WEAVE THEORY ("Pseudo-Tilings")
Ralph Griswold:
Design Inspirations from Multivariate Polynomials, Part 1
Design Inspirations from Multivariate Polynomials, Part 2
[differentiation; integration]
Constrained Patterns,
Part 1: Basic Concepts
Part 2: Neighborhood Analysis
Part 3: Representing Constraint Sets
Continued Fraction Sequences and Weave Design, Part 1: Introduction
Design Inspirations from Multivariate Polynomials, Part 2
[differentiation; integration]
Constrained Patterns,
Part 1: Basic Concepts
Part 2: Neighborhood Analysis
Part 3: Representing Constraint Sets
Continued Fraction Sequences and Weave Design, Part 1: Introduction
Design Sequences: Meandering Strings
Designing Weave Structures Using Boolean Operations,
Part 1
Part 2
Part 3
Designing with Farey Fractions
Fractal Sequences, Part 1: Overview
Designing with L-Systems,
Part 1: String Rewriting Systems
Part 2: A Side Trip to Graphics
Part 3: Back to Basics – T-Sequence Design
Part 4: Articulated L-Systems
Part 5: Termination
Part 6: Generating T-Sequence Expressions
Part 7: T-Sequence Models
Part 8: Non-Terminal T-Sequence Generation
Part 9: Devious Interpretation
Part 10: Profile Drafts
Designing Weave Structures Using Boolean Operations,
Part 1
Part 2
Part 3
Designing with Farey Fractions
Fractal Sequences, Part 1: Overview
Designing with L-Systems,
Part 1: String Rewriting Systems
Part 2: A Side Trip to Graphics
Part 3: Back to Basics – T-Sequence Design
Part 4: Articulated L-Systems
Part 5: Termination
Part 6: Generating T-Sequence Expressions
Part 7: T-Sequence Models
Part 8: Non-Terminal T-Sequence Generation
Part 9: Devious Interpretation
Part 10: Profile Drafts
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
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
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
2012
Andrew Jay Chung
Andrew Jay Chung
COMPUTING
Introduction to Parallel Computing
2014 (last modified)
Blaise Barney (Lawrence Livermore National Laboratory)
Parallel Processing with the Perfect Shuffle
1971
Harold S. Stone
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
2008
Stephen Burt
How a Medieval Troubadour Became a Mathematical Figure
2011
Michael P. Saclolo
[Arnaut Daniel, Raymond Queneau, Quenine]
SYMMETRY
Symmetry, Crystals and Polyhedra (class notes)
1997, 1999
Steven Dutch
1952
Hermann Weyl
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
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]
How the Emotional Climate Impacts Performance
2003
George M. Prince
The Real Neuroscience of Creativity
2013
Scott Barry Kaufman
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
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