相关论文: Music By Numbers
In this note, we consider ordered partitions of integers such that each entry is no more than a fixed portion of the sum. We give a method for constructing all such compositions as well as both an explicit formula and a generating function…
Our goal is to be able to build a generative model from a deep neural network architecture to try to create music that has both harmony and melody and is passable as music composed by humans. Previous work in music generation has mainly…
A model of music needs to have the ability to recall past details and have a clear, coherent understanding of musical structure. Detailed in the paper is a neural network architecture that predicts and generates polyphonic music aligned…
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…
The harmonic number $H_k=\sum_{j=1}^k1/j(k=1,2,3\cdots)$ play an important role in mathematics. Let $p>3$ be a prime. In this paper, we establish a number of congruences with the form $\sum_{k=1}^{p-1}k^mH_k^n(\mod p^2)$ for…
Real music signals are highly variable, yet they have strong statistical structure. Prior information about the underlying physical mechanisms by which sounds are generated and rules by which complex sound structure is constructed (notes,…
Maximal chord diagrams up to all isomorphisms are enumerated. The enumerating formula is based on a bijection between rooted one-vertex one-face maps on locally orientable surfaces and a certain class of symmetric chord diagrams. This…
Due to the increased complexity of software development projects more and more systems are described by models. The sheer size makes it impractical to describe these systems by a single model. Instead many models are developed that provide…
We propose a method to recommend background music for videos. Current work rarely considers the emotional information of music, which is essential for video music retrieval. To achieve this, we design two paths to process content…
The new formulas, which determine sign and amplitude of utilitarian emotions, are proposed on the basis of the information theory of emotions. In area of perception of musical chords the force of emotions depends on the relative pitch of…
We study, through new recurrence relations for certain binomial coefficients modulo a power of a prime, the evolution of the primitives of a modular periodic sequence. We prove that we can reduce to study primitives of constant sequences…
The set of prime numbers has been analyzed, based on their algebraic and arithmetical structure. Here by obtaining a sort of linear formula for the set of prime numbers, they are redefined and identified; under a systematic procedure it has…
In this paper, we consider the MUltiple SIgnal Classification (MUSIC) algorithm for identifying the locations of small electromagnetic inhomogeneities surrounded by random scatterers. For this purpose, we rigorously analyze the structure of…
We obtain for the Kempner series (i.e. harmonic series where certain digits are excluded from all denominators, for example the digit 9 in base 10) new representations as geometrically convergent series. The coefficients for these…
Mode clustering is a nonparametric method for clustering that defines clusters using the basins of attraction of a density estimator's modes. We provide several enhancements to mode clustering: (i) a soft variant of cluster assignment, (ii)…
In this paper we cluster 330 classical music pieces collected from MusicNet database based on their musical note sequence. We use shingling and chord trajectory matrices to create signature for each music piece and performed spectral…
The motion of a particle in 6-dimensional phase space in the presence of linear coupling can be written as the sum of 3 normal modes. A cubic equation is found for the tune of the normal modes, which allows the normal mode tunes to be…
This paper introduces HarmonySet, a comprehensive dataset designed to advance video-music understanding. HarmonySet consists of 48,328 diverse video-music pairs, annotated with detailed information on rhythmic synchronization, emotional…
The perception of consonance/dissonance of musical harmonies is strongly correlated with their periodicity. This is shown in this article by consistently applying recent results from psychophysics and neuroacoustics, namely that the just…
Combining the derivative operator with a binomial sum from the telescoping method, we establish a family of summation formulas involving generalized harmonic numbers.