An all-interval tetrachord is a tetrachord, a collection of four pitch classes, containing all six interval classes. There are only two possible all-interval tetrachords (to within inversion), when expressed in prime form. In set theory notation, these are [0,1,4,6] (4-Z15) and [0,1,3,7] (4-Z29). Their inversions are [0,2,5,6] (4-Z15b) and [0,4,6,7] (4-Z29b). The interval vector for all all-interval tetrachords is [1,1,1,1,1,1]. (Wikipedia).
Arctan(1) + Arctan(2) + Arctan(3) = π
From playlist Trigonometry TikToks
From playlist Trigonometry TikToks
Area of a Regular Polygon: Quick Demo
From playlist Geometry TikToks
Lecture 14. Ostinato Form in the Music of Purcell, Pachelbel, Elton John and Vitamin C
Listening to Music (MUSI 112) This lecture begins with a review of all the musical forms previously discussed in class: sonata-allegro, rondo, theme and variations, and fugue. Professor Wright then moves on to discuss the final form that will be taught before the students' next exam: osti
From playlist Listening to Music with Craig Wright
R - Item Response Theory Analysis Lecture
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From playlist Structural Equation Modeling
Trigonometry 8 The Tangent and Cotangent of the Sum and Difference of Two Angles.mov
Derive the tangent and cotangent trigonometric identities.
From playlist Trigonometry
From playlist Trigonometry TikToks
CCHF VS 13.3 - Prof. Huw Davies
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From playlist CCHF Virtual Symposia
The alternating series. Solved problems. Estimating error and partial sum estimation for a set maximum error.
From playlist Advanced Calculus / Multivariable Calculus
Tragic Passions from Shakespeare to Verdi
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From playlist Reunion Homecoming
Trigonometry 7 The Cosine of the Sum and Difference of Two Angles
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From playlist Trigonometry
Worldwide Calculus: Prelude to the Definite Integral: Riemann Sums (part A)
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From playlist Continuous Sums: the Definite Integral
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From playlist Using Interval Notation
Nested Interval Property and Proof | Real Analysis
We introduce and prove the nested interval property, or nested interval theorem, or NIP, whatever you like to call it. This theorem says that, given a sequence of nested and closed intervals, that is, closed intervals J1, J2, J3, and so on such that each Jn contains Jn+1, this infinite seq
From playlist Real Analysis
Topics in Combinatorics lecture 2.0 --- Intersecting families
The main result discussed here is a beautiful proof by Gyula Katona of the Erdos-Ko-Rado theorem, which answers the following question: how many subsets of {1,2,...,n} of size k is it possible to pick if any two of them must intersect? 0:00 The largest size of a general intersecting fami
From playlist Topics in Combinatorics (Cambridge Part III course)
Worldwide Calculus: Improper Integrals
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From playlist Continuous Sums: the Definite Integral
What is a Manifold? Lesson 4: Countability and Continuity
In this lesson we review the idea of first and second countability. Also, we study the topological definition of a continuous function and then define a homeomorphism.
From playlist What is a Manifold?
