Related papers: 2:3:4-Harmony within the Tritave
Even though chord roots constitute a fundamental concept in music theory, existing models do not explain and determine them to full satisfaction. We present a new method which takes sequential context into account to resolve ambiguities and…
The Pythagorean school attributed consonance in music to simplicity of frequency ratios between musical tones. In the last two centuries, the consonance curves developed by Helmholtz, Plompt and Levelt shifted focus to psycho-acoustic…
In the production of modern music, the musical characteristics of the guitar or keyboard amplifier play an integral role in the creative process. This article explores the physics of music with an emphasis on the role of distortion in the…
To date, calculating the frequencies of musical notes requires one to know the frequency of some reference note. In this study, first-order ordinary differential equations are used to arrive at a mathematical model to determine tonal…
After our book---Mathematics and Music: Composition, Perception, and Performance, 2nd edition, CRC Press, 2020---was published, we found a striking example of the importance of the Tonnetz for analyzing the harmonic structure of The…
Systems such as Microsoft Songsmith automatically assign chords and harmony to a melody by minimizing the dissonance across all chord changes. Although this produces harmonious music, it is not what practicing musicians do. In this paper, I…
A song's backbone is its chord progressions, a series of chords that improve the harmony and add to the overall composition. For individuals ranging from beginners to creative artists, comprehending and implementing music theory grammar for…
Aims. This study suggests that the use of multiple perceived pitches arising from a single harmonic complex tone is an active and intentional feature of contemporary popular music. The phenomenon is illustrated through examples drawn from…
Modern keyboards allow a musician to play multiple instruments at the same time by assigning zones -- fixed pitch ranges of the keyboard -- to different instruments. In this paper, we aim to further extend this idea and examine the…
While motivated by structural problems in mathematical music theory, this article introduces a novel combinatorial framework that advances the classification of cyclic cubic bipartite graphs. We extend the classical study of Levi graphs by…
Several prior works have proposed various methods for the task of automatic melody harmonization, in which a model aims to generate a sequence of chords to serve as the harmonic accompaniment of a given multiple-bar melody sequence. In this…
Some relations among Pythagorean triples are established. The main tool is a fundamental characterization of the Pythagorean triples through a chatetus which allows to determine relationships with Pythagorean triples having the same…
In this paper, we present a novel state of the art system for automatic downbeat tracking from music signals. The audio signal is first segmented in frames which are synchronized at the tatum level of the music. We then extract different…
In this article indicators to describe the "beauty" of noises are proposed. Rhythmic, tonal and harmonic suavity are introduced. They give a characterization of a noise in terms of rhythmic regularity (rhythmic suavity), of auditory…
The standard 2-dimensional Tonnetz describes parsimonious voice-leading connections between major and minor triads as the 3-dimensional Tonnetz does for dominant seventh and half-diminished seventh chords. In this paper, I present a…
There are four characteristic circles for each triangle on a plane. All for are tangential to the three straight lines containing the triangles' three sides. Three are exterior circles, the fourth is the in-circle. When the triangle is…
This paper deals with the algebraic structure of the sequence of harmonics when combined with equal temperaments. Fractals and the golden ratio appear surprisingly on the way. The sequence of physical harmonics is an increasingly enumerable…
Piano cover generation aims to automatically transform a pop song into a piano arrangement. While numerous deep learning approaches have been proposed, existing models often fail to maintain structural consistency with the original song,…
The presence of skew quadrupole fields will linearly couple the x and y motions. The x and y motions can then be written as the sum of two normal modes >. This paper presents analytical perturbation theory results for the tunes of the…
This paper introduces four different artificial intelligence algorithms for music generation and aims to compare these methods not only based on the aesthetic quality of the generated music but also on their suitability for specific…