Ah, the big, terrifying elephant in the room. Let me dispel the first myth: THE MINOR BLUES SCALE IS NOT THE BEST CHOICE FOR A MAJOR BLUES PROGRESSION (or any progression, really). Many band directors teach this for several reasons: some know it is a good way to give students a simple approach that can help build confidence, some want to have a simple approach so they can spend a smaller amount of time on the subject and get back to preparing for marching contest, and some simply don't know better and they are doing their best.
I'm here to help, and I believe my approach is superior. Also, I am an expert. Listen up (I'm very modest, and a stable genius).
The Major Blues Scale
Whaaat!? What is this thing?
I'm so glad you asked. The major blues scale is based on the dominant chord, which is also the fundamental building block of the blues progression. Let's take D7, the first chord (for alto) of the solo changes for Williemakeit Blues.
This chord is a dominant chord. I'm not digging into theory, but this is a chord about which entire books on improvisation and jazz theory can and have been written. For now, just know that is is a major triad (D F# A) with a lowered seventh added (C natural). Let's start building.
Hit the brakes!!!
I'm going to adjust these changes (sorry, Brian). The chords in bars 1, 11, and 12 are unnecessary. While there is nothing wrong with them, they are not necessary to the progression, and they interfere with most students' ability to learn from the progression. So, the new progression is four bars of D7, two bars of G7, two bars of D7, one bar of A7, one bar of G7, then two bars of D7. That is the most basic three-chord, twelve-bar blues.
OK, back in...
Notable missing notes: G natural (pretty much the worst note, and for some reason, the one most young improvisers gravitate to), C# (the major seventh), and Ab/G#, the "blue" note from the minor blues scale.
Notable blues saxophone solos using only the minor blues scale: 0.
Notable blues saxophone solos using only the scale we just built: literally too many to list.
The catch? You have to learn three scales for the progression instead of just one. D, G, and A, the three keys we traverse in a three-chord blues progression. Nearly the entire canon of rock and roll/blues saxophone solos uses these three scales for 99% of the notes.
I play saxophone.*