Related papers: Relativity of musical mood
After a quick exposition of Mazzola's quantum modulation model for the so-called triadic interpretation of the major scale within the equal temperament, we study the model for the tetradic interpretation of the same scale. It is known that…
The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently…
Laplacian eigenmodes on homogeneous Clifford--Klein factors of the three--sphere are obtained as pullbacks of harmonics on the orbifolded two--sphere using the Hopf map. A method of obtaining these polyhedral, or crystal, harmonics using…
In this paper I want to suggest a new solution to the problem of musical tuning. On one hand, I see it as a generalization of Just Intonation (JI) to inharmonic timbers, on another, as a unification of spectral interference and harmonicity…
The well-known conditions for a simplicial set to be the nerve of a small category generalize with respect to two parameters: the dimension n of the things which compose, and the position i of the thing which is the result of the…
Generation of odd harmonics by a super strong focused laser beam in vacuum is considered. The process occurs due to the plural light-by-light scattering effect. In the leading order of perturbation theory, generation of $(2k+1)$th harmonic…
We study compositions whose parts are colored by subsequences of the Fibonacci numbers. We give explicit bijections between Fibonacci colored compositions and several combinatorial objects, including certain restricted ternary and…
In this paper we propose numerical measures for evaluating the aesthetic interest of simple patterns. The patterns consist of elements (symbols, pixels, etc.) in regular square arrays. The measures depend on two characteristics of the…
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…
We define a notion of concordance based on Euler characteristic, and show that it gives rise to a concordance group of links in the three-sphere, which has the concordance group of knots as a direct summand with infinitely generated…
For centuries, the history and music of Joseph Franz Haydn and Wolfgang Amadeus Mozart have been compared by scholars. Recently, the growing field of music information retrieval (MIR) has offered quantitative analyses to complement…
We describe the Doppler effect between equally accelerated light source and observer under the special relativity. The proper accelerations are constant and parallel. An English version is available by request. - - - - - - - - - - - Ni…
Modeling polyphonic music is a particularly challenging task because of the intricate interplay between melody and harmony. A good model should satisfy three requirements: statistical accuracy (capturing faithfully the statistics of…
A superdiagonal composition is one in which the $i$-th part or summand is of size greater than or equal to $i$. In this paper, we study the number of palindromic superdiagonal compositions and colored superdiagonal compositions. In…
We present conclusive evidence showing that different sources of diversity, such as those represented by quenched disorder or noise, can induce a resonant collective behavior in an ensemble of coupled bistable or excitable systems. Our…
A study of around 13,000 musical compositions from the Western classical tradition is carried out, spanning 33 major composers from the Baroque to the Romantic, with a focus on the usage of major/minor key signatures. A 2-dimensional…
The ability of the auditory system to perceive the fundamental frequency of a sound even when this frequency is removed from the stimulus is an interesting phenomenon related to the pitch of complex sounds. This capability is known as…
The standard theory of musical scales since antiquity has been based on harmony, rather than melody. While recent analyses provide mixed support for a role of melody as well as harmony, we lack a comparative analysis based on cross-cultural…
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. This work introduces bispectral mode decomposition as a direct means of educing flow structures that are associated with triadic interactions from…
This chapter considers how string-based methods might be adapted to address music-analytic questions related to the discovery of musical organization, with particular attention devoted to the analysis of tonal harmony. I begin by applying…