Volume 57
, Issue 2

2021

Dear Reader, welcome to this issue of Parabola!

In this paper we look at musical scales, particularly equally tempered scales. Using continued fractions to approximate irrational numbers with optimal fractions, we develop an algorithm to classify musical scales with any number of notes to an octave based on their consonance.

In this note, we prove a useful general formula for limits involving two or more two square roots with quadratic radicands.

In previous issues of Parabola, Randell Heyman showed that $c_n = (1 + \sqrt{2})^n + (1 - \sqrt{2})^n$ is an integer for each natural number $n$ and Xiaoyan Hu derived a recursion relation for this sequence. This article extends upon these results, by providing another method to arrive at the recursive relation.
Q1647 A monk visits $t$ temples and burns a number of incense sticks, the same number at each temple. The temples are located on different islands in a magic lake and he visits them by boat. The lake doubles the number of sticks he holds each time he reaches an island.