The circle of fifths is a remarkably useful diagram for the analysis of music. It shows the twelve notes of the chromatic scale arranged in a circle, with notes that are harmonically related (like C and G) being close together and notes that are discordant (like C and C♯) more distant from each other. The … Continue reading Doughnuts and Tonnetze
Month: December 2017
Darker Mornings, Brighter Evenings
Today is the winter solstice, the shortest day of the year. We might expect that the latest sunrise and earliest sunset also occur today. In fact, the earliest sunset, the darkest day of the year, was on 13 December, over a week ago, and the latest sunrise is still more than a week away. This … Continue reading Darker Mornings, Brighter Evenings
Vanishing Hyperballs
We all know that the area of a disk --- the interior of a circle --- is $latex {\pi r^2}&fg=000000$ where $latex {r}&fg=000000$ is the radius. Some of us may also remember that the volume of a ball --- the interior of a sphere --- is $latex {\frac{4}{3}\pi r^3}&fg=000000$. The unit disk and ball have … Continue reading Vanishing Hyperballs
The Star of Bethlehem … or was it a Planet?
People of old were more aware than we are of the night sky and took a keen interest in unusual happenings above them. The configuration of the stars was believed to be linked to human affairs and many astronomical phenomena were interpreted as signs of good or evil in the offing. The Three Wise Men … Continue reading The Star of Bethlehem … or was it a Planet?
ThatsMaths 