Ptolemy's intense diatonic scale

A Beautiful Proof of Ptolemy's Theorem.

Ptolemy's Theorem seems more esoteric than the Pythagorean Theorem, but it's just as cool. In fact, the Pythagorean Theorem follows directly from it. Ptolemy used this theorem in his astronomical work. Google for the historical details. Thanks to this video for the idea of this visual

From playlist Mathy Videos

A more rational / integral Scale Notation | Mathematics and Music | N J Wildberger

Let's use our logical mathematical notation for the 12 tones of the chromatic scale to discuss various important scales that are found in a variety of cultures and idioms, including the major, minor, blues, pentatonic and Indian or uniform scales. But we have to let go of the unfortunate "

From playlist Maths and Music

Ptolemy's theorem and generalizations | Rational Geometry Math Foundations 131 | NJ Wildberger

The other famous classical theorem about cyclic quadrilaterals is due to the great Greek astronomer and mathematician, Claudius Ptolemy. Adopting a rational point of view, we need to rethink this theorem to state it in a purely algebraic way, without resort to `distances' and the correspon

From playlist Math Foundations

Special Relativity B1 Time Dilation

Relativistic time dilation.

From playlist Physics - Special Relativity

Special Relativity B3 Time Dilation

Relativistic time dilation.

From playlist Physics - Special Relativity

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 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

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 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 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

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

Modes of Minor and other Scales | Maths and Music | N J Wildberger

We use the mathematical 12 tone chromatic scale as a framework for an expanded view of modes in music, focusing first on minor scales, and then branching out to other scales. This frees us from the somewhat limiting pre-occupation with the usual Dorian, Lydian, Mixolydian etc modes for the

From playlist Maths and Music

Special Relativity B4 Time Dilation

Relativistic time dilation.

From playlist Physics - Special Relativity

Special Relativity B2 Time Dilation

Relativistic time dilation.

From playlist Physics - Special Relativity

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

Episode 6: Sines And Cosines Part III - Project MATHEMATICS!

Episode 6. Sines and Cosines, Part III: (Addition formulas) Animation relates the sine and cosine of an angle with chord lengths of a circle, as explained in Ptolemy’s Almagest. This leads to elegant derivations of addition formulas, with applications to simple harmonic motion. A Program

From playlist Courses and Series

The Maths of General Relativity (3/8) - Geodesics

In this series, we build together the theory of general relativity. This third video focuses on the notions of geodesics, Christoffel symbols, and the geodesic equation. For more videos, subscribe to the YouTube channel : https://www.youtube.com/ScienceClicEN And if you liked this video,

From playlist The Maths of General Relativity

Boris Springborn: Discrete Uniformization and Ideal Hyperbolic Polyhedra

CATS 2021 Online Seminar Boris Springborn, Technical University of Berlin Abstract: This talk will be about two seemingly unrelated problems: 00:46:00 A discrete version of the uniformization problem for piecewise flat surfaces, and 00:35:48 Constructing ideal hyperbolic polyhedra with p

From playlist Computational & Algorithmic Topology (CATS 2021)

The Maths of General Relativity (1/8) - Spacetime and Worldlines

In this series, we build together the theory of general relativity. This first video focuses on the notions of worldline, proper time, and coordinate systems. For more videos, subscribe to the YouTube channel : https://www.youtube.com/ScienceClicEN And if you liked this video, you can sha

From playlist The Maths of General Relativity

Cleopatra - A Drunken Bet - Extra History - #1

Watch this video ad-free on Nebula: https://nebula.tv/videos/extra-history-cleopatra-a-drunken-bet-extra-history-1 Cleopatra VII Philopator. One of the most famous women of all history with one of the most dramatic stories. We've all heard how she gained the affections of two of the most

From playlist Extra History: Cleopatra