(1.7)  Octaves

An octave is the difference in pitch between two notes where one has twice the frequency of the other.  Two notes which are an octave apart always sound similar and have the same note name, while all of the notes in between sound distinctly different, and have other note names.

This is a very important concept in music.  Although notes are arranged, like a piano keyboard, in a long series from low to high, there is a repeating pattern.

Notes naturally fall into groups of twelve, which are all one octave apart from each other.  These groups repeat going up and down the piano keyboard (and indeed, the musical spectrum for any instrument).