Harmonics are tones that are multiples of the original tone (the fundamental), therefore, there's plenty of them on the neck of your bass. The 12th, 7th and 5th are just the beginning. Note that the fundamental is basically a "nullth" harmonic (or the first overtone), though some people call THAT the first harmonic, so maybe it's easier to remember them by position and the tone you get.
Take, for instance, the G string.
The 12th fret harmonic is the first harmonic and sounds like the G, an octave above the open string. Note, it's halfway along the string length.
The 7th fret harmonic is the second, and sounds like a D, a fifth above the first harmonic. It's also exactly an octave above the 7th fretted note on the G-string. It's 1/3 of the way along the string, from the nut.
The 5th fret harmonic is the third, sounds like a G, two octaves above the open string. It's 1/4 of the way along the string.
The 4th fret harmonic is the fourth, sounds like an A#, two octaves above the fretted fourth string. It's also there on the 9th fret harmonic - it's exactly the same, but tougher to nail. At 1/5 of the string.
After this, there are harmonics before and after the third fret, before the second fret and so on...
In short:
http://www.guitar-and-bass.com/sixst...reference.html
If you have under 6 strings, just ignore the ones you don't have.
There're also pinch and tap harmonics, but those are a special category. The basic idea is to fret the note on the neck and then find where the harmonic lies down.
For decent harmonic usage, look around on Youtube for recordings of:
Jaco Pastorius - Portrait of Tracy
Michael Manring - The Enormous Room
Victor Wooten - Amazing Grace
