Tension is a very powerful tool in music.  It can bring identity to a piece if used correctly.  And thank God for it because music would be boring without it.  But wherever you have tension, you also must resolution.  The use of this when writing a song or improvising defines the mastery of the musician.  One way of adding tension is to change the diatonic notes of a chord to chromatic tones.  This creates more tension and in return a more powerful resolution. 

Building Altered Chords

The quality of a chord is defined by the root, third and the seventh.  If you had nothing else in the chord you can still define it's quality.  This means that the 5th, 9th, 11th, and 13th can be altered without changing a chord's quality.  Resulting in a lot of fun for musicians.

These chords are written by first the symbol for their chord quality.  After which the alteration of the chord in parentheses, like C7(#9).  An exception is the augmented fifth which is shown by a "+" sign like in an augmented chord.  Chords may have more than one alteration.

Alteration Resolution

But this tension must resolve correctly to sound its best.  Alterations resolve as follows:

• Raised Fifth - resolves upward a half step
• Lowered Fifth - resolves downward a half step
• Raised Ninth - resolves upward a half step 
• Lowered Ninth - resolves downward a half step
• Raised Eleventh - resolves upward a half step
• Lowered Thirteenth - resolves downward a half step