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Scales, sets of discrete pitches that form the basis of melodies, are thought to be one of the most universal hallmarks of music. But we know relatively little about cross-cultural diversity of scales or how they evolved. To remedy this, we…

We present a technique to search for the presence of crucial events in music, based on the analysis of the music volume. Earlier work on this issue was based on the assumption that crucial events correspond to the change of music notes,…

Noise is widely understood to be something that interferes with a signal or process. Thus, it is generally thought to be destructive, obscuring signals and interfering with function. However, early in the 20th century, mechanical engineers…

Even if the tuning between the first and second register of a clarinet has been optimized by instrument makers, the lowest twelfths remain slightly too large (inharmonicity). In this article, we study the problem from two different points…

In this paper we present a mathematical way of defining musical modes, we derive a formula for the total number of modes and define the musicality of a mode as the total number of harmonic chords whithin the mode. We also give an algorithm…

Much of Western classical music relies on instruments based on acoustic resonance, which produce harmonic or quasi-harmonic sounds. In contrast, since the mid-twentieth century, popular music has increasingly been produced in recording…

Time-frequency representations of audio signals often resemble texture images. This paper derives a simple audio classification algorithm based on treating sound spectrograms as texture images. The algorithm is inspired by an earlier visual…

We explore the chaotic dynamics and complexity of a neuro-system with respect to variable synaptic weights in both noise free and noisy conditions. The chaotic dynamics of the system is investigated by bifurcation analysis and 0-1 test. A…

An important problem in physics concerns the analysis of audio time series generated by transduced acoustic phenomena. Here, we develop a new method to quantify the scaling properties of the local variance of nonstationary time series. We…

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…

Noise is a result of stochastic processes that originate from quantum or classical sources. Higher-order cumulants of the probability distribution underlying the stochastic events are believed to contain details that characterize the…

Listening habits are strongly influenced by two opposing aspects, the desire for variety and the demand for uniformity in music. In this work we quantify these two notions in terms of musical instrumentation and production technologies that…

We investigate a dynamically adapting tuning scheme for microtonal tuning of musical instruments, allowing the performer to play music in just intonation in any key. Unlike other methods, which are based on a procedural analysis of the…

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…

We test a segmentation algorithm, based on the calculation of the Jensen-Shannon divergence between probability distributions, to two symbolic sequences of literary and musical origin. The first sequence represents the successive appearance…

We analyze the influence of music in a network of FitzHugh-Nagumo oscillators with empirical structural connectivity measured in healthy human subjects. We report an increase of coherence between the global dynamics in our network and the…

We present a class of systems for which the signal-to-noise ratio always increases when increasing the noise and diverges at infinite noise level. This new phenomenon is a direct consequence of the existence of a scaling law for the…

Music is a universal feature of human culture, linked to embodied cognitive functions that drive learning, action, and the emergence of creativity and individuality. Evidence highlights the critical role of statistical learning an implicit…

The nervous system displays a variety of rhythms in both waking and sleep. These rhythms have been closely associated with different behavioral and cognitive states, but it is still unknown how the nervous system makes use of these rhythms…

The collaboration of mathematics in the two musical systems of Pythagorean sounds and of equal sounds is evident and opportune for generating the elements and managing their relationships. The only essential notion for a rational…