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

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…

In order to explore tonality outside of the `Pythagorean' paradigm of integer ratios, Robert Schneider introduced a musical scale based on the logarithm function. We seek to refine Schneider's scale so that the difference tones generated by…

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…

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…

The perception of consonance/dissonance of musical harmonies is strongly correlated with their periodicity. This is shown in this article by consistently applying recent results from psychophysics and neuroacoustics, namely that the just…

We investigate a dynamically adapting tuning scheme for microtonal tuning of musical instruments, allowing the performer to play music in just intonation in any key. Unlike other methods, which are based on a procedural analysis of the…

The tonnetz, which is commonly represented as a tessellation of the plane by a triangular network of tones, can also be represented as a bipartite graph of degree three with twelve vertices denoting major triads and twelve vertices denoting…

A method is proposed which enables one to produce musical compositions by using transposition in place of harmonic progression. A transposition scale is introduced to provide a set of intervals commensurate with the musical scale, such as…

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…

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

The human sense of hearing perceives a combination of sounds 'in tune' if the corresponding harmonic spectra are correlated, meaning that the neuronal excitation pattern in the inner ear exhibits some kind of order. Based on this…

Why are white and black piano keys in an octave arranged as they are today? This article examines the relations between abstract algebra and key signature, scales, degrees, and keyboard configurations in general equal-temperament systems.…

We study the wave equation for a string with stiffness. We solve the equation and provide a uniqueness theorem with suitable boundary conditions. For a pinned string we compute the spectrum, which is slightly inharmonic. Therefore, the…

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 dichotic method of hearing sound adapts in the region of musical harmony. The algorithm of the separation of the being dissonant voices into several separate groups is proposed. For an increase in the pleasantness of chords the…

We make some general observations about partial orders on quotient spaces, and explore their use in music theory, in two different contexts. In the first, we show that many of the most familiar chord and scale types in Western music appear…

We introduce the concept of dynamical score networks for the representation and analysis of tonal compositions: a score is interpreted as a dynamical network where every chord is a node and each progression links successive chords. This…

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…

After briefly revising the concepts of consonance/dissonance, a respective mathematic-computational model is described, based on Helmholtz's consonance theory and also considering the partials intensity. It is then applied to characterize…

This article deals with the construction of surfaces that are suitable for representing pentachords or 5-pitch segments that are in the same $T/I$ class. It is a generalization of the well known \"Ottingen-Riemann torus for triads of…