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We investigate correlations among pitches in several songs and pieces of piano music by mapping them to one-dimensional walks. Two kinds of correlations are studied, one is related to the real values of frequencies while they are treated…
We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of {\it temporal dynamics} in music. (i) Phase space portraits are…
The abstraction of musical structures (notes, melodies, chords, harmonic or rhythmic progressions, etc.) as mathematical objects in a geometrical space is one of the great accomplishments of contemporary music theory. Building on this…
Quantum cognition emerged as an important discipline of mathematical psychology during the last two decades. Using abstract analogies between mental phenomena and the formal framework of physical quantum theory, quantum cognition…
This paper presents a geometric approach to pitch estimation (PE)-an important problem in Music Information Retrieval (MIR), and a precursor to a variety of other problems in the field. Though there exist a number of highly-accurate…
The relationship between perceptual loudness and physical attributes of sound is an important subject in both computer music and psychoacoustics. Early studies of "equal-loudness contour" can trace back to the 1920s and the measured…
The perception of consonance/dissonance of musical harmonies is strongly correlated with their periodicity. This is shown in this article by consistently applying recent results from psychophysics and neuroacoustics, namely that the just…
The concept of complexity as considered in terms of its algorithmic definition proposed by G.J. Chaitin and A.N. Kolmogorov is revisited for the dynamical complexity of music. When music pieces are cast in the form of time series of pitch…
There has been an everlasting discussion around the concept of form in music. This work is motivated by such debate by using a complex systems framework in which we study the form as an emergent property of rhythm. Such a framework…
How do different musical traditions achieve tonal coherence? Most computational measures to date have analysed tonal coherence in terms of a single dimension, whereas a multi-dimensional analyses have not been sufficiently explored. We…
Pitch and timing information work hand in hand to create a coherent piece of music; but what happens when this information goes against the norm? Relationships between musical expectancy and emotional responses were investigated in a study…
Music is a structured and perceptually rich sequence of sounds in time, whose perception is shaped by the interplay of expectation and uncertainty about what comes next. Yet the uncertainty we infer from music depends on how the musical…
If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…
While Large Language Models (LLMs) make symbolic music generation increasingly accessible, producing music with distinctive composition and rich expressiveness remains a significant challenge. Many studies have introduced emotion models to…
The melodic consonance of a sequence of tones is explained using the overtone series: the overtones form "flow lines" that link the tones melodically; the strength of these flow lines determines the melodic consonance. This hypothesis…
Mathematical music theory has assumed without proof that musical notes can be associated with the equivalence classes of $\mathbb{Z}_n$. We contest the triviality of this assertion, which we call the Pitch-class Integer Theorem (PCIT).…
The average individual is typically a mediocre singer, with a rather restricted capacity to sing a melody in tune. Yet when many singers are assembled to perform collectively, the resulting melody of the crowd is suddenly perceived by an…
The human sense of hearing perceives a combination of sounds 'in tune' if the corresponding harmonic spectra are correlated, meaning that the neuronal excitation pattern in the inner ear exhibits some kind of order. Based on this…
There is a wide variety of music similarity detection algorithms, while discussions about music plagiarism in the real world are often based on audience perceptions. Therefore, we aim to conduct a study to examine the key criteria of human…
Automatic melody generation for pop music has been a long-time aspiration for both AI researchers and musicians. However, learning to generate euphonious melody has turned out to be highly challenging due to a number of factors.…