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Correlations between quantum theory and music theory - specifically between principles of quantum computing and musical harmony - can lead to new understandings and new methodologies for music theorists and composers. The quantum principle…
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…
Gioseffo Zarlino reintroduced the Pythagorean paradigm into Renaissance musical theory. In a similar fashion, Nicolaus Copernicus, Galileo Galilei, Johannes Kepler, and Isaac Newton reinvigorated Pythagorean ideas in celestial mechanics;…
We have recently seen great progress in learning interpretable music representations, ranging from basic factors, such as pitch and timbre, to high-level concepts, such as chord and texture. However, most methods rely heavily on music…
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 discuss differential-- versus integral--equation based methods describing out--of thermal equilibrium systems and emphasize the importance of a well defined reduction to statistical observables. Applying the projection operator approach,…
Music is a complex socio-cultural construct, which fascinates researchers in diverse fields, as well as the general public. Understanding the historical development of music may help us understand perceptual and cognition, while also…
We make some general observations about partial orders on quotient spaces, and explore their use in music theory, in two different contexts. In the first, we show that many of the most familiar chord and scale types in Western music appear…
We outline an unified introduction to the evolution equations of classical and quantum systems intended for a high school students audience. The attempt consists in circumventing the lack of mathematical knowledge with the use of simplified…
Music, enchanting and poetic, permeates every corner of human civilization. Although music is not unfamiliar to people, our understanding of its essence remains limited, and there is still no universally accepted scientific description.…
This paper introduces a novel recurrent model for music composition that is tailored to the structure of polyphonic music. We propose an efficient new conditional probabilistic factorization of musical scores, viewing a score as a…
Following the approach of Julien Lesgourgues [astro-ph/0409426], we analyze the mathematical structure of the time co-ordinate of present day cosmological models, where these models include a cosmological constant term to account for the…
We provide a brief survey of quantum statistical characterisations of order, disorder and coherence in systems of many degrees of freedom. Here, order and coherence are described in terms of symmetry breakdown, while disorder is described…
In this work we show a technique that allows for the musical interpretation of the brightness variations of stars. This method allows composers a lot of freedom to incorporate their own ideas into the score, based on the melodic line…
Einstein-Smoluchowski diffusion, damped harmonic oscillations, and spatial decoherence are special cases of an elegant class of Markovian quantum Brownian motion models that is invariant under linear symplectic transformations. Here we…
We consider a particular (exactly soluble) model of the one discussed in a previous work. We show numerical results for the time evolution of the main dynamical quantities and compare them with analytical results.
This contribution analyses the classical laws of motion by means of an approach relating time and entropy. We argue that adopting the notion of change of states as opposed to the usual derivation of Newton's laws in terms of fields a…
Among quantum Langevin equations describing the unitary time evolution of a quantum system in contact with a quantum bath, we completely characterize those equations which are actually driven by classical noises. The characterization is…
To many people, music is a mystery. It is uniquely human, because no other species produces elaborate, well organized sound for no particular reason. It has been part of every known civilization on earth. It has become a very part of man's…
Most music theory books are like medieval medical textbooks: they contain unjustified superstition, non-reasoning, and funny symbols glorified by Latin phrases. How does music, in particular harmony, actually work, presented as a real,…