Related papers: A Non-Pythagorean Musical Scale Based on Logarithm…
It is shown that quantum logic is a logic in the very same way in which classical logic is a logic. Soundness and completeness of both quantum and classical logics have been proved for novel lattice models that are not orthomodular and…
We introduce a $q$-deformation of the Pythagoras equation $a^2 + b^2 = c^2$, which is a polynomial version of it different from the standard one. We construct a polynomial analogue, or ``$q$-analogue'', of every primitive Pythagorean…
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…
Conventional Music Notation (CMN) is the well-established foundation for the written communication of musical information, such as rhythm, harmony, or timbre. However, CMN suffers from the complexity of its visual encoding and the need for…
In this paper, we consider the problem of probabilistically modelling symbolic music data. We introduce a representation which reduces polyphonic music to a univariate categorical sequence. In this way, we are able to apply state of the art…
In North-Indian-Music-System(NIMS),tabla is mostly used as percussive accompaniment for vocal-music in polyphonic-compositions. The human auditory system uses perceptual grouping of musical-elements and easily filters the tabla component,…
The authors present SHarmonic, a new implementation of the spherical harmonics targeted for electronic-structure calculations. Their approach is to use explicit formulas for the harmonics written in terms of normalized Cartesian…
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…
In standard quantum theory, time is not an observable. It enters as a parameter in the Schr\"odinger equation, but there is no measurement operator associated to it. Nevertheless, one may take an operational viewpoint and regard time as the…
A genuinely three-dimensional system, viz. the hyperbolic 4-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and…
This article deals with the problem of the statistical performance analysis of the MUSIC ( Multiple Signal Classification ) algorithm which is an eigen decomposition based method for the estimation of the angles of arrival of signals…
We consider the space of all musical scales with the ambition to systematize it. To do this, we pursue the idea to view certain scales as basic constituents and to "mix" all remaining scales from these. The German version of this article…
Popular music is a key cultural expression that has captured listeners' attention for ages. Many of the structural regularities underlying musical discourse are yet to be discovered and, accordingly, their historical evolution remains…
Quantum computing can be employed in computer-aided music composition to control various attributes of the music at different structural levels. This article describes the application of quantum simulation to model compositional decision…
In current applied research the most-used route to an analysis of composition is through log-ratios -- that is, contrasts among log-transformed measurements. Here we argue instead for a more direct approach, using a statistical model for…
Nonclassical symmetries and reductions of polynomial equations and systems of polynomial equations are considered. It is shown that specific polynomial equations having "hidden" symmetries can be reduced to classical symmetric systems of…
Many quantum systems may have the same classical limit. We argue that in the classical limit their traces do not necessarily converge one to another. The trace formula allows to express quantum traces by means of classical quantities as…
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…
A combination of three or more tones played together is called a chord. In the chromatic scale, chords which are consonant are of particular interest and can be divided into several groups, two main ones being the major and minor chords.…
The Leggett-Garg inequalities probe the classical-quantum boundary by putting limits on the sum of pairwise correlation functions between classical measurement devices that consecutively measured the same quantum system. The apparent…