Note: this post requires a basic knowledge of intervals.
A chord tension is any note in a chord that is not considered integral to the chord (the integral notes are called ‘chord tones’). Tensions are also referred to as ‘added colors’ or ”non-chord tones’ (I try to avoid using the latter term because means something different in Traditional/Classical harmony).
There are only three possible tensions: 9, 11, and 13 (in other words: 2nds, 4ths, and 6th, respectively). But these notes are not considered tensions on every chord–the only way to know for sure is to have a good knowledge of chords (to get started, read our article on chord abbreviations). These tensions may also be modified by a # (sharp) or b (flat).
Chord tensions are written up an octave (by adding 7 to the interval number) because chords can sound muddy or cluttered if the note intervals are too close together. Tensions tend to come in between chord tones, so these notes are often placed in higher octaves to keep things clean (not to say that chord tones are usually all within one octave-they aren’t). The only exception that comes to mind is that a Cadd9 chord (C major chord with a major 2nd added) is sometimes written C2.