MathJax

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WEAVE THEORY ("Pseudo-Tilings") 

     Ralph Griswold:


Designing with Power Sequences

Designing with Smarandache Systems

Grid Overlay Patterns, Part 1: Introduction

Drawdown Automata,
     Part 1: Basic Concepts
     Part 2: Neighborhoods and State-Transition Rules
     Part 3: Pattern Sequences
     Part 4: A Few Good Rules
     Part 5: A Catalog of Weaving Patterns

Image Permutations

Nonlinear Grid Design,
     Part 1: Introduction
     Part 2: Fractal Grids

Number Drafting,
     Part 1: Introduction
     Part 2: Foraging for (Modestly) Large Numbers
     Part 3: A Trip to a Strange Place

Operations on Patterns,
     Part 1: Basic Notions
     Part 2: Geometrical Transformations
     Part 3: Concatenation
     Part 4: Repetition

Pantactic Designs,
     Part 1: 5X5 Pantactic Squares

Pattern Extension Schemata,
     Part 1: Replication and Inversion
     Part 2: Symbols

Pattern Tours,
     Part 1: Basic Concepts
     Part 2: Tour Basics
     Part 3: Representing Tours

Residue Sequences in Weave Design

T-Squences,
     Part 1: Introduction
     Part 2: Extension
     Part 3: Runs
     Part 4: Symmetries
     Part 5: Motifs Along Paths
     Part 6: Modular Operations
     Part 7: Collation

The Morse-Thue Sequence




TILING




COMBINATORICS

de Bruijn's Combinatorics (classroom notes)
         1970s-1980s
     J. W. Nienhuys
     [Nienhuys’ lecture notes on a course given by de Bruijn starting in
          the late 1970s and all through the 1980s.]




GROUP THEORY

Mathematics and Music: The Mathieu Group M12
          2011
     Emma Ross




SERIAL THEORIES

A Tale of Two Twelve-Tone Techniques: Milton Babbitt and the Darmstadt Courses for New Music
          xxx
     Daniel Wolf




SHUFFLES

The Mathematics of perfect Shuffles
          1983
     Persi Diaconis, R. L. Graham, William M. Kantor

The Cycles of the Multiway Perfect Shuffle Permutation
          2002
     John Ellis, Hongbing Fan, Jeffrey Shallit

Shuffling, Cycles, and Matrices
          xxxx
     E. Johnston

The Monge Shuffle for Two-Power Decks
          2006
     Arne Ledet

How Many Times Should You Shuffle a Deck of Cards?
          xxxx
     Brad Mann

The Mathematics of the Flip and Horseshoe Shuffles
          xxxx
     Steve Butler, Persi Diaconis, Ron Graham




MAXIMAL EVENNESS




HOMOMETRY (Z-SET THEORY)
     See also: ENUMERATION

          xxxx
     Jeremiah Goyette
     Interactive program generates z-related n-tuples mod m≦30

Multisets: Applications to Music (slides)
          xxxx
     Godfried Toussaint

The Structure of Z-related Sets
          2013
     Franck Jedrzejewski, Tom Johnson

A Pumping Lemma for Homometric Rhythms
          2008
     Joseph O'Rourke, Perouz Taslakian, Godfrid Toussaint




HOMOTHETIC TRANSFORMATIONS




COMPOSITION RESOURCES

Manipulations of Music Patterns
          1981
     Laurie Spiegel




RHYTHM THEORY

Math for Poets and Drummers
         2007
     Rachel Hall

The Distance Geometry of Music
          xxxx
     Erik Demaine, Francisco Gomez-martin, Henk Meijer, David Rappaport, Perouz Taslakian, Godfried Toussaint, Terry Winograd, David R. Wood
     List of ME rhythms in trad. world musics; good bibl.

Comparative Musicology – Musical Rhythm and Mathematics (Toussaint bibliography)
          xxxx
     Godfried Toussaint




TRANSFORMATION THEORY

          2009
    Scott Alexander Cook

Morphisms in a Musical Analysis of Schoenberg, String Quartet No. 1, Opus 7 [slides]
     Thomas M. Fiore (with Thomas Noll and Ramon Satyendra)

Incorporating Voice Permutations into the Theory of Neo-Riemannian Groups and Lewinian Duality
          2013
     Thomas M. Fiore, Thomas Noll, Ramon Satyendra

Morphisms of Generalized Interval Systems and PR-Groups
          2013
     Thomas M. Fiore, Thomas Noll, Ramon Satyendra

Some Remarks on the Use of Riemann Transformations
          1994
     Henry Klumpenhouwer




COMPUTING

Introduction to Parallel Computing
          2014 (last modified)
     Blaise Barney (Lawrence Livermore National Laboratory)

Parallel Processing with the Perfect Shuffle
          1971
     Harold S. Stone




POETRY

Math for Poets and Drummers
         2007
     Rachel Hall

Sestina! or, The Fate of the Idea of Form
          2008
     Stephen Burt

How a Medieval Troubadour Became a Mathematical Figure
          2011
     Michael P. Saclolo
               [Arnaut Daniel, Raymond Queneau, Quenine]

          


SYMMETRY

          1997, 1999
     Steven Dutch

          1952
     Hermann Weyl

Symmetry: A Unifying Concept
          1994
     István Hargittai, Magdolna Hargittai
     [book; 222 p.]

Mazes and Labyrinths
          1922
     W. H. Matthews

On Growth and Form
          1917
     D'Arcy Wentworth Thompson




ENUMERATION (SET CLASS LISTS)
     See also: HOMOMETRY

          1917
     Ernst Lecher Bacon

Enumeration in Musical Theory
          xxxx
     Harald Fripertinger

Why Are There Twenty-Nine Tetrachords? A Tutorial on Combinatorics and Enumeration in Music Theory
          2007
     Julian Hook

Database on tone rows and tropes
          2015
     Harald Fripertinger & Peter Lackner




TUNING

Dynamic Tonality: Extending the Framework of Tonality into the 21st Century
          2009
     Jim Plamendon, Andrew Milne, William Sethares




MICROTONE THEORY

Toward a Quarter-Tone Syntax: Selected Analyses of Works by Blackwood, Hába, Ives, and Wyschnegradsky.
          2001-2015 dissertation WIP
     Myles L. Skinner




MATHS & LOGICS (UNCATEGORIZED)

Wolfram Mathworld

Combinatorial Object Server

The On-Line Encyclopedia of Integer Sequences

Encyclopedia of Mathematics

Interval Linear Algebra
          2010
     W. B. Vasantha Kandasamy, Florentin Smarandache

George Spencer Brown (Website with links for Laws of Form: Calculus of Indications)

Laws of Form: An Exploration in Mathematics and Foundations
          xxxx
     Louis H. Kauffman

Laws of Form (Website)
         2000-2013
     Richard Shoup

Kabbalah Logic and Semantic Foundation for a Postmodern Fuzzy Set and Fuzzy Logic Theory
          Applied Mathematics vol.5 no.9 May 22, 2014
     Gabriel Burstein, Constantin Virgil Negoita, Menachem Kranz




SCALE THEORY

       


PSYCHOLOGY / NEUROSCIENCE

Math, Music and Mind
         2012
     Ian Quinn
     [excellent presentation on the "hard-wired" issue]

          2010
     Steven L. Bressler, Vinod Menon

How the Emotional Climate Impacts Performance
          2003
     George M. Prince

The Real Neuroscience of Creativity
          2013
     Scott Barry Kaufman




MISCELLANEOUS

Constructive Dissonance
          1997
     ed. Juliane Brand and Christopher Hailey
     [On Schoenberg] [ebook]

Richard Feynman and the Connection Machine
          1989
     W. Daniel Hillis

          1888 (tr.)
     Mauritz Hauptmann

The Technique of My Musical Language
         1944
     Olivier Messiaen








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