Related papers: Melody and Variation Generation Through KAM Theory

We propose Polyffusion, a diffusion model that generates polyphonic music scores by regarding music as image-like piano roll representations. The model is capable of controllable music generation with two paradigms: internal control and…

In this paper, we propose to adapt the method of mutual information maximization into the task of Chinese lyrics conditioned melody generation to improve the generation quality and diversity. We employ scheduled sampling and force decoding…

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…

The purpose of this lecture is to describe the KAM theorem in its most basic form and to give a complete and detailed proof. This proof essentially follows the traditional lines laid out by the inventors of this theory, and the emphasis is…

This paper presents a generative AI model for automated music composition with LSTM networks that takes a novel approach at encoding musical information which is based on movement in music rather than absolute pitch. Melodies are encoded as…

Melody estimation or melody extraction refers to the extraction of the primary or fundamental dominant frequency in a melody. This sequence of frequencies obtained represents the pitch of the dominant melodic line from recorded music audio…

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…

We consider the KAM theory for rotational flows on an $n$-dimensional torus. We show that if its frequencies are diophantine of type $n-1$, then Moser's KAM theory with parameters applies to small perturbations of weaker regularity than…

In classical music and in any genre of contemporary music, the tonal elements or notes used for playing are the same. The numerous possibilities of chords for a given instance in a piece make the playing, in general, very intricate, and…

We develop convergent variational perturbation theory for quantum statistical density matrices. The theory is applicable to polynomial as well as nonpolynomial interactions. Illustrating the power of the theory, we calculate the…

Polyphonic music generation is still a challenge direction due to its correct between generating melody and harmony. Most of the previous studies used RNN-based models. However, the RNN-based models are hard to establish the relationship…

In this paper we explore techniques for generating new music using a Variational Autoencoder (VAE) neural network that was trained on a corpus of specific style. Instead of randomly sampling the latent states of the network to produce free…

This paper investigates the effect of random perturbations, in particular multiplicative noise, on the integrable structure of Hamiltonian systems, with a particular focus on KAM theory for stochastic Hamiltonian dynamics. We prove that,…

We evaluate five Transformer-based strategies for chord-conditioned melody and bass generation using a set of music theory-motivated metrics capturing pitch content, pitch interval size, and chord tone usage. The evaluated models include…

We introduce the notion of multi-pattern, a combinatorial abstraction of polyphonic musical phrases. The interest of this approach lies in the fact that this offers a way to compose two multi-patterns in order to produce a longer one. This…

We consider the Non-Abelian Chern-Simons term coupled to external particles, in a gauge and diffeomorphism invariant form. The classical equations of motion are perturbativelly studied, and the on-shell action is shown to produce…

The paper presents a method of the music generation based on LSTM (Long Short-Term Memory), contrasts the effects of different network structures on the music generation and introduces other methods used by some researchers.

The homology and cohomology of quandles and racks are used in knot theory: given a finite quandle and a cocycle, we can construct a knot invariant. This is a quick introductory survey to the invariants of knots derived from quandles and…

We propose a model for the quantum theory of gravity. the model has diffeomorphism invariance, a natural length scale, and (plausibly) propagating modes. in the new addendum, we alter the model in a way which makes the propagating modes…

We present a KAM theorem for presymplectic dynamical systems. The theorem has a " a posteriori " format. We show that given a Diophantine frequency $\omega$ and a family of presymplectic mappings, if we find an embedded torus which is…