Counterpoint Lession 9: Real imitation and double counterpoint

 Real imitation and double counterpoint

Part I - Real imitation at the Octave and Fifth
Counterpoint at the Octave and fifth is just as the name suggests.  the first voice  states the theme, and the second voice imitates that same melody at either a fifth or octave away from the first melody.  Here is the first page of Bach's Two-part Invention in C.

Notice that the second voice imitates the cantus at  the octave.  The first voice begins on C, as does the second.  This is by far the most common form of counterpoint.  Of course, Imitation at the fifth does exist.  This is exemplified in Bach's Two-Part Invention in G
Here is the first page of the piece. 

Notice that the counterpointing voice imitates the cantus at the fifth.  The first voice begins on G, and the second on D. 

Part II - Double Counterpoint at the Octave
It is possible to have two voices imitate each other at the octave while a third voice imitates at the fifth or sixth.  This is known at double counterpoint.