In music theory and tuning, the kleisma (κλείσμα), or semicomma majeur, is a minute and barely perceptible comma type interval important to musical temperaments. It is the difference between six justly tuned minor thirds (each with a frequency ratio of 6/5) and one justly tuned tritave or perfect twelfth (with a frequency ratio of 3/1, formed by a 2/1 octave plus a 3/2 perfect fifth). It is equal to a frequency ratio of 15625/15552 = 2−6 3−5 56, or approximately 8.1 cents. It can be also defined as the difference between five justly tuned minor thirds and one justly tuned major tenth (of size 5/2, formed by a 2/1 octave plus a 5/4 major third) or as the difference between a chromatic semitone (25/24) and a greater diesis (648/625). The interval was named by Shohé Tanaka after the Greek for "closure", who noted that it was tempered to a unison by 53 equal temperament. It is also tempered out by 19 equal temperament, 34 equal temperament and 72 equal temperament, but it is not tempered out in 12 equal temperament. Namely, in 12 equal temperament the difference between six minor thirds (18 semitones) and one perfect twelfth (19 semitones) is not a comma, but exaggerated to a semitone (100 cents). The same is true for the difference between five minor thirds (15 semitones) and one major tenth (16 semitones). The interval was described but not used by Rameau in 1726. Larry Hanson independently discovered this interval which also manifested in a unique mapping using a generalized keyboard capable of accommodating all the above temperaments as well as just intonation constant structures (periodicity blocks) with these numbers of scale degrees The kleisma is also an interval important to the Bohlen–Pierce scale. (Wikipedia).
Clustering 1: monothetic vs. polythetic
Full lecture: http://bit.ly/K-means The aim of clustering is to partition a population into sub-groups (clusters). Clusters can be monothetic (where all cluster members share some common property) or polythetic (where all cluster members are similar to each other in some sense).
From playlist K-means Clustering
The KL Divergence : Data Science Basics
understanding how to measure the difference between two distributions Proof that KL Divergence is non-negative : https://www.youtube.com/watch?v=LOwj7UxQwJ0&t=520s My Patreon : https://www.patreon.com/user?u=49277905 0:00 How to Learn Math 1:57 Motivation for P(x) / Q(x) 7:21 Motivation
From playlist Data Science Basics
Raimar WULKENHAAR - Solvable Dyson-Schwinger Equations
Dyson-Schwinger equations provide one of the most powerful non-perturbative approaches to quantum field theories. The quartic analogue of the Kontsevich model is a toy model for QFT in which the tower of Dyson-Schwinger equations splits into one non-linear equation for the planar two-point
From playlist Talks of Mathematics Münster's reseachers
What is Kurtosis? (+ the "peakedness" controversy!)
See all my videos at http://www.zstatistics.com/videos/ 0:00 Introduction 1:05 Definition of kurtosis 3:30 How to calculate kurtosis 7:11 Describing kurtosis 9:45 Controversy!
From playlist Descriptive Statistics (13 videos)
Peter Scholze: On topological cyclic homology
The lecture was held within the framework of the Hausdorff Trimester Program : Workshop "K-theory in algebraic geometry and number theory" Abstract: Topological cyclic homology is an approximation to algebraic K-theory that has been very useful for computations in algebraic K-theory. Rece
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Homophily - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
How the little guy can compete against the big guy
How microbreweries are like shrubs and ferns. LEARN MORE ************** To learn more about this topic, start your googling with these keywords: - Ecological niche: is the match of a species to a specific environmental condition. - Niche differentiation: refers to the process by which co
From playlist Society, Culture & Technology
Andrew Mathas: Cyclotomic KLR algebras (Part 2 of 4)
The lecture was held within the framework of the Hausdorff Trimester Program: Symplectic Geometry and Representation Theory. Abstract: The cyclotomic KLR algebras are certain quotients of the quiver Hecke algebras, or Khovanov–Lauda–Rouquier algebras. These algebras are important because
From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"
Clustering is the process of grouping a set of data given a certain criterion. In this way it is possible to define subgroups of data, called clusters, that share common characteristics. Determining the internal structure of the data is important in exploratory data analysis, but is also u
From playlist “How To” with MATLAB and Simulink
Andrew Mathas: Cyclotomic KLR algebras (Part 3 of 4)
The lecture was held within the framework of the Hausdorff Trimester Program: Symplectic Geometry and Representation Theory. Abstract: The cyclotomic KLR algebras are certain quotients of the quiver Hecke algebras, or Khovanov–Lauda–Rouquier algebras. These algebras are important because
From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"