# The Mathematics of Musical Tuning and Temperament [G]

**Eric Mack • North Idaho College**

I have created and teach an interdisciplinary class titled “The Mathematics and Aesthetics of Musical Tuning.” At the heart of this topic is the impossibility of obtaining an integer solution to the equation `2x = 3x`, two being the ratio between frequencies that our human ears hear as octaves and three the ratio of frequencies we hear as perfect 12ths. In this presentation we will explore the nature of the conundrum, some of its many imperfect solutions, the philosophy behind them, and the art they have given rise to over the millennia. Computer programs will make the math audible, bringing this ancient quadrivium subject to life.

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