Why when playing 12 bar blues why does the min7th note seem to set up the change to the 4th chord
When playing a 12 bar blues progression, playing a min7th note over the I chord seems to naturally set up the change to the IV chord. Why is this?
For example: in the key of A, it sounds good to play the notes from A down to G chromatically just prior to changing to the D chord, even though G is not a chord tone of D.
Maybe it's that the G is semitone away from F#, which is the 3rd and is a chord tone.
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Let's pretend we are in key D. The V chord will be A, and to make it more dominant, we include the G - which is in key D. That would usually resolve to something as close to itself as possible - hence your F# - M3 of D. So, it almost sounds like, after 4 bars (often) in A, there's a modulation into D. It's only temporary, but at the time, who knows?
That, and the fact that in Blues the underlying chords are usually dominant 7ths anyway, it's hardly surprising it sounds good. The M7 that you may use in between the root (A) and the m7 (G) is a chromatic note, going in the general direction of that m7, so a nice chromatic set of moves works well.
That the G is not a chord tone of D matters not: we're not quite onto that D bar anyway!
Another way to look at it from the 'D' perspective is that the G note can be used on a D chord, as a suspension, which inevitably resolves to the F# - which is where the series of notes is heading anyway.
The basic Blues progression - A7,D7,A7,E7,D7,A7 - is all dominant 7th shape chords. A7 is the dominant 7th chord of D. That's why.
It's a little harder to explain (in a 'circle of 5ths' way, at least) why the last part of the progression - E7, D7, A7 - is so satisfactory.
A 7th chord tends to pull down fifthwise (or up fourthwise), so changing the I to a I7 is a way to pull to the IV. It's just like in a perfect cadence, where you have V7 > I, but in a smaller way. You also see the same thing in Latin music in a minor key, they'll swap the i (minor) for I7 (dom7) to lead into the 4 chord.
Example of the minor variety (simplified to its most basic form):
Dm Dm Am Am
E7 E7 Am A7 (turnaround) or Am (final)
What you'll usually see is something more like this though, but that's just a "fancier" version of the above (with some pre-dominants added in)
Dm Dm Am6 Am6
B7 E7 Eř A7 (turnaround) or Am6 (final)
If you play the 12 bar blues so that the tonic is just a plain triad until adding the minor 7th in bar 4 (which is actually how a lot of blues work) it is easier to see what happens.
With Roman numeral analysis under the chord letters:
A A A A7
I V7/IV
D D A A
IV I
G7 D A G7
V7 IV I V7
I left the seventh off of the IV chord to keep the analysis simple.
In bar 4 you can see that adding the minor seventh changes the function of the chord and it becomes a secondary dominant to the IV chord.
The reason this sounds so smooth to IV is because it exploits one the most important voice leading concepts in western music: the scale degree FA descends by half step to MI.
In this case A7 to D temporarily shifts the tonic to D. The seventh of the A7 chord is the tone G which is FA in D major, it descends to the F# of the D chord which is MI in D major.
It gets kind of wordy explaining exactly what happens and accounting for tonics, scale degrees, chord tones, etc. But that is the complete explanation.
Secondary dominant
Voice leading FA to MI
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