Twelve-tone equal temperament (12-TET) is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 (12√2 ≈ 1.05946). That resulting smallest interval, 1⁄12 the width of an octave, is called a semitone or half step. Twelve-tone equal temperament is the most widespread system in music today. It has been the predominant tuning system of Western music, starting with classical music, since the 18th century, and Europe almost exclusively used approximations of it for millennia before that. It has also been used in other cultures. In modern times, 12-TET is usually tuned relative to a standard pitch of 440 Hz, called A440, meaning one note, A, is tuned to 440 hertz and all other notes are defined as some multiple of semitones apart from it, either higher or lower in frequency. The standard pitch has not always been 440 Hz. It has varied and generally risen over the past few hundred years. (Wikipedia).

Factorial Notation (2 of 3: Formal definition)

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From playlist Working with Combinatorics

From playlist Mr Ronald's Year 10 Groups

How would one sum the factors of a number so immense as 11 factorial? 11! = 39916800 has 540 distinct positive factors, most of them very large. It turns out that, when cleverly arranged, the factors of 11! and any number in general lend themselves nicely to summation. In this video, I dem

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From playlist Arithmetic and Pre-Algebra: Factors and Multiples

Determine Prime and Composite Numbers (Common Core 3/4 Math Ex 20)

This video provides example of how to determine if numbers are prime or composite.

From playlist Common Core Grade 3/4 Practice Standardized Test Math Problems

In this video we break down and simplify radicals

From playlist Skill 14 Attempt 2

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

Metauni event #3: Lucas Cantor presents Music @ Metaverse

Lucas spoke on the emerging role of AI in music, and how this brings into focus some of the arbitrariness about the way we construct music, using the example of equal temperament. There was a very interesting question and discussion period after the talk, which among other things touched o

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How Pythagoras Broke Music (and how we kind of fixed it)

How does music work? What did an Ancient Greek philosopher have to do with it? Why did he keep drowning people? Discover the answers to these questions and more as we take a tour through musical tuning systems, examining how the power of mathematics has helped us build and rebuild our met

From playlist Mathematics

17.5 Transverse Standing Waves

This video covers Section 17.5 of Cutnell & Johnson Physics 10e, by David Young and Shane Stadler, published by John Wiley and Sons. The lecture is part of the course General Physics - Life Sciences I and II, taught by Dr. Boyd F. Edwards at Utah State University. This video was produced

From playlist Lecture 17B. Linear Superposition and Interference Phenomena

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

Superior Base Number 18 #MegaFavNumbers

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Prealgebra 3.05b - Reciprocals Practice Problems 1 - 2

Some practice problems dealing with reciprocals.

From playlist Prealgebra Chapter 3 (Complete chapter)

The History, The Power and the Perspectives of Numerical Simulations of Spin... by Enzo Marinari

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From playlist Celebrating the Science of Giorgio Parisi (ONLINE)

Introduction to Pitch Systems in Tonal Music Part 9: A 12-Tone Pythagorean Set

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From playlist Introduction to Pitch Systems in Tonal Music

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From playlist Experts in Emotion Series with June Gruber

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