Related papers: Some mathematical and computational relations betw…
Music generation has always been a hot topic. When discussing symbolic music, melody or harmonies are usually seen as the only generating targets. But in fact, playing techniques are also quite an important part of the music. In this paper,…
In signal processing, a signal is a function. Conceptually, replacing a function by its graph, and extending this approach to a more abstract setting, we define a signal as a submanifold M of a Riemannian manifold (with corners) that…
After briefly revising the concepts of consonance/dissonance, a respective mathematic-computational model is described, based on Helmholtz's consonance theory and also considering the partials intensity. It is then applied to characterize…
Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…
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…
Structured light fields, featuring unique topological properties and high tunability, have opened new frontiers in light-matter interactions with magnetic systems. However, the ultrafast and reconfigurable optical encoding of various types…
This paper presents an algorithm that transforms color visual images, like photographs or paintings, into tactile graphics. In the algorithm, the edges of objects are detected and colors of the objects are estimated. Then, the edges and the…
We use some fundamental ideas from complex analysis to create symmetric images and animations. Using a domain coloring algorithm, we generate mappings to the entire complex plane or the hyperbolic upper half-plane. The resulting designs can…
Mathematics can help analyze the arts and inspire new artwork. Mathematics can also help make transformations from one artistic medium to another, considering exceptions and choices, as well as artists' individual and unique contributions.…
Musical mode is one of the most critical element that establishes the framework of pitch organization and determines the harmonic relationships. Previous works often use the simplistic and rigid alignment method, and overlook the diversity…
As a planet orbits, it causes periodic modulations in the light curve of its host star. Due to the combined effects of the planet raising tides on the host star, relativistic beaming of the starlight, and reflection of light off the…
Hypersubstitutions are mappings which map operation symbols to terms. Terms can be visualized by trees. Hypersubstitutions can be extended to mappings defined on sets of trees. The nodes of the trees, describing terms, are labelled by…
Musicians produce individualized, expressive performances by manipulating parameters such as dynamics, tempo and articulation. This manipulation of expressive parameters is informed by elements of score information such as pitch, meter, and…
A $t$-tone coloring of a graph $G$ assigns to each vertex a set of $t$ colors such that any pair of vertices $u, v$ with distance $d$ can share at most $d-1$ colors. In this note, we prove several new results on $t$-tone coloring. For…
A new definition of musical pitch is proposed. A Finite-Difference Time Domain (FDTM) model of the cochlea is used to calculate spike trains caused by tone complexes and by a recorded classical guitar tone. All harmonic tone complexes,…
We describe how to construct a spanning set of linearly-independent, automatically orthogonal colour tensors for scattering amplitudes involving coloured particles transforming under arbitrary representations of any gauge theory, sufficient…
Emotion-driven melody harmonization aims to generate diverse harmonies for a single melody to convey desired emotions. Previous research found it hard to alter the perceived emotional valence of lead sheets only by harmonizing the same…
Mechanical metamaterials are increasingly attracting interest in engineering applications due to their unique mechanical properties and lightweight nature. This study develops a novel sound-based representation to characterize the…
The results of our experiments on categorical perception of different shades of gray are reported. A special color generator was created for conducting the experiments on categorizing a random sequence of colors into two classes, light-gray…
Emotion alignment between music and palettes is crucial for effective multimedia content, yet misalignment creates confusion that weakens the intended message. However, existing methods often generate only a single dominant color, missing…