论文标题
在12色调相等的调节的4维亚代甲板上
On a 4-dimensional subalgebra of the 12-tone Equal Tempered Tuning
论文作者
论文摘要
在{Euclidean Vector Space} $ \ Mathbb {E} _4 $上对关联，交换和分配乘法的操作由一个偏斜的循环矩阵引入。在$ \ mathbb {r}上$ \ mathbb {r} $上产生的代数$ \ mathbb {w} $是$ \ mathbb {c} \ times \ times \ mathbb {c}。$相关的代数，几何学和拓扑属性是$ \ b的。 Clifford复数飞机。 $ \ mathbb {w} $上的拓扑由两个规范的标准提供。提示如何将这个4维代数超过$ \ mathbb {r} $将其应用于12色调的同等调谐代数。
An operation of associative, commutative and distributive multiplication on { Euclidean vector space} $\mathbb{E}_4$ is introduced by a skew circulant matrix. The resulting algebra $\mathbb{W}$ over $\mathbb{R}$ is isomorphic to $\mathbb{C} \times \mathbb{C}.$ The related algebraic, geometrical, and topological properties are given.There are subplanes of $\mathbb{W}$ isomorphic to the Gauss and Clifford complex number planes. A topology on $\mathbb{W}$ is given by a norm which is a sum of two norms. A hint how to apply this 4 dimensional algebra over $\mathbb{R}$ to the 12-tone Equally Tempered Tuning algebra is given.
