Related papers: A Non-Pythagorean Musical Scale Based on Logarithm…
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…
In this work, we present a new method for generating a threshold structure. This kind of structure can be advantageously used in various halftoning algorithms such as clustered-dot or dispersed-dot dithering, error diffusion with threshold…
In musical compositions that include vocals, lyrics significantly contribute to artistic expression. Consequently, previous studies have introduced the concept of a recommendation system that suggests lyrics similar to a user's favorites or…
We present a novel approach for data set scaling based on scale-measures from formal concept analysis, i.e., continuous maps between closure systems, and derive a canonical representation. Moreover, we prove said scale-measures are lattice…
Creativity, or the ability to produce new useful ideas, is commonly associated to the human being; but there are many other examples in nature where this phenomenon can be observed. Inspired by this fact, in engineering and particularly in…
After presenting the general framework of 'mathemusical' dynamics, we focus on one music-theoretical problem concerning a special case of homometry theory applied to music composition, namely Milton Babbitt's hexachordal theorem. We briefly…
In this paper, we explore the tokenized representation of musical scores using the Transformer model to automatically generate musical scores. Thus far, sequence models have yielded fruitful results with note-level (MIDI-equivalent)…
Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropriate distance for a given task is an endeavor. Instead of…
The structure of the Euclidean algorithm can be used to generate a very large family of rhythms. In this paper, we explore a very specific family of Euclidean rhythms, the Euclidean rhythms in which the rests have a palindromic structure.…
Audio processing methods operating on a time-frequency representation of the signal can introduce unpleasant sounding artifacts known as musical noise. These artifacts are observed in the context of audio coding, speech enhancement, and…
"Clarithmetic" is a generic name for formal number theories similar to Peano arithmetic, but based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html) instead of the more traditional classical or intuitionistic logics.…
The complexity of a system description is a function of the entropy of its symbolic description. Prior to computing the entropy of the system description, an observation scale has to be assumed. In natural language texts, typical scales are…
We propose a continuous measure of tonal ambiguity that extends the established concept of uniqueness. While uniqueness is widely regarded as necessary for tonality, it cannot (i) discriminate among sets that possess it, (ii) capture…
Automatic music transcription converts audio recordings into symbolic representations, facilitating music analysis, retrieval, and generation. A musical note is characterized by pitch, onset, and offset in an audio domain, whereas it is…
In this paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales.
In [Kat94b], Kato defined his notion of a log regular scheme and studied the local behavior of such schemes. A toric variety equipped with its canonical logarithmic structure is log regular. And, these schemes allow one to generalize toric…
A logarithmic scaling for structure functions, in the form $S_p \sim [\ln (r/\eta)]^{\zeta_p}$, where $\eta$ is the Kolmogorov dissipation scale and $\zeta_p$ are the scaling exponents, is suggested for the statistical description of the…
This paper focuses on the nominal durations of musical events (notes and rests) in a symbolic musical score, and on how to conveniently handle these in computer applications. We propose the usage of a temporal unit that is directly related…
Arranging music for a different set of instruments that it was originally written for is traditionally a tedious and time-consuming process, performed by experts with intricate knowledge of the specific instruments and involving significant…
It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can't contain more…