Now I realize that these examples aren't exactly the most exciting licks you've ever heard, but I think you'll be surprised at how good they can sound with just a little bit of help. The following example uses exactly the same double-stop major 3rd run in D as before, but underneath there is a simple ringing D chord. With this addition, the double-stop run takes on an almost classical feel . As I said before, double-stops are extremely versatile. There is some cool double-stop theory lurking inside that innocent looking D chord that we should touch on here before you dig into the sequence.
Like any other major chord, the D chord is composed of the root, 3rd, and 5th tones of the root scale. In the case of the D these tones are D, F#, and A respectively. For now though, let's only concern ourselves with the A/F# double-stop. Using the same numbering system as we used before let's figure out the relationship between these two inside the D chord.
First let's consider the A as the root of the double-stop. Counting the A major scale we find that the F# is the 6th tone of the scale. Therefore the relationship is a major 6th
Simple right? For kicks let's drop the F# a whole octave and put on the fourth string, fourth fret. Let's count again, but this time using the F# as the root. The A note is one half step below the third tone of the scale. The A is the minor third
(flat third) of the F# scale.
Luckily, this isn't some kind of bizzare coincidence. It's a constant relationship between 3rds and 6ths. This constant even has its own name. It's called an interval inversion
. All this means is that if you turn a major 6th upside down, by either dropping the top note down one octave, or raising the bottom note up one octave, you end up with the same tones, but in this pattern they are a minor 3rd. Just the same if you turn a major 3rd upside down (or invert it) you end up with a minor 6th. This might sound kind of confusing, but give it a chance to sink in and it will make more sense.
Here's another way to think of it... the original interval and the inverted interval will always equal 9. A 3rd when inverted will become a sixth... 3+6=9. It's the same with every other interval (2nds become 7ths... 7+2=9, 5ths become 4ths... 5+4=9 etc). Just remember that the quality of the chord, whether minor or major, will become the opposite when inverted. Minor becomes major, major becomes minor... ENOUGH THEORY!!! now dig into the sequence.