I got a question from a Twitter friend:
Let's find out! The note in question comes at 1:28.
The solo is played by the great James Cotton. He begins it with a C-sharp, the major third in the song's key of A. This would not seem to be a very weird choice. But usually in the blues, you put your major thirds in the lower register, inside the chord. In the higher register above the chord, it's more typical to play the minor third, a C natural in the key of A. Blues harmonica players don't usually play this high to begin with; James Cotton is drawing through the harmonica's seventh hole, and blues harp usually sticks to the bottom six holes.
So a C-sharp is an unusual note choice to begin with. But also, Cotton is bending the note a little flat. It's not so flat that it becomes a C natural, or a "C neutral", but it's definitely flat enough that it gets your attention. In fact, the note is an exact just intonation major third, which is conspicuously flatter than the standard 12-TET major third. If you have a guitar handy, you can confirm this the same way I did. The A string harmonic between the third and fourth frets produces the C-sharp that's a just intonation major third higher than A, and it matches James Cotton's note exactly. The standard 12-TET major third is sharper than the one from the natural overtone series, and while you are used to it from a lifetime of enculturation, it doesn't actually sound good. James Cotton isn't playing his C-sharp note out of tune, he's playing it more in tune than you're used to. That's why it sounds so surprising, yet also so good.
People might reasonably push back on me here and say that there is no proof that blues musicians are bending notes to produce just intonation intervals. Maybe James Cotton bent that note by some arbitrary amount, and he produced a just intonation major third by accident. Maybe! But you hear an awful lot of these things in the blues once you start listening for them. If it's a coincidence, it's a very strange coincidence.