相关论文: Music By Numbers

In this paper we present a mathematical way of defining musical modes and we define the musicality of a mode as a product of three different factors. We conclude by classifying the modes which are most musical according to our definition.

The mathematics of musical intervals and scales has been extensively studied. Vastly simplified, our ears seem to prefer intervals whose frequency ratios have small numerator and denominator, such as 2:1 (octave), 3:2 (perfect fifth), 4:3…

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…

Multi-modal music generation, using multiple modalities like text, images, and video alongside musical scores and audio as guidance, is an emerging research area with broad applications. This paper reviews this field, categorizing music…

There has been an everlasting discussion around the concept of form in music. This work is motivated by such debate by using a complex systems framework in which we study the form as an emergent property of rhythm. Such a framework…

For the tasks of automatic music emotion recognition, genre recognition, music recommendation it is helpful to be able to extract mode from any section of a musical piece as a perceived amount of major or minor mode (majorness) inside that…

We give a formal definition of the musical concept of voice leading in mathematical terms, based on the idea of partial permutations of certain ordered multisets. Then we associate a partial permutation matrix with a voice leading in a…

We develop aspects of music theory related to harmony, such as scales, chord formation and improvisation from a combinatorial perspective. The goal is to provide a foundation for this subject by deriving the basic structure from a few…

We present an algebraic construction of music notes and show how to associate them inseveral ways to construct music ranges. Then a family of ranges emerge with a fixed number of notes: two, three, five, seven, twelve, seventeen, etc. A…

Understanding music popularity is important not only for the artists who create and perform music but also for the music-related industry. It has not been studied well how music popularity can be defined, what its characteristics are, and…

Notes in a musical piece are building blocks employed in non-random ways to create melodies. It is the "interaction" among a limited amount of notes that allows constructing the variety of musical compositions that have been written in…

In this work we show a technique that allows for the musical interpretation of the brightness variations of stars. This method allows composers a lot of freedom to incorporate their own ideas into the score, based on the melodic line…

Musical chords, harmonies or melodies in Just Intonation have note frequencies which are described by a base frequency multiplied by rational numbers. For any local section, these notes can be converted to some base frequency multiplied by…

This paper focuses on the modeling of musical melodies as networks. Notes of a melody can be treated as nodes of a network. Connections are created whenever notes are played in sequence. We analyze some main tracks coming from different…

Consonance is related to the perception of pleasantness arising from a combination of sounds and has been approached quantitatively using mathematical relations, physics, information theory, and psychoacoustics. Tonal consonance is present…

Understanding the structural characteristics of harmony is essential for an effective use of music as a communication medium. Of the three expressive axes of music (melody, rhythm, harmony), harmony is the foundation on which the emotional…

The equable, Pythagorean and natural scales are built on the basis of a mathematical logic.

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…

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…

Melodic similarity measurement is of key importance in music information retrieval. In this paper, we use geometric matching techniques to measure the similarity between two melodies. We represent music as sets of points or sets of…