Frederick the Great of Prussia, a devoted patron of the arts, had a particular interest in music, and admired the music of Johann Sebastian Bach. In 1747, Bach visited Potsdam, where his son Carl Philipp Emanuel was the Kapellmeister in Frederick’s court. When Frederick learned of this, he summoned ‘Old Bach’ to the palace and invited him to try out his collection of pianofortes. As they went from room to room, Bach improvised a new piece of music on each instrument [TM243 or search for “thatsmaths” at irishtimes.com].
Johann Sebastian Bach and Leonhard Euler.
for various values of the phase-shift. Despite the different appearances, all sound pretty much the same. 
The links between music and mathematics stretch back to Pythagoras and many leading mathematicians have studied the theory of music. Music and mathematics were pillars of the 
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