In musical tuning, the Pythagorean comma (or ditonic comma), named after the ancient mathematician and philosopher Pythagoras, is the small interval (or comma) existing in Pythagorean tuning between two enharmonically equivalent notes such as C and B♯, or D♭ and C♯. It is equal to the frequency ratio (1.5)12⁄27 = 531441⁄524288 ≈ 1.01364, or about 23.46 cents, roughly a quarter of a semitone (in between 75:74 and 74:73). The comma that musical temperaments often refer to tempering is the Pythagorean comma. The Pythagorean comma can be also defined as the difference between a Pythagorean apotome and a Pythagorean limma (i.e., between a chromatic and a diatonic semitone, as determined in Pythagorean tuning), or the difference between twelve just perfect fifths and seven octaves, or the difference between three Pythagorean ditones and one octave (this is the reason why the Pythagorean comma is also called a ditonic comma). The diminished second, in Pythagorean tuning, is defined as the difference between limma and apotome. It coincides, therefore, with the opposite of a Pythagorean comma, and can be viewed as a descending Pythagorean comma (e.g. from C♯ to D♭), equal to about −23.46 cents. (Wikipedia).
From playlist Miscellaneous
This geometry video tutorial provides a basic introduction into the pythagorean theorem. It explains how to use it to find missing sides and solve for x. In addition, it provides examples of solving word problems using pythagorean theorem for shapes such as right triangles, squares, rhom
From playlist Geometry Video Playlist
Converse Pythagorean Theorem & Pythagorean Triples
I explain the Converse Pythagorean Theorem and what Pythagorean Triples are. Find free review test, useful notes and more at http://www.mathplane.com If you'd like to make a donation to support my efforts look for the "Tip the Teacher" button on my channel's homepage www.YouTube.com/Profro
From playlist Geometry
Pythagorean theorem - What is it?
► My Geometry course: https://www.kristakingmath.com/geometry-course Pythagorean theorem is super important in math. You will probably learn about it for the first time in Algebra, but you will literally use it in Algebra, Geometry, Trigonometry, Precalculus, Calculus, and beyond! That’s
From playlist Geometry
Pythagorean identity explanation
Hello, this is my first Hope you liked it! :D 3blue1brow math contest submision
From playlist Summer of Math Exposition Youtube Videos
Pythagorean theorem in Geogebra [PART 1] [Tutorial]
Pythagorean theorem in Geogebra [PART 1] [Tutorial] Pitagorina teorema u Geogebri [prvi dio] [Tutorial] In case you wanna to pay me a drink: https://www.paypal.me/admirsuljicic/
From playlist Geogebra [Tutoriali]
Pythagorean Theorem I (visual proof)
This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using the hypotenuses of scaled triangles. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side lengths. #mathshorts #mathvide
From playlist Pythagorean Theorem
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
Pythagorean theorem in Geogebra [PART 2] [Tutorial]
Pythagorean theorem in Geogebra [PART 2] [Tutorial] Pitagorina teorema u Geogebri [prvi dio] [Tutorial] In case you wanna to pay me a drink: https://www.paypal.me/admirsuljicic/
From playlist Geogebra [Tutoriali]
Pythagorean trig identity from unit circle | Trigonometry | Khan Academy
Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/trigonometry/less-basic-trigonometry/pythagorean-identity/e/circles-and-pythagorean-identities?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry Watch the next lesson: https://www.khanacade
From playlist Precalculus | Get Ready for Grade Level | Khan Academy
Pythagorean Trig ID via Areas (2)
Pythagorean Trig Identity via Areas. Made with #GeoGebra: https://www.geogebra.org/m/xmhyyapn
From playlist Trigonometry: Dynamic Interactives!
The dynamics of Apollonian circle packings by Sneha Chaubey
PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.
From playlist Smooth And Homogeneous Dynamics
Distance Formula // Lesson 10-5 [Glencoe Texas Algebra 1]
The Distance Formula is an abstraction of the Pythegorean Theorem for the coordinate plane. Like all abstractions, it gains power by losing specificity. But by losing specificity, it can sometimes be harder to understand and implement. Subscribe: http://bit.ly/SubTimRicchuiti | Enable AL
From playlist Glencoe Texas Algebra 1 Lessons
Mathematica Tutorial 10 - Pythagorean triples
Learn to construct a list of Pythagorean triples and decide if one of the sides of a right triangle must be even when they are made from integers.
From playlist Mathematica Tutorials
Pythagorean Party by Karen Campe
Karen Campe will guide you through a series of interactive activities in GeoGebra that will help you understand the Pythagorean Theorem and its applications. You'll also explore Pythagorean Triples and dive into the Converse Pythagorean Theorem by using GeoGebra to explore this theorem and
From playlist FLGGB 2023
Deriving Values on the Unit Circle
Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Deriving Values on the Unit Circle. In this video, I show how to actually DERIVE the values in the first quadrant of the unit circle (so that you are not just
From playlist All Videos - Part 3
Math 023 Fall 2022 091222 From one variable to two: the Cartesian plane
1.4 Going from one variable to two variables: the number line to the Cartesian plane. Distance formula for points on the plane. Converse of the Pythagorean Theorem. Midpoint formula. Applications of the midpoint formula. Digression: Babylonian algorithm. Percentage error. 1.5 Grap
From playlist Course 1: Precalculus (Fall 2022)
Distance formula | Analytic geometry | Geometry | Khan Academy
How to find the distance between lines using the Pythagorean Formula Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/geometry/analytic-geometry-topic/cc-distances-between-points/e/distance_formula?utm_source=YT&utm_medium=Desc&utm_campaign=Geo
From playlist Precalculus | Get Ready for Grade Level | Khan Academy
Math 023 Fall 2022 120522 Polar Coordinates
Definition of polar coordinates. Examples: what points are these? Going from polar to Cartesian coordinates; going from Cartesian to polar coordinates. Distance formula (using the Law of Cosines!). Application: equations of circles. Examples: going from equations in polar coordinates
From playlist Course 1: Precalculus (Fall 2022)