I don't think either that transpose function have to be an option to be assigned on a Slider

or knob

It is easier to press button + or - of transpose instead of moving slider up or down, or to rotate the knob. You will never know how much higher or lowest you have to move the slider to reach your desire note. And, BTW, what you will do when your slider is up (so it has to be somewhere +12 on transpose in that position) and you have to go to -2 ? In that position, if you have the transposition in 0 and you move the slider, it will increase the transposition with 8, 9 or a higher value, and after that will decrease, which is not a good approach. It is easier to press both buttons of transpose, to reset the transposition, if it is a transposition set already, and press twice the minus button to go to -2. I have set on the screen, in replacement of Demo button, the transposition, to be easier to view the transposition quickly, if it is set one!
Regards,
Vali