The blues scale
The blues scale is the minor pentatonic with one note added — a ♭5, the "blue note." Six notes, and it carries the whole vocal, bent, aching sound of the blues.
From minor pentatonic to blues
Minor pentatonic: ^1 ♭^3 ^4 ^5 ♭^7. Add a ♭5 between the ^4 and the ^5, and you have the blues scale: ^1 ♭^3 ^4 ♭^5 ^5 ♭^7.
The blue note is meant to be bent
In real blues playing, the ♭5 (and often the ♭3 and ♭7) aren't fixed pitches — they're bent, slid into, played a little sharp or flat of dead centre. On the violin you can actually do this: place the ♭5 slightly low and slide up toward the ^5, or add a wide, slow finger vibrato. A blue note played dead in tune barely sounds blue.
Try it
Try
On the A string, play B♭ (1st finger, pulled back), C (low 2), then slide your 2nd finger up a fraction toward D — don't stop cleanly, just smear through — then back down. Keep it loose and slightly out of time. That slippery, vocal quality is the blues scale doing its job.
The usual mistake
Playing the blues scale stiff and metronomic, every note in tune and on the beat. The blues is about bend, slide and behind-the-beat phrasing — the notes are a starting point, not the whole story. A classically-trained ear wants to clean it up; resist that.