The A# blues scale is one of the quickest routes to sounding like a blues player. It's only six notes, it sits comfortably under your fingers, and it has that gritty, crying quality you hear in a good blues solo. If you already know a minor pentatonic shape, you're one note away. If you don't, this is a great place to start.
Here are the six notes of A# minor blues:
A#, C#, D#, E, E#, G#
The first note, A#, is the root: the home base, the note everything else is measured from. When you end a phrase on A#, it sounds settled, like coming back to your front door.
Musicians describe each note by its distance from the root using a numbered formula. For this scale it's 1, b3, 4, b5, 5, b7:
If you're wondering why there's an E# instead of an F, don't worry, nothing is wrong. On the guitar, E# is played at exactly the same fret as F. The reason it's written E# is a naming rule: each letter is used once in a run of notes, in order, so the 5th of A# gets called E#. Since the scale also has a plain E (the blue note), you get E and E# side by side, one fret apart. Same sounds you'd expect, just spelled the tidy way. You'll also see this key called Bb, which is the same pitch as A#.
A half step (H) is the distance of one fret. A whole step (W) is two frets. W+H means three frets. The blues scale follows this pattern: W+H, W, H, H, W+H, W.
Start on A# and walk it up a single string:
Try this on your A string, starting at the 1st fret. Playing a scale on one string is slow, but it shows you the shape of the pattern clearly, especially that cluster of three notes in a row in the middle.
This scale is built from the A# minor pentatonic scale: A#, C#, D#, E#, G#. That five-note scale already sounds bluesy and strong. The blues scale adds just one extra note: E, the b5.
That E is the secret ingredient. It sits right between D# and E#, and on its own it sounds tense, almost wrong. That's the point. The magic happens when you use it as a passing note: slide from D# up through E to E#, or bend D# up toward E and let it hang. You'll hear that unmistakable whiny, expressive sound.
What to listen for: when you land on E, notice the tension. When you move off it to E# or D#, notice the relief. Don't park on the blue note for too long; treat it like hot sauce, a little goes a long way.
Fun fact: the C# major blues scale uses these exact same notes. The difference is which note feels like home. Over A# chords, it sounds like A# minor blues.
The most natural chord here is A#m7 (A# minor seven), made of A#, C#, E# and G#. Every one of those notes is in the scale, so anything you play will fit. A m7 chord is just a minor chord with that b7 added, which gives it a smooth, slightly jazzy blues colour.
Other chords built only from scale notes include C# major (C#, E#, G#) and the power chords D#5 (D#, A#) and G#5 (G#, D#). A power chord is just a root and a 5th, the two-finger chord rock and blues players love.
A simple progression to jam over:
Record it, loop it, or have a friend play it, then improvise with the scale on top. Even just vamping on A#m7 by itself is a classic blues and funk groove.
Once you can find the root, you can find the scale. On a standard-tuned six-string guitar:
The 6th fret on the low E string is a very comfortable spot. Put your first finger there, and the common minor pentatonic box shape starting on that fret gives you A#, C#, D#, E#, G#. Then add the E by reaching one fret above D# wherever it appears. On the 6th string, that's the D# at fret 11 and the blue note E at fret 12. Your A#m7 barre chord also lives at the 6th fret, so scale and chord sit right next to each other.
Loop the A#m7 to D#5 groove and play only three notes over it: D#, E and E#. Slide between them, bend into them, and play with the rhythm. After five minutes, open up to the full scale and finish every phrase on A#. Keep it slow, keep it loose, and let that blue note do the talking.
For the bigger picture, read The Blues Scale (Minor Blues).