In music theory, the chromatic hexachord is the hexachord consisting of a consecutive six-note segment of the chromatic scale. It is the first hexachord as ordered by Forte number, and its complement is the chromatic hexachord at the tritone. For example, zero through five and six through eleven. On C: * C, C♯, D, D♯, E, F and * F♯, G, G♯, A, A♯, B. This is the first of the six hexachords identified by Milton Babbitt as all-combinatorial source sets, a "source set" being "a set considered only in terms of the content of its hexachords, and whose combinatorial characteristics are independent of the ordering imposed on this content" . In the larger context of thirty-five source hexachords catalogued by Donald Martino, it is designated "Type A" . Applying the circle of fifths transformation to the chromatic hexachord produces the diatonic hexachord . As with the diatonic scale, the chromatic hexachord is, "hierarchical in interval makeup," and may also be produced by, or contains, 3-1, 3-2, 3-3, 3-6, and 3-7 . Serial compositions including Karlheinz Stockhausen's Kreuzspiel and Klavierstück I feature the chromatic hexachord in permuted orderings, as do certain pieces composed by Milton Babbitt, Alban Berg, Ernst Krenek, Luigi Nono, Karlheinz Stockhausen, Igor Stravinsky, and Anton Webern in various fixed-order derivations (twelve-tone rows and arrays). Babbitt's Second Quartet and Reflections for piano and tape feature the hexachord . The retrograde-symmetrical all-interval series employed by Luigi Nono for the first time in Canti per tredeci in 1955, also used in his Il canto sospeso and nearly all subsequent works up to Composizione per orchestra n. 2: Diario polacco ’58 in 1959, is built from two chromatic hexachords . Stefan Wolpe's Suite in Hexachord (1936) begins with a chromatic hexachord on G, introducing the complementary hexachord in the final movement, while Elliott Carter calls his own piece, "Inner Song" for solo oboe—the second movement of Trilogy for oboe and harp (1992)—"some thoughts about Wolpe's hexachord" . (Wikipedia).
The fundamental scale is the chromatic 12 tone scale! | Maths and music | N J Wildberger
What is the most natural scale? Can we transcend our cultural indoctrinations when it comes to music and try to see the mathematical essence of things? And can we also move beyond the familiar musical thought patterns that the architecture of the piano (and to a lesser extent that of the g
From playlist Maths and Music
In this video, we explore the differences between starting with a random dot in a regular hexagon and iterating the procedure of choosing a hexagon vertex at random and moving either half the distance from the current dot to the chosen vertex OR two thirds the distance from the current dot
From playlist Fractals
Organic Chemistry - Ch 1: Basic Concepts (19 of 97) What is an Optical Isomer?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is an optical isomer: a mirror image of another. There are 2 types. Achiral-when the 2 are superimposable, and chiral-molecules that exhibit handedness. Next video in this series can be
From playlist ORGANIC CHEMISTRY CH1 INTRODUCTION
What's a Hexagon? Geometry Terms and Definitions
Some polygons have 6 sides. Some animals have 6 legs. Coincidence?? Geometer: Louise McCartney Artwork: Kelly Vivanco Director: Michael Harrison Written & Produced by Kimberly Hatch Harrison and Michael Harrison ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://w
From playlist Socratica: The Geometry Glossary Series
Geometry: Ch 4 - Geometric Figures (11 of 18) The Regular Hexagon Analyzed with Trig
Visit http://ilectureonline.com for more math and science lectures! In this video I will further explain the regular hexagon using trigonometry the details of the regular hexagon. Next video in this series can be seen at: https://youtu.be/oaT0pSYDVZI
From playlist GEOMETRY 4 - GEOMETRIC FIGURES
OC#7c Functional Group Isomerism
HSC Chemistry Mod 7 Organic Chemistry Isomerism - Function group isomerism
From playlist Y12 Chem Mod 7 Organic Chem
Chladni Figures - random couscous snaps into beautiful patterns
These are called Chladni Figures and they demonstrate 2 dimensional standing waves. Visit my blog here: http://stevemould.com Follow me on twitter here: http://twitter.com/moulds Buy nerdy maths things here: http://mathsgear.co.uk
From playlist Best of
The hexagonal quantum billiard: probability density
A solution to Schrödinger's equation in a hexagonal domain. The conditions are the same as in the video https://youtu.be/8WTIjRWjG1o , but this time the colors correspond to the probability of finding the quantum particle at any given place (the modulus of the wave function squared). Green
From playlist Billiards in polygons
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
Maria Chudnovsky: Induced cycles and coloring
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Combinatorics
Edge Colorings and Chromatic Index of Graphs | Graph Theory
We introduce edge colorings of graphs and the edge chromatic number of graphs, also called the chromatic index. We'll talk about k-colorings/k-edge colorings, minimum edge colorings, edge colourings as matchings, edge colourings as functions, and see examples and non-examples of edge color
From playlist Graph Theory
Upper and Lower Bounds for the Chromatic Number of a Graph
This video explains how to determine the upper and lower bounds of the chromatic number to various graphs. Then the chromatic number is found. mathispower4u.com
From playlist Graph Theory (Discrete Math)
Paul Seymour: Colouring graphs with no odd holes, and other stories
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Combinatorics
Random Cayley Graphs - Noga Alon
Noga Alon Tel Aviv University; Member, School of Mathematics November 25, 2013 The study of random Cayley graphs of finite groups is related to the investigation of Expanders and to problems in Combinatorial Number Theory and in Information Theory. I will discuss this topic, describing the
From playlist Mathematics
Francisco Martinez Figueroa (8/19/22): Chromatic number of G-Borsuk graphs
The Borsuk graph has vertex set the sphere S^d, and edges x∼y whenever x and y are ϵ-almost antipodal. It is well known that when epsilon is small, its chromatic number is d+2, which follows from the topology of S^d via Borsuk-Ulam's Theorem. Given a finite group G acting freely over a com
From playlist Vietoris-Rips Seminar
Graph Theory: 65. 2-Chromatic Graphs
In this video we begin by showing that the chromatic number of a tree is 2. Yet, if the chromatic number of a graph is 2, this does not imply that the graph is a tree. We then prove that the chromatic number of a graph is 2 if and only if the graph is bipartite. -- Bits of Graph Theory
From playlist Graph Theory part-11
Chromatic Number of Bipartite Graphs | Graph Theory
What is the chromatic number of bipartite graphs? If you remember the definition, you may immediately think the answer is 2! This is practically correct, though there is one other case we have to consider where the chromatic number is 1. We'll explain both possibilities in today's graph th
From playlist Graph Theory
Math for Liberal Studies - Lecture 1.7.3 Upper and Lower Bounds
This is the third and final video lecture for Math for Liberal Studies Section 1.7: Coloring Graphs. In this video, we discuss the "chromatic number" for a graph, which is the smallest number of colors needed to properly color the vertices of the graph. In general, finding the exact chroma
From playlist Math for Liberal Studies Lectures
Graph Theory: 66. Basic Bound on the Chromatic Number
In this video we prove by induction that every graph has chromatic number at most one more than the maximum degree. Odd cycles and complete graphs are examples for which the chromatic number meets this upper bound exactly. For other graphs, Brook's Theorem tells us that the chromatic num
From playlist Graph Theory part-11
Diamagnetic Anisotropy - H NMR Spectroscopy - Organic Chemistry
This organic chemistry video tutorial provides a basic introduction into the concept of diamagnetic anisotropy as it relates to H NMR spectroscopy. It explains why the chemical shift of molecules such as benzene and ethylene are much higher than for those of acetylene. It also uses 18-An
From playlist New Organic Chemistry Playlist