Related papers: Music, Complexity, Information
The mathematics of musical intervals and scales has been extensively studied. Vastly simplified, our ears seem to prefer intervals whose frequency ratios have small numerator and denominator, such as 2:1 (octave), 3:2 (perfect fifth), 4:3…
The development of new statistical and computational methods is increasingly making it possible to bridge the gap between hard sciences and humanities. In this study, we propose an approach based on a quantitative evaluation of attributes…
This paper delves into the intersection of computational theory and music, examining the concept of undecidability and its significant, yet overlooked, implications within the realm of modern music composition and production. It posits that…
The abstraction of musical structures (notes, melodies, chords, harmonic or rhythmic progressions, etc.) as mathematical objects in a geometrical space is one of the great accomplishments of contemporary music theory. Building on this…
I bring forward some arguments to support the thesis that nature is fundamentally discrete, and present my own thoughts about the direction in which one could look for a possible, consistent "theory of everything" describing gravitation and…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
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,…
Compositionality is a key property for dealing with complexity, which has been studied from many points of view in diverse fields. Particularly, the composition of individual computations (or programs) has been widely studied almost since…
Natural language numbers are an example of compositional structures, where larger numbers are composed of operations on smaller numbers. Given that compositional reasoning is a key to natural language understanding, we propose novel…
In this article, we aim to provide a review of the key ideas and approaches proposed in 20 years of scientific literature around musical version identification (VI) research and connect them to current practice. For more than a decade, VI…
In science and beyond, numbers are omnipresent when it comes to justifying different kinds of judgments. Which scientific author, hiring committee-member, or advisory board panelist has not been confronted with page-long "publication…
We present a rigorous and relatively fast method for the computation of the "complexity" of a natural number (sequence A005245), and answer some "old and new" questions related to the question in the title of this note. We also extend the…
Nowadays, humans are constantly exposed to music, whether through voluntary streaming services or incidental encounters during commercial breaks. Despite the abundance of music, certain pieces remain more memorable and often gain greater…
We use coupled hidden Markov models to automatically annotate the 371 Bach chorales in the Riemenschneider edition, a corpus containing approximately 100,000 notes and 20,000 chords. We give three separate analyses that achieve…
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…
We measure the complexity of songs in the Million Song Dataset (MSD) in terms of pitch, timbre, loudness, and rhythm to investigate their evolution from 1960 to 2010. By comparing the Billboard Hot 100 with random samples, we find that the…
The distinction between sciences is becoming increasingly more artificial -- an approach from one area can be easily applied to the other. More exciting research nowadays is happening perhaps at the interfaces of disciplines like Physics,…
Mathematical notations around the world are diverse. Not as much as requiring computing machines' makers to adapt to each culture, but as much as to disorient a person landing on a web-page with a text in mathematics. In order to understand…
In the last few decades or so, we witness a paradigm shift in our nature studies - from a data-processing based computational approach to an information-processing based cognitive approach. The process is restricted and often misguided by…
Correlations in music that exist within its waveform are studied. Monophonic wave files of random music are generated and the probability distribution function of time interval between large signal values is analyzed. A power law behavior…