Blues Chord Progression

"Is an E, A and B blues chord progression 1 4 5 in the key of E?"

These three chords are indeed 1 4 and 5 in the key of E, but when used in blues there is more guitar theory to understand.

The blues concept is based on dominant seven chords (which unlike major seven chords can simply be called "seven" or "7"). This means that blues vocal melodies, bass lines and guitar solos use intervals and scales that correspond to dominant 7th chords whether or not one of the instruments is physically playing them. So a progression with the chords E, A and B is treated as if the chords were E7, A7 and B7.

If you know anything about music theory, then you know that only the fifth major scale degree has a major third and flat seventh interval necessary to build a dominant seven chord. So 7th chords only occur once per key. A progression with three different dominant 7th chords is actually three different keys. E7 stems from the key of A (or A major scale). A7 stems from the key of D (or D major scale). B7 stems from the of E (or E major scale). E7, A7 and B7 is actually a 5 5 5 chord progression with each chord produce a key change. But musicians and guitar players refer to this type of blues chord progression as 1 4 5 anyway. 

There are a few different ways guitar players can play over this type of blues chord progression.

The first is to ignore the whole progression and simply follow the root chord (where everything begins and resolves). In this case it's E. Since the E chord is base on an E major triad you can play the E major pentatonic scale over it. But blues players also break the rules a bit and play the E minor pentatonic instead. The tension and dissonance that results contributes to the much loved and edgy blues sound. In fact, this minor-over-major approach has become the standard in this style of music and many blues players rely on it alone. But most blues music incorporates the major pentatonic too usually by mixing it together with minor pentatonic patterns.

Another option is to use full major scale patterns. Since the E chord is treated as if it were an E7, and since E7 stems from the A major scale, then A major scales patterns are the correct ones to play. Since the fifth note E is functioning as the root this produces the fifth mode, Mixolydian (a.k.a. "Dominant scale" because it goes together with dominant chords). Full major scale patterns can also be mixed with both major and minor pentatonic patterns. Throw in some chromatic passing tones and you have quite a palette of notes to choose from!

Another option when playing over dominant seventh blues chord progressions is to follow the key changes with the scales you play. So when the progression goes to A, play A major and minor pentatonic and A mixolydian mode (D major scale patterns). When the progression is on B7 play B major and minor pentatonic and B mixolydian mode (E major scale patterns). Switching scales like this can be tricky and many blues players prefer a simpler approach. But country and jazz players, who are usually more trained in music theory for guitar, love this challenging method of playing.