Perplexed

Are you sure he didn't say three frets down? That's the usual... because then the chord progression is in E, and your solo is in C# minor (the relative minor of E)

If you move down two, you're working from the b7 of the scale. Moving the Em pentatonic down to D gives you:

D-F-G-A-C-D. You'd have the root note of the IV chord (A)... but no notes at all in the I or V, so it would be really tough to resolve - although you could end on F I suppose, making a suspension.

What's got me confused is how you'd focus on E as the tonal center when E isn't in the scale!

In the example you cite, when you play the D major scale but use E as the tonal center, you are playing the E Dorian mode (E, F#, G, A, B, C#, D). Dorian modes are primarily minor in mood. You'll note that if you make triads out of this mode, you'll have the following:

E, G, B, which is Em

F#, A, C#, which is F#m

G, B, D, which is G major

A, C#, E, which is A major

B, D, F#, which is Bm

C#, E, G, which is C# diminished

D, F#, A, which is D major

Dorian modes are often the choice when you have a song that moves between a minor tonic and a Major IV chord. Using this example, a song that switches between Em and A major. Using the Em pentatonic (E, G, A, B, D) you lose the C# and F# which add so much to the color of this particular mode.

If you're playing blues in E (E, A and B) and you use the Dorian mode, you'll by working the typical blue notes (G and D for the E chord and D and A for the B chord), but you'll also be stressing the C# with the A chord. It makes it a little more flavorful than the straight pentatonic. It's not the norm, but it definitely can work.

This is a truly simple explanation, but I hope it helps.

Peace

LOL I mis-read the post and thought you were moving the minor pentatonic or the blues scale... the D major scale works completely, because the E minor pentatonic is a subset of it:

D-E-F#-G-A-B-C#-D

The only added notes are F# and C#, which are both also in the key of E major.