It's pretty common for groupings of two or three notes in scales. Perhaps the most popular guitar scale of all time, the Minor Pentatonic, is built on a two-note-per-string 'box' shape which keeps every note easily within reach, promotes the option of big bends, double-stops, super-fast repeated sequences and of course the much-copied 'Chuck Berry lick.' It works because it's easy to play, it's expressive, and it allows even beginner guitarists to sound like they know where they're going, because it's very hard to hit a wrong note with this scale (and even if you do, you can easily find the next note to make things right again).
Three-note-per-string scales are also very popular. Frank Gambale was instrumental in popularizing three-note-per-string versions of various scales and modes, and with good reason: they allow you to really wail on high-speed legato licks, they give you a lot of options in sliding from one note to another, they widen the number of available notes for improvised chord shapes, and (as Gambale demonstrated) they lend themselves to all sorts of endlessly entertaining sweep-picking, economy picking and string-skipping ideas. Three-note-per-string scales are probably the coolest thing to happen to the electric guitar since the low-slung strap. The Major scale is particularly handy as a three-note-per-string scale because it breaks down to three patterns, each one played on two adjacent strings before the next pattern takes over. It looks like this (in the key of A):
But my favorite way of playing the Major Scale is to spread it out over four notes per string. Before we take a look at how that falls on the fretboard, let's see what happens when we play the Major scale on a single string. We'll go all the way up past the first octave, and we'll do this one in the key of A too.
Notice anything? Let's look at the note intervals:
Half Step (This last one is actually the next octave of the root note).
So what we've got there, really, is a single pattern, repeated once. That pattern involves a span of two frets, a span of two frets, a span of two frets and a span of one fret. Then it repeats. So all we have to do is take the 'break point' and shift over to the next string. When you do that, the A Major scale goes from the three-note-per-string figure you saw in the first example, to this:
In this method there's a doubling-up of the root note each time you progress through the octave. That's not the traditional way to play a scale, of course, but this isn't an 'official' method anyway - it's one of the little rut-busters I've stumbled upon over the years. This 'doubling-up' opens up some interesting melodic possibilities, prompting you to play the same note on consecutive strings at times when you might instinctively just keep charging up the scale. But like all scales, the real magic happens not when you simply play it up and down in sequential order, but when you use it as a springboard for melodic ideas. This four-note-per-string version is a very useful way of visualizing bit chunks of the neck and giving your melodies the room to roam all around musical prairie, instead of being penned in to a very small, very particular box.
Now, to put this all in a musical context, here's a musical idea that is part John Petrucci, part Guthrie Govan and part Marco Sfogli. It'll work quite nicely over big, dramatic, sustained A chords for each bar, but as a little bonus exercise I'd recommend recording yourself playing this lick over a drum beat, then create a whole bunch of separate tracks to experiment with different chordal backings. For instance, try a bar of A5, a bar of B5 and two bars of E5. Or a bar of A5, a bar of C#5, one of D5 and then another of A5. Whichever chords you choose will recontextualize the melody, sometimes quite drastically.
So there you have it! A cool new way of approaching a common scale, and some bonus homework to help sharpen your arranging skills.