相关论文: 2:3:4-Harmony within the Tritave

In a certain way, this paper presents the continuation of the previous one which discussed the harmonic structure of the genetic code (Rakocevic, 2004). Several new harmonic structures presented in this paper, through specific unity and…

The generation of harmonics by atoms or ions in a two-color, coplanar field configuration with commensurate frequencies is investigated through both, an analytical calculation based on the Lewenstein model and the numerical ab initio…

We show that certain iteration systems lead to fractal measures admitting exact orthogonal harmonic analysis.

We apply geometric group theory to study and interpret known concepts from Western music. We show that chords, the circle of fifths, scales and certain aspects of the first species of counterpoint are encoded in the Cayley graph of the…

Statistical models and information theory have provided a useful set of tools for studying music from a quantitative perspective. These approaches have been employed to generate compositions, analyze structural patterns, and model cognitive…

We develop a model of musical rhythm and meter based on optimizing the trade-off between human psychological preferences for perceiving repeated patterns in time with a desire for variety and complexity. By mapping these competing…

Steiner triple systems form one of the most studied classes of combinatorial designs. Configurations, including subsystems, play a central role in the investigation of Steiner triple systems. With sporadic instances of small systems, ad-hoc…

This paper presents a web application for visualizing the tonality of a piece of music -- the organization of its chords and scales -- at a high level of abstraction and with coordinated playback. The application applies the discrete…

A number theoretic algorithm is given for writing gauge theory amplitudes in a compact manner. It is possible to write down all details of the complete $L$ loop amplitude with two integers, or a complex integer. However, a more symmetric…

In this paper we present a new definition of the distortion matrix for a score following framework based on DTW. The proposal consists of arranging the score information in a sequence of note combinations and learning a spectral pattern for…

Fourier Series is the second of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such as partial…

If we label the vertices of a triangle with 1, 2 and 4, and the orthocentre with 7, then any of the four numbers 1, 2, 4, 7 is the nim-sum of the other three and is their orthocentre. Regard the triangle as an orthocentric quadrangle.…

Multi-track music generation has garnered significant research interest due to its precise mixing and remixing capabilities. However, existing models often overlook essential attributes such as rhythmic stability and synchronization,…

Music creation involves not only composing the different parts (e.g., melody, chords) of a musical work but also arranging/selecting the instruments to play the different parts. While the former has received increasing attention, the latter…

In this work we were aimed to study music using visibility algorithms. This algorithms are used as a way to get a network, from a time series. However the main idea of this paper was not to study music from the perspective of complex…

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…

The aim of this work is to define a model based on deep learning that is able to identify different instrument timbres with as few parameters as possible. For this purpose, we have worked with classical orchestral instruments played with…

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…

Mathematics is a far reaching discipline and its tools appear in many applications. In this paper we discuss its role in music and signal processing by revisiting the use of mathematics in algorithms that can extract chord information from…

We present a method for the generation of Midi files of piano music. The method models the right and left hands using two networks, where the left hand is conditioned on the right hand. This way, the melody is generated before the harmony.…