Related papers: Harmony and Duality: An introduction to Music Theo…

We give a new analysis of a tuning problem in music theory, pertaining specifically to the approximation of harmonics on a two-dimensional keyboard. We formulate the question as a linear programming problem on families of constraints and…

We investigate correlations among pitches in several songs and pieces of piano music by mapping them to one-dimensional walks. Two kinds of correlations are studied, one is related to the real values of frequencies while they are treated…

The complex organization of syntax in hierarchical structures is one of the core design features of human language. Duality of patterning refers for instance to the organization of the meaningful elements in a language at two distinct…

This paper proves that arrangement of music is NP-hard when subject to various constraints: avoiding musical dissonance, limiting how many notes can be played simultaneously, and limiting transition speed between chords. These results imply…

Music similarity search is useful for a variety of creative tasks such as replacing one music recording with another recording with a similar "feel", a common task in video editing. For this task, it is typically necessary to define a…

This paper attempts to look for a mathematical method of composing music by incorporating Schonbergs idea of tone rows and matrix theory from linear algebra. The elements of a note set S are considered as the integer values for the natural…

This paper approaches the problem of separating the notes from a quantized symbolic music piece (e.g., a MIDI file) into multiple voices and staves. This is a fundamental part of the larger task of music score engraving (or score…

The collaboration of mathematics in the two musical systems of Pythagorean sounds and of equal sounds is evident and opportune for generating the elements and managing their relationships. The only essential notion for a rational…

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 will discuss how certain group theory structures are found in music theory. Western music splits the octave into 12 equal tones called half-steps. We can take this division further and split the octave into 24 equal tones by splitting…

We classify almost all classical string configurations, considered in the framework of the semi-classical limit of the string/gauge theory duality. Then, we describe a procedure for obtaining the conserved quantities and the exact classical…

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…

A Pythagorean scale is a mathematical encoding of a musical scale as a finite list of numbers of the form 3^b/2^a. Previous work of the first author discussed the 2-step property as a way to measure which Pythagorean scales are the most…

Music segmentation refers to the dual problem of identifying boundaries between, and labeling, distinct music segments, e.g., the chorus, verse, bridge etc. in popular music. The performance of a range of music segmentation algorithms has…

We give a formal definition of the musical concept of voice leading in mathematical terms, based on the idea of partial permutations of certain ordered multisets. Then we associate a partial permutation matrix with a voice leading in a…

Music source separation is the task of separating a mixture of instruments into constituent tracks. Music source separation models are typically trained using only audio data, although additional information can be used to improve the…

The relationship between sensory consonance and Western harmony is an important topic in music theory and psychology. We introduce new methods for analysing this relationship, and apply them to large corpora representing three prominent…

In the production of modern music, the musical characteristics of the guitar or keyboard amplifier play an integral role in the creative process. This article explores the physics of music with an emphasis on the role of distortion in the…

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,…

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…