论文标题
在欧几里得算法上：没有递归的节奏
On The Euclidean Algorithm: Rhythm Without Recursion
论文作者
论文摘要
在Toussaint 2005年对世界音乐中所谓的Euclidean Rhythms的调查之后，欧几里得算法的一种改良形式在音乐作曲家中广受欢迎。我们提供了一种方法，可以用手轻松计算欧几里得的算法，以修改布雷森纳姆的线绘制算法。值得注意的是，这种修改的算法是一种非恢复矩阵构造，仅使用模块化算术和组合学。这种结构的表现并不优于传统的划分与雕刻方法。它是为了组合兴趣和易于手动计算而提出的。
A modified form of Euclid's algorithm has gained popularity among musical composers following Toussaint's 2005 survey of so-called Euclidean rhythms in world music. We offer a method to easily calculate Euclid's algorithm by hand as a modification of Bresenham's line-drawing algorithm. Notably, this modified algorithm is a non-recursive matrix construction, using only modular arithmetic and combinatorics. This construction does not outperform the traditional divide-with-remainder method; it is presented for combinatorial interest and ease of hand computation.
