The most convenient scale for improvising or writing melodies in a major key is probably the pentatonic scale shown in Ex. 1, which, at the ninth position as shown, is in the key of E major. This comfortable shape seems tailor-made for the human hand. In this fingering, the major 3, G#, occurs twice: at the 9th fret of the second string and at the 11th fret of the fifth string. From the Allman Brothers to B.B. King, this scale has provided more than enough inspiration to get many guitar heroes through many an amazing solo. Experiment with it, and you may come up with some catchy pentatonic phrases of your own.
Then try Ex. 2, which has added spice—the minor 3 [the G natural that occurs at the 12th fret of the third string]. Fretted with the 3rd finger, this note creates momentary dissonance against the E major background harmony and, the first time it occurs [last sixteenth-note of beat one], it is slid down a fret to the eleventh-position F#. We get resolution when we finally tag G#, the major 3, at the 9th fret of the second string.
It’s also satisfying to bend the minor 3 up to a major 3 [Ex. 3]. As long as you’re not emphasizing the minor 3 too hard, you can get away with it. Remember that the minor 3 is also accessible at the 10th fret of the fifth string, and can be used as both a neighbor and a passing tone in lines like Ex. 4. Eventually, you’ll be able to string together longer more advanced lines that touch on both major and minor 3s and span most of the fretboard [Ex. 5].