Related papers: Mathematical Harmony Analysis
Harmony in visual compositions is a concept that cannot be defined or easily expressed mathematically, even by humans. The goal of the research described in this paper was to find a numerical representation of artistic compositions with…
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…
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…
Metrics obtained by integrating within the generalised invariant formalism are structured around their intrinsic coordinates, and this considerably simplifies their invariant classification and symmetry analysis. We illustrate this by…
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…
We consider a specific scenario of text aggregation, in the realm of musical harmonization. Musical harmonization shares similarities with text aggregation, however the language of harmony is more structured than general text. Concretely,…
Representations in the auditory cortex might be based on mechanisms similar to the visual ventral stream; modules for building invariance to transformations and multiple layers for compositionality and selectivity. In this paper we propose…
In this paper we present a mathematical way of defining musical modes, we derive a formula for the total number of modes and define the musicality of a mode as the total number of harmonic chords whithin the mode. We also give an algorithm…
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…
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 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.
For music indexing robust to sound degradations and scalable for big music catalogs, this scientific report presents an approach based on audio descriptors relevant to the music content and invariant to sound transformations (noise…
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…
Rhythm patterns can be performed with a wide variation of tempi. This presents a challenge for many music information retrieval (MIR) systems; ideally, perceptually similar rhythms should be represented and processed similarly, regardless…
Any constructive continuous function must have a gradually varied approximation in compact space. However, the refinement of domain for $\sigma-$-net might be very small. Keeping the original discretization (square or triangulation), can we…
Harmonic maps are nonlinear extensions of harmonic functions. They are critical points of natural energy functionals between Riemannian manifolds. Such type of problems appear in Physics, Geometry of Finance and the study of regularity and…
Vibrational dynamics governs the fundamental properties of molecular crystals, shaping their thermodynamics, mechanics, spectroscopy, and transport phenomena. However desirable, the first-principles calculation of solid-state vibrations,…
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…
Rhythms and vibrations represent the quintessence of life, they are ubiquitous (systemic) in all living systems. Recognising, unfolding these rhythms is paramount in medicine, for example in the physiology of the heart, lung, hearing,…
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…