeled and Unlabeled Data
Previous Article in Journal
A Matrix Information-Geometric Method for Change-Point Detection of Rigid Body Motion
Previous Article in Special Issue
Attention to the Variation of Probabilistic Events: Information Processing with Message Importance Measure
Open AccessArticle

Melodies as Maximally Disordered Systems under Macroscopic Constraints with Musical Meaning

Departamento de Física, Universidad Nacional de Colombia, Carrera 45 No. 26-85, Bogotá 111321, Colombia
*
Authors to whom correspondence should be addressed.
Entropy 2019, 21(5), 532; https://doi.org/10.3390/e21050532
Received: 25 March 2019 / Revised: 14 May 2019 / Accepted: 15 May 2019 / Published: 25 May 2019
(This article belongs to the Special Issue Information Theoretic Measures and Their Applications)
One of the most relevant features of musical pieces is the selection and utilization of musical elements by composers. For connecting the musical properties of a melodic line as a whole with those of its constituent elements, we propose a representation for musical intervals based on physical quantities and a statistical model based on the minimization of relative entropy. The representation contains information about the size, location in the register, and level of tonal consonance of musical intervals. The statistical model involves expected values of relevant physical quantities that can be adopted as macroscopic constraints with musical meaning. We studied the occurrences of musical intervals in 20 melodic lines from seven masterpieces of Western tonal music. We found that all melodic lines are strictly ordered in terms of the physical quantities of the representation and that the formalism is suitable for approximately reproducing the final selection of musical intervals made by the composers, as well as for describing musical features as the asymmetry in the use of ascending and descending intervals, transposition processes, and the mean dissonance of a melodic line. View Full-Text
Keywords: consonance; Kullback–Leibler divergence; melody; musical interval; relative entropy consonance; Kullback–Leibler divergence; melody; musical interval; relative entropy
Show Figures

Graphical abstract

MDPI and ACS Style

Useche, J.; Hurtado, R. Melodies as Maximally Disordered Systems under Macroscopic Constraints with Musical Meaning. Entropy 2019, 21, 532.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop