The intervals of 5-limit just intonation (prime limit, not odd limit) are ratios involving only the powers of 2, 3, and 5. The fundamental intervals are the superparticular ratios 2/1 (the octave), 3/2 (the perfect fifth) and 5/4 (the major third). That is, the notes of the major triad are in the ratio 1:5/4:3/2 or 4:5:6. In all tunings, the major third is equivalent to two major seconds. However, because just intonation does not allow the irrational ratio of √5/2, two different frequency ratios are used: the major tone (9/8) and the minor tone (10/9). The intervals within the diatonic scale are shown in the table below. (Wikipedia).
Closed Intervals, Open Intervals, Half Open, Half Closed
00:00 Intro to intervals 00:09 What is a closed interval? 02:03 What is an open interval? 02:49 Half closed / Half open interval 05:58 Writing in interval notation
From playlist Calculus
The Mathematical Problem with Music, and How to Solve It
There is a serious mathematical problem with the tuning of musical instruments. A problem that even Galileo, Newton, and Euler tried to solve. This video is about this problem and about some of the ways to tackle it. It starts from the basic physics of sound, proves mathematically why s
From playlist Summer of Math Exposition 2 videos
Measurement, approximation + interval arithmetic (II) | Real numbers and limits Math Foundations 82
We continue on with a short intro to interval arithmetic, noting the difference between the laws of arithmetic over the natural numbers and the integers. The case of rational number intervals is also briefly discussed. We end the lecture with some remarks on the vagueness of ``real number'
From playlist Math Foundations
The video introduces the concept of determining if sequence converges or diverges. http://mathispower4u.yolasite.com/
From playlist Limits
DON'T use logarithms (Limit Example 9)
Epsilon Definition of a Limit In this video, I illustrate the epsilon-N definition of a limit by showing directly, without using ln or l'Hopital's rule, that n^1/n goes to 1 as n goes to infinity. Enjoy this beautiful analysis example :) Other examples of limits can be seen in the playli
From playlist Sequences
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Calculus 1 Lecture 3.1 Part 7: Intervals of Increasing, Decreasing, and Concavity. How to Find Absolute Maximum and Absolute Minimum.
From playlist Calculus 1 Playlist 1
Summer of Math Exposition 2022 - Mathematics and Music
"Better Late Than Never". I started taking Guitar lessons for the first time in my life in 2022. So I wanted to use Math to describe some musical concepts. This is a very rough draft and I wanted to share more but it's August 15th 2022. I created a slightly better video last year: h
From playlist Summer of Math Exposition 2 videos
David Burguet: Some new dynamical applications of smooth parametrizations for C∞ systems - lecture 3
Smooth parametrizations of semi-algebraic sets were introduced by Yomdin in order to bound the local volume growth in his proof of Shub’s entropy conjecture for C∞ maps. In this minicourse we will present some refinement of Yomdin’s theory which allows us to also control the distortion. We
From playlist Dynamical Systems and Ordinary Differential Equations
MIT 9.13 The Human Brain, Spring 2019 Instructor: Nancy Kanwisher View the complete course: https://ocw.mit.edu/9-13S19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60IKRN_pFptIBxeiMc0MCJP The functional organization of music in human beings. * NOTE: Lecture 17: MEG
From playlist MIT 9.13 The Human Brain, Spring 2019
Calculus 2: Infinite Sequences and Series (3 of 62) Sequences and Limits
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and give examples of sequences and their limits. Next video in the series can be seen at: https://youtu.be/Z_Y_FKV68sI
From playlist CALCULUS 2 CH 14 SERIES AND SEQUENCES
Scaling Virtual Assistants | Catherine Breslin
Presented by Catherine Breslin, Solutions Architect at Cobalt Speech at Rasa's Level 3 AI Assistant Conference. Virtual assistants like Alexa, Siri and Google Assistant have been widely adopted by consumers, and now many businesses are considering building their own custom assistants. Buil
From playlist Level 3 AI Assistant Conference 2020
From playlist SACS Academic Skills Workshop Series
#5 Set Interval Notation Practice
Practice using set interval notation
From playlist Middle School This Year
Vibrational properties in the continuum limit of amorphous solids by Hideyuki Mizuno
PROGRAM ENTROPY, INFORMATION AND ORDER IN SOFT MATTER ORGANIZERS: Bulbul Chakraborty, Pinaki Chaudhuri, Chandan Dasgupta, Marjolein Dijkstra, Smarajit Karmakar, Vijaykumar Krishnamurthy, Jorge Kurchan, Madan Rao, Srikanth Sastry and Francesco Sciortino DATE: 27 August 2018 to 02 Novemb
From playlist Entropy, Information and Order in Soft Matter
Massoumeh Dashti: Bayesian methods for inverse problems - lecture 2
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From playlist Virtual Conference
Maximum and Minimum Values (Closed interval method)
A review of techniques for finding local and absolute extremes, including an application of the closed interval method
From playlist 241Fall13Ex3
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.
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