Your're sort of on the right track there Timo1. Here's an example. Say you record the first variation and it's (4 measures long). You record the drums, and then the bass. We'll just say you recorded the bass line in the key of C. Now when you're finished that variation will continue to loop for you in the key of C. Now let's say you record the 2nd variation and do a bass line for it as well and record it in the key of E. When you press the fill in when switching from variation one to variation two, you'll get the chord change.
Now this if you do it all manually. Here's the cool part. There's a HUGE shortcut with the Boss DR-3. Lets say that your bass line is going to be the same through all (3) variations, but the key signature just changes. All you have to do is record the first bass line under variation one (either manually or using step record). Then when you're done you can copy and paste that same bass line to the other variations without having to re-record it. Then you can press the (KEY SHIFT) button and select the key you want. It's just like manually transposing on a keyboard. It really speeds up the time.
Squeak
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