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I'm not a professional pianist but I have been messing around with blues and jazz so I thought I'd show you how to play some very simple blues piano. Simple blues consists of only three chords, let's play in the key of G. This makes our blues have the following chords.

G7 . . . | G7 . . . | G7 . . .| G7 . . .|
C7 . . . | C7 . . . | G7 . . .| G7 . . .|
D7 . . . | C7 . . . | G7 . . .| G7 . . .|

Just play 2 notes of each chord, the root and 7th. I.E

G7 = G + F
C7= C + Bb
D7 = D + C

So if you play it through it should be something like this:
Simple Blues Chords

Next you need a melody, blues is great because you simply mess around with the blues scale which has 5 notes in it!:

G, Bb, C, C#, D, F

Try messing around till it sounds something like this:

Simple Blues Melody Improvisation

Now all thats left is to put them together into something like this!:

Simple Blues

Keep in mind all the 'right hand' stuff your hearing is made up of exactly those 5 notes above, sometimes I might play more than one note at a time but never any notes other than those 5. The left hand is only ever the root and 7th as I described above. The great thing is when you put it together it sounds more complex than it really is! Timing is very important, and something I struggle with, you have to get that 'swing' feel to make it work.

Bouncy Blues

Lets go through a few more ideas for what you can do with a Blues chord progression. Try playing the bass line with your left hand as follows

Bouncy Blues Bass Line

This is what I'm playing to get this sound:

G7: G, G(one octave up), B,D..B,D

C7: C, C (one octave up), E,G..E,G

D7: D, D , F#, A.. F#, A

Now with your right hand noodle around the G pentatonic scale. G,A,B,D,E,G(up high). It's almost identical to the blues scale, in fact you can play both interchangibly, or play mostly pentatonic and throw in the extra notes from the blues scale (Bb, Db) here and there to 'blues up' your sound. I find the pentatonic is more of a happy sound and the blues scale is, well more of a bluesy sound. This is very personal though, just play around and see what feels right.

Put them together and you've got something like this!

Bouncy Blues

Classic Blues

Lets try a very classic sounding blues, the bass line should sound like this

Classic Blues Bass Line

Here's what we're doing with the left hand for bass

Left hand

G7: G+D G+D, E, E

C7: C+G C+G, A, A

D7: D+A D+A, B, B

Now play with the blues scale on your right to get this

Classic Blues

Walkin Blues

Here's an example of a walkin bass line style blues.

Walkin blues

This is a very simple walking bass line, basically walk up and down the notes of the chords.

G7: G, B, D, E, F, E, D,B

C7: C, E, G, A, Bb, A, G, E

D7: D, F#, A, D (You only sit on D7 for one bar so there isn't enough time to walk up and down)

With the right you can dab the chords on the off beat or improvise around the blues scale.

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