Grade 11:The Musical Magic of 12

Why are there 12 notes in an octave? Why not 9? Why not 14? What is it about 12? Here we take a leisurely walk through the multiplicative structure of the music scale. Think of the piano keyboard. It has roughly 8 octaves, each one twice the frequency of the one before, each one consisting of n multiplicatively ascending notes. Now put on your designer’s hat––you get to choose n, the number of notes in an octave. What should it be, 8, 10, 12, 15, 16? Your choice. The columns in the table below are the frequencies of the octave’s notes (relative to the starting note) for different choices of n.

musical magic


What shall it be? Can you see why the n = 12 column cries out to be chosen, why it offers you more than you might have possibly hoped to gain. This is what we will discover.

Teacher manual
Student workbook