Diatonic set theory is a subdivision or application of musical set theory which applies the techniques and analysis of discrete mathematics to properties of the diatonic collection such as maximal evenness, Myhill's property, well formedness, the deep scale property, cardinality equals variety, and structure implies multiplicity. The name is something of a misnomer as the concepts involved usually apply much more generally, to any periodically repeating scale. Music theorists working in diatonic set theory include Eytan Agmon, Gerald J. Balzano, Norman Carey, David Clampitt, John Clough, Jay Rahn, and mathematician Jack Douthett. A number of key concepts were first formulated by David Rothenberg (the Rothenberg propriety), who published in the journal Mathematical Systems Theory, and Erv Wilson, working entirely outside of the academic world. (Wikipedia).
Set Theory (Part 2): ZFC Axioms
Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their
From playlist Set Theory by Mathoma
Set Theory (Part 2b): The Bogus Universal Set
Please feel free to leave comments/questions on the video below! In this video, I argue against the existence of the set of all sets and show that this claim is provable in ZFC. This theorem is very much tied to the Russell Paradox, besides being one of the problematic ideas in mathematic
From playlist Set Theory by Mathoma
Introduction to sets || Set theory Overview - Part 2
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Introduction to Pitch Systems in Tonal Music Part 8: Tuning with Pure Major and Minor Triads
UCI Introduction to Pitch Systems in Tonal Music (Fall 2012) Lec 08. Pitch Systems in Tonal Music -- Tuning with Pure Major and Minor Triads -- View the complete course: http://ocw.uci.edu/courses/introduction_to_pitch_systems_in_tonal_music.html Instructor: John Crooks, MFA License: Cre
From playlist Introduction to Pitch Systems in Tonal Music
The perfect number of axioms | Axiomatic Set Theory, Section 1.1
In this video we introduce 6 of the axioms of ZFC set theory. My Twitter: https://twitter.com/KristapsBalodi3 Intro: (0:00) The Axiom of Existence: (2:39) The Axiom of Extensionality: (4:20) The Axiom Schema of Comprehension: (6:15) The Axiom of Pair (12:16) The Axiom of Union (15:15) T
From playlist Axiomatic Set Theory
Set Theory 1.1 : Axioms of Set Theory
In this video, I introduce the axioms of set theory and Russel's Paradox. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/5ITQHUW
From playlist Set Theory
Introduction to Pitch Systems in Tonal Music Part 7: The Minor Triad and a Circular System of Thirds
UCI Introduction to Pitch Systems in Tonal Music (Fall 2012) Lec 07. Pitch Systems in Tonal Music -- The Minor Triad and a Circular System of Thirds -- View the complete course: http://ocw.uci.edu/courses/introduction_to_pitch_systems_in_tonal_music.html Instructor: John Crooks, MFA Lice
From playlist Introduction to Pitch Systems in Tonal Music
Introduction to Pitch Systems in Tonal Music Part 5: Building a Diatonic Set with 3:2 Ratios
UCI Introduction to Pitch Systems in Tonal Music (Fall 2012) Lec 05. Pitch Systems in Tonal Music -- Building a Diatonic Set with 3:2 Ratios -- View the complete course: http://ocw.uci.edu/courses/introduction_to_pitch_systems_in_tonal_music.html Instructor: John Crooks, MFA License: Cre
From playlist Introduction to Pitch Systems in Tonal Music
Introduction to Pitch Systems in Tonal Music Part 6: Pythagorean Tuning and the Pure Triad
UCI Introduction to Pitch Systems in Tonal Music (Fall 2012) Lec 06. Pitch Systems in Tonal Music -- Pythagorean Tuning and the Pure Triad -- View the complete course: http://ocw.uci.edu/courses/introduction_to_pitch_systems_in_tonal_music.html Instructor: John Crooks, MFA License: Creat
From playlist Introduction to Pitch Systems in Tonal Music
Introduction to Pitch Systems in Tonal Music Part 9: A 12-Tone Pythagorean Set
UCI Introduction to Pitch Systems in Tonal Music (Fall 2012) Lec 09. Pitch Systems in Tonal Music -- A 12-Tone Pythagorean Set -- View the complete course: http://ocw.uci.edu/courses/introduction_to_pitch_systems_in_tonal_music.html Instructor: John Crooks, MFA License: Creative Commons B
From playlist Introduction to Pitch Systems in Tonal Music
Introduction to Pitch Systems in Tonal Music Part 3: Octave equivalence and More
UCI Introduction to Pitch Systems in Tonal Music (Fall 2012) Lec 03. Pitch Systems in Tonal Music -- Octave equivalence, circular pitch systems, and the major triad -- View the complete course: http://ocw.uci.edu/courses/introduction_to_pitch_systems_in_tonal_music.html Instructor: John Cr
From playlist Introduction to Pitch Systems in Tonal Music
Introduction to Set Theory (Discrete Mathematics)
Introduction to Set Theory (Discrete Mathematics) This is a basic introduction to set theory starting from the very beginning. This is typically found near the beginning of a discrete mathematics course in college or at the beginning of other advanced mathematics courses. ***************
From playlist Set Theory
Introduction to sets || Set theory Overview - Part 1
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
What is set subtraction? In this video we go over that, the set minus set operation, and an example of subtraction in set theory. This is a handy concept to grasp to understand the complement of a set and universal sets, which I also have videos on. Links below. I hope you find this vide
From playlist Set Theory
Guest Artist Workshop 4.1: Tim Ray and Eugene Friesen
MIT 21M.355 Musical Improvisation, Spring 2013 View the complete course: http://ocw.mit.edu/21M-355S13 Instructor: License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 21M.355 Musical Improvisation, Spring 2013
Introduction to the Cardinality of Sets and a Countability Proof
Introduction to Cardinality, Finite Sets, Infinite Sets, Countable Sets, and a Countability Proof - Definition of Cardinality. Two sets A, B have the same cardinality if there is a bijection between them. - Definition of finite and infinite sets. - Definition of a cardinal number. - Discu
From playlist Set Theory
Mandelbrot fractal zoom // featuring Euler bio
Mandelbrot fractal zoom // featuring Euler bio Come hang out and watch a fractal zoom through the Mandelbrot set. To celebrate Euler's contributions to mathematics, this video features a brief bio. of Leonhard Euler! ---------------------------------------------------------------------
From playlist Misc.
What are Supersets? | Set Theory, Subsets, Set Relations
What are supersets? We'll be going over the definition and examples of supersets in today's video set theory lesson! If B is a subset of A then A is a superset of B. The superset relation is the same as the subset relation but in the opposite direction! Remember if every element of B is
From playlist Set Theory
A. J. Racy | Resonance | Interview | Exploratorium
Join Resonance host, Nicole Minor in conversation with performer, composer, and ethnomusicologist A.J. Racy. Dr. Racy ushered in the third season of Resonance on December 10th, 2015 with a range of compositions and improvisations that explore ancient modes and forms endemic to Middle Eas
From playlist Resonance: Unheard Sounds, Undiscovered Music