The development of harmony, the ratios of vibration that introduce degrees of dissonance into music, evolved out of the organum of the late 10th and 11th centuries.  While credit for this development is unquestionably shared by many composers of the age, let’s focus on two. Hildegard of Bingen was by any measure a remarkable woman.  … Continue reading Revolutionaries

A brief introduction

At its core, music is as much mathematics as art: The godfather of Western music—all Western music—is none other than Pythagoras, the Triangle King himself.  In or around 500 BC, Pythagoras developed the modern scale by taking metal bars and dividing them sequentially by 2/3 to create successive notes.  Pythagoras’ scale had 12 tones—you can … Continue reading A brief introduction