Mathematics and Computation in Music (original) (raw)

The Mathematics Behind the Music Volume 2

The relation to music and Mathematics is quite a thick topic to discuss because, in a very general sense, music is mathematics. It is a difference and consistency of changes in melody and rhythm that generates sound in a way that we enjoy and appreciate it. Many different applications have been used to describe these changes from logarithmic fluctuation in sound wave frequency to the difference and scale relations of transposed music. This topic interests me in particular because I have always loved composing music and the differences in melodies via Music theory. Being both a mathematician and a musician I've never been terribly impressed with, and consequently interested in, attempts to combine the two. It is perhaps even more surprising that music, with all its passion and emotion, is also based upon mathematical relationships. Such musical notions as octaves, chords, scales, and keys can all be demystified and understood logically using simple mathematics. Mathematical models can be found from theoretical analysis to actual composition or sound production. Increasingly in the last few decades, musical scholarship has incorporated modern mathematical content. One example is the application of methods from Algebraic Combinatorics, or Topology and Graph Theory, to the classification of different musical objects. However, these applications of mathematics in the understanding of music have also led to interesting open problems in mathematics itself. The reach and depth of the contributions on mathematical music theory presented in this volume is significant. Each contribution is in a section within these subjects: (i) Algebraic and Combinatorial Approaches; (ii) Geometric, Topological, and Graph-Theoretical Approaches; and (iii) Distance and Similarity Measures in Music.

The Mathematics of Music and Art

The Mathematics of Music and Art, 2023

This book explores the relationships between music, the sciences, and mathematics, both ancient and modern, with a focus on the big picture for a general audience as opposed to delving into very technical details. The language of music is deciphered through the language of mathematics. Readers are shown how apparently unrelated areas of knowledge complement each other and in fact propel each other’s advancement. The presentation as well as the collection of topics covered throughout is unique and serves to encourage exploration and also, very concretely, illustrates the cross- and multidisciplinary nature of knowledge. Inspired by an introductory, multidisciplinary course, the author explores the relationships between the arts, sciences, and mathematics in the realm of music. The book has no prerequisites; rather it aims to give a broad overview and achieve the integration of the three presented themes. Mathematical tools are introduced and used to explain various aspects of music theory, and the author illustrates how, without mathematics, music could not have been developed.

The Mathematics of Music and Art (Frontmatter)

The Mathematics of Music and Art, 2023

This book explores the relationships between music, the sciences, and mathematics, both ancient and modern, with a focus on the big picture for a general audience as opposed to delving into very technical details. The language of music is deciphered through the language of mathematics. Readers are shown how apparently unrelated areas of knowledge complement each other and in fact propel each other’s advancement. The presentation as well as the collection of topics covered throughout is unique and serves to encourage exploration and also, very concretely, illustrates the cross- and multidisciplinary nature of knowledge. Inspired by an introductory, multidisciplinary course, the author explores the relationships between the arts, sciences, and mathematics in the realm of music. The book has no prerequisites; rather it aims to give a broad overview and achieve the integration of the three presented themes. Mathematical tools are introduced and used to explain various aspects of music theory, and the author illustrates how, without mathematics, music could not have been developed.

Musical Mathematics: On the Art and Science of Acoustic Instruments

2010

Musical Mathematics is the definitive tome for the adventurous musician. Weaving together mathematical analysis, music history, and hands-on expertise, this volume is a comprehensive guide to discoveries regarding acoustic music and tunings. Author, composer, instrument-builder, and musical innovator Cris Forster presents both scholarship from primary sources and practical instruction regarding the invention and construction of new musical instruments - allowing the reader to actually begin to build unique and monumental instruments such as the ones pictured in the book's 16 color plates.

A Foundations-of-Computation Approach to Formalizing Musical Analysis

2020

In the last century, two trends have increased the scope of musical analysis: music theorists have provided mathematical insight into specific musical scenarios, while musicologist have examined the nature of musical analysis as a cultural, cognitive, and scholarly endeavor [1] [2] [3] [4] [5]. This paper intends to bring these two strands of research together by providing a constructive mathematical foundation for the process of musical analysis. By establishing a mathematical description of the generation of an analysis of a piece of music, useful mathematical tools for performing operations frequently used in analysis, and possible precise definitions for loaded terms such as “musical similarity” and “musical form”, I will extend the analyst and the meta-analyst’s ability to create abstractions from musical surfaces, the core of every process of analy-

Music and Math: Foundations of Music

2011

Mathematicians throughout history primarily designed the western musical scale. This thesis tells the story of the mathematicians that contributed to this process of developing the scale and how mathematical concepts were applied. The story spans from Pythagoras around to Rene Descartes and examines the development of the musical scale most commonly used today.

Quantifying Harmony: The Mathematical Essence of Music

This research delves into the intricate correlation between music and mathematics, examining how mathematical principles play a fundamental role in shaping various aspects of musical theory and composition. Starting from Pythagoras' early insights on harmonic intervals to the complex patterns found in the Fibonacci sequence and fractal geometry, this study uncovers the deep connections between numerical concepts and musical notes. By extensively exploring historical perspectives, theoretical frameworks, and practical applications, we gain valuable insight into how mathematical ideas influence the melodies, harmonies, and rhythms that elevate our auditory experiences.