Related papers: The axiom system of classical harmony

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 numerically study the work distributions in a chaotic system and examine the relationship between quantum work and classical work. Our numerical results suggest that there exists a correspondence principle between quantum and classical…

We investigate the dynamics of classical and quantum N-component phi^4 oscillators in the presence of an external field. In the large N limit the effective dynamics is described by two-degree-of-freedom classical Hamiltonian systems. In the…

This paper introduces the ACCompanion, an expressive accompaniment system. Similarly to a musician who accompanies a soloist playing a given musical piece, our system can produce a human-like rendition of the accompaniment part that follows…

We classify three-tone and four-tone chords based on subgroups of the symmetric group acting on chords contained within a twelve-tone scale. The actions are inversion, major-minor duality, and augmented-diminished duality. These actions…

The divergence of the harmonic series is proved by direct comparison with a series whose nth partial sum telescopes to the natural logarithm of n. The key idea is to apply the classical inequality x>=log(1+x) (valid for x>-1) with x=1/k and…

To date, calculating the frequencies of musical notes requires one to know the frequency of some reference note. In this study, first-order ordinary differential equations are used to arrive at a mathematical model to determine tonal…

We consider a quantum two-level system perturbed by classical noise. The noise is implemented as a stationary diffusion process in the off-diagonal matrix elements of the Hamiltonian, representing a transverse magnetic field. We determine…

The paper explains why the de Broglie-Bohm theory reduces to Newtonian mechanics in the macroscopic classical limit. The quantum-to-classical transition is based on three steps: (i) interaction with the environment produces effectively…

Giving a convincing experimental evidence of the quantum supremacy over classical simulations is a challenging goal. Noise is considered to be the main problem in such a demonstration, hence it is urgent to understand the effect of noise.…

We find the conditions for one quantum system to function as a classical controller of another quantum system: the controller must be an open system and rapidly diagonalised in the basis of the controller variable that is coupled to the…

We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…

We use coupled hidden Markov models to automatically annotate the 371 Bach chorales in the Riemenschneider edition, a corpus containing approximately 100,000 notes and 20,000 chords. We give three separate analyses that achieve…

This is the first of a series of papers in which a new formulation of quantum theory is developed for totally constrained systems, that is, canonical systems in which the hamiltonian is written as a linear combination of constraints…

I give a pedagogical overview of decoherence and its role in providing a dynamical account of the quantum-to-classical transition. The formalism and concepts of decoherence theory are reviewed, followed by a survey of master equations and…

In this article indicators to describe the "beauty" of noises are proposed. Rhythmic, tonal and harmonic suavity are introduced. They give a characterization of a noise in terms of rhythmic regularity (rhythmic suavity), of auditory…

We consider a class of perturbations of the 2D harmonic oscillator, and of some other dynamical systems, which we show are isomorphic to a function of a toric system (a Birkhoff canonical form). We show that for such systems there exists a…

Chords in musical harmony can be viewed as objects having shapes (major/minor/etc.) attached to base sets (pitch class sets). The base set and the shape set are usually given the structure of a group, more particularly a cyclic group. In a…

If we reduce coherence in a given quantum system, the result is an increase in entropy. Does this necessarily convert this quantum system into a classical system? The answer to this question is No. The decrease of coherence means more…

This article examines the relationship between classical and quantum propagation of chaos. (In this context, "chaos" refers to the Boltzmann's Ansatz of molecular disorder, not to chaotic dynamics.) Classical propagation of chaos is shown…