The Locrian Mode

The mode is created by playing the notes of a major scale starting from the seventh note.
Here's an example of the mode starting from B, based on a C major scale.

The result is a minor scale with a lowered second and fifth.
Here's the formula of the Mode:

How to use the Locrian mode When Improvising?

First of all you should remember that the mode is no a very steady one.
It starts with a half note and contains a flat fifth.
We'll use the mode when we want to have lots of color in our improvisation.

From a harmonic point of view we're going to play the Locrian mode over a half diminished scale since the chord hides inside the scale.

We could use the mode when we play a II-V-I chord progression ending in a minor chord just like this example below.

Compositions in the Mode

"Symptom of the Universe" by Black Sabbath
The beginning of "YYZ" by Rush
Sad But True by Metallica
Enter Sandman by Metallica
The main riff of Painkiller by Judas Priest