Related papers: The axiom system of classical harmony
Algorithmic harmonization - the automated harmonization of a musical piece given its melodic line - is a challenging problem that has garnered much interest from both music theorists and computer scientists. One genre of particular interest…
Melody harmonization has long been closely associated with chorales composed by Johann Sebastian Bach. Previous works rarely emphasised chorale generation conditioned on chord progressions, and there has been a lack of focus on assistive…
Music is a complex socio-cultural construct, which fascinates researchers in diverse fields, as well as the general public. Understanding the historical development of music may help us understand perceptual and cognition, while also…
Most music theory books are like medieval medical textbooks: they contain unjustified superstition, non-reasoning, and funny symbols glorified by Latin phrases. How does music, in particular harmony, actually work, presented as a real,…
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…
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 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…
Music is a fundamental human construct, and harmony provides the building blocks of musical language. Using the Kunstderfuge corpus of classical music, we analyze the historical evolution of the richness of harmonic vocabulary of 76…
Harmonic theory provides a mathematical framework to describe the structure, behavior, evolution and emergence of harmonic systems. A harmonic system is context aware, contains elements that manifest characteristics either collaboratively…
This chapter considers how string-based methods might be adapted to address music-analytic questions related to the discovery of musical organization, with particular attention devoted to the analysis of tonal harmony. I begin by applying…
In the Pythagorean tuning system, the fifth is used to generate a scale of 12 notes per octave. In this paper, we use the octave to generate a scale of 19 notes per tritave; one can play this scale on a traditional piano. In this system,…
Is the specific structure of Western tonal harmony a physical inevitability derived from acoustics, or is it merely one solution among many in a purely algebraic landscape? In this paper, we strip away the physics of vibrating strings and…
How do different musical traditions achieve tonal coherence? Most computational measures to date have analysed tonal coherence in terms of a single dimension, whereas a multi-dimensional analyses have not been sufficiently explored. We…
The classical three-body harmonic system in $\mathbb{R}^d$ ($d>1$) with finite rest lengths and zero total angular momentum $L=0$ is considered. This model describes the dynamics of the $L=0$ near-equilibrium configurations of three point…
Correlations between quantum theory and music theory - specifically between principles of quantum computing and musical harmony - can lead to new understandings and new methodologies for music theorists and composers. The quantum principle…
Computational aesthetics evaluation has made great achievements in the field of visual arts, but the research work on music still needs to be explored. Although the existing work of music generation is very substantial, the quality of music…
Algorithmic composition of music has a long history and with the development of powerful deep learning methods, there has recently been increased interest in exploring algorithms and models to create art. We explore the utility of state…
Unique set of coherent states for the anharmonic oscillator is obtained by requiring i. under the quantum mechanical time evolution a coherent state evolves into another, governed by trajectory in the classical phase space (of a related…
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…
Driven many-body systems have been shown to exhibit discrete time crystal phases characterized by broken discrete time-translational symmetry. This has been achieved generally through a subharmonic response, in which the system undergoes…