Related papers: 2:3:4-Harmony within the Tritave
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,…
We study a generalization of the classical Riemannian Tonnetz to N-tone equally tempered scales (for all N) and arbitrary triads. We classify all the spaces that result. The torus turns out to be the most common possibility, especially as N…
Following the ideas of von Helmholtz and Plomp-Levelt, an algorithm for calculating the total dissonance of complex sounds, free from logical inconsistencies and useful for comparing different chords, is proposed. The method is tested by…
This paper attempts to look for a mathematical method of composing music by incorporating Schonbergs idea of tone rows and matrix theory from linear algebra. The elements of a note set S are considered as the integer values for the natural…
The tone hole geometry of a clarinet is optimized numerically. The instrument is modeled as a network of one dimensional transmission line elements. For each (non-fork) fingering, we first calculate the resonance frequencies of the input…
We give a new analysis of a tuning problem in music theory, pertaining specifically to the approximation of harmonics on a two-dimensional keyboard. We formulate the question as a linear programming problem on families of constraints and…
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…
We propose AccoMontage2, a system capable of doing full-length song harmonization and accompaniment arrangement based on a lead melody. Following AccoMontage, this study focuses on generating piano arrangements for popular/folk songs and it…
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…
Recently, multi-instrument music generation has become a hot topic. Different from single-instrument generation, multi-instrument generation needs to consider inter-track harmony besides intra-track coherence. This is usually achieved by…
This paper introduces a novel method for emulating piano sounds. We propose to exploit the sines, transient, and noise decomposition to design a differentiable spectral modeling synthesizer replicating piano notes. Three sub-modules learn…
We present a new system for simultaneous estimation of keys, chords, and bass notes from music audio. It makes use of a novel chromagram representation of audio that takes perception of loudness into account. Furthermore, it is fully based…
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…
After a quick exposition of Mazzola's quantum modulation model for the so-called triadic interpretation of the major scale within the equal temperament, we study the model for the tetradic interpretation of the same scale. It is known that…
Music tone quality evaluation is generally performed by experts. It could be subjective and short of consistency and fairness as well as time-consuming. In this paper we present a new method for identifying the clarinet reed quality by…
Several musical scales, like the major scale, can be described as finite arithmetic sequences modulo octave, i.e. chunks of an arithmetic sequence in a cyclic group. Hence the question of how many different arithmetic sequences in a cyclic…
This paper develops a formal theory of musical scales and their harmonic coverings and introduces orbit covers: coverings obtained by translating a fixed subset across a scale via a group action. Orbit covers generalize familiar…
This application-oriented study concerns computational musicology, which makes use of grammar systems. We define multi-generative rule-synchronized scattered-context grammar systems (without erasing rules) and demonstrates how to…
While deep generative models have become the leading methods for algorithmic composition, it remains a challenging problem to control the generation process because the latent variables of most deep-learning models lack good…
A new definition of musical pitch is proposed. A Finite-Difference Time Domain (FDTM) model of the cochlea is used to calculate spike trains caused by tone complexes and by a recorded classical guitar tone. All harmonic tone complexes,…