Showing papers in "The Mathematical Gazette in 1978"
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TL;DR: In this article, it is shown that if we have a system of m linear equations to solve, it is a great simplification to write them in matrix form Ax = b, where A is an m x n matrix of coefficients, b is a m-dimensional vector of constants and x is an n-dimensional unknowns.
Abstract: If we have a system of m linear equations to solve, it is a great simplification to write them in matrix form Ax = b , where A is an m x n matrix of coefficients, b is an m-dimensional vector of constants and x is an n-dimensional vector of unknowns.
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TL;DR: The cyclic group C 12 provides a mathematical model for the tempered intervals as discussed by the authors, where the diminished seventh chords are shown to correspond to an appropriate subgroup of C 12 and its cosets.
Abstract: Group theory has been used in the study of various properties of musical scales. The cyclic group C 12 provides a mathematical model for the tempered intervals (see for example Budden [1] Chapter 23, where the diminished seventh chords are shown to correspond to an appropriate subgroup of C 12 and its cosets).
15 citations