Related papers: A Non-Pythagorean Musical Scale Based on Logarithm…
Describing the geometry of the dual amplituhedron without reference to a particular triangulation is an open problem. In this note we introduce a new way of determining the volume of the tree-level NMHV dual amplituhedron. We show that…
In this paper we give a framework for describing how abstract systems can be used to compute if no randomness or error is involved. Using this we describe a class of classical "physical" computation systems whose computational capabilities…
In this paper, we introduce a mathematical method to extract similarities between paintings and musical tracks. Our approach is based on the digitalization of both paintings and musical tracks by means of finite expansions in terms of…
The aim of this paper is twofold: on one side we review the classical concept of musical mode from the viewpoint of modern music, reading it as a superimposition of a base-chord (seventh chord) and a tension-chord (triad). We associate to…
Music information retrieval distinguishes between low- and high-level descriptions of music. Current generative AI models rely on text descriptions that are higher level than the controls familiar to studio musicians. Pitch strength, a…
Noise-based logic, by utilizing its multidimensional logic hyperspace, has significant potential for low-power parallel operations in beyond-Moore-chips. However universal gates for Boolean logic thus far had to rely on either time…
This essay recounts my personal journey towards a deeper understanding of the mathematical foundations of algorithmic music composition. I do not spend much time on specific mathematical algorithms used by composers; rather, I focus on…
Noise-based logic is a practically deterministic logic scheme inspired by the randomness of neural spikes and uses a system of uncorrelated stochastic processes and their superposition to represent the logic state. We briefly discuss…
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,…
In this paper, graph theory is used to explore the musical notion of tonal modulation, in theory and application. We define (pivot) modulation graphs based on the common scales used in popular music. Properties and parameters of these…
Multiple polylogarithms are periods of variations of mixed Tate motives. Conjecturally, they deliver all such periods. We introduce deformations of multiple polylogarithms depending on a complex parameter h. We call them quantum…
Rhythm is ubiquitous in human culture and in nature, but hard to capture in all its complexity. A key dimension of rhythm, integer ratio categories occur when the relationship between temporal intervals can be expressed as small-integer…
The Number Pieces are a corpus of works by composer John Cage, which rely on a particular time-structure used for determining the temporal location of sounds, named the "time-bracket". The time-bracket system is an inherently stochastic…
In this study, the notion of perceptual features is introduced for describing general music properties based on human perception. This is an attempt at rethinking the concept of features, in order to understand the underlying human…
We use an analytic toy model of turbulent convection to show that most of the scaling regimes are spoiled by logarithmic corrections, in a way consistent with the most accurate experimental measurements available nowadays. This sets a need…
The natural logarithm can be represented by an infinite series that converges for all positive real values of the variable, and which makes concavity patently obvious. Concavity of the natural logarithm is known to imply, among other…
Computational harmony analysis is important for MIR tasks such as automatic segmentation, corpus analysis and automatic chord label estimation. However, recent research into the ambiguous nature of musical harmony, causing limited…
In ancient Greek mathematics, magnitudes such as lengths were strictly distinguished from numbers. In modern quantity calculus, a distinction is made between quantities and scalars that serve as measures of quantities. It can be argued that…
In the early part of the paper, various geometrical formulas are derived. Then, at some point in the paper, the concept of a Pythagorean rational is introduced. A Pythagorean rational is a rational number which is the ratio of two integers…
Measurement is a fundamental building block of numerous scientific models and their creation. This is in particular true for data driven science. Due to the high complexity and size of modern data sets, the necessity for the development of…