This exercise is from the Core Skills section on developing Speed Techniques.
Listen to the Normal speed audio first (under 'Tools' in the menu) before checking out the ActionTab. Also, you will find the Tablature View (also under 'Tools') useful for this exercise.
Staying with alternate picking along 1 string, let's now make a tune. We're going to use notes from an altered E major scale - along the high E string. The scale we'll use here is sometimes called the Hindu scale, or E7b6. It's just a standard E major scale, except the 6th and 7th notes are flattened (lowered by 1 fret):
E Major Scale:
E - F# - G# - A - B - C# - D# - E
E Hindu Scale:
E - F# - G# - A - B - C - D - E
It may be called a Hindu scale, but when used in this example it sounds nothing like a Hindu tune. Scale names can be misleading at times ;)
In this exercise, every other note is the open E string. This means that if you start on a downstroke, then every fretted note is played with an upstroke. The important thing here is to learn the overall picking technique. If you don't like the melody, then pick different notes. It really doesn't matter. The point is that you can create a cool melody from any scale really quickly once you learn this alternate picking method.
Once your picking hand has got used to going fast, and your fretboard fingers are co-ordinated enough to always land a note on the right beat, then you can hit any notes you like along that string and produce a fast melody that sounds cool.
I often use this technique in freestyle solos, because it is easy (once you have the hang of it) but sounds good.