Changing Voltages in a Circuit?
It's not a good idea to replace the voltage levels that a system is expecting. Unless you're modding the synthesizer to accept your GND, 10V and 20V. Audio systems generally have a bipolar supply because it's necessary for the opamps inside to properly amplify an AC signal ( you can't amplify a negative voltage if your supply only has a positive rail). 

Regarding your second question, yes a voltage divider is a terrible way to source a reduced voltage from. You'd need a buck converter to help you out there. Probably an adjustable one, never came across a fixed 10V buck converter. Be aware of he current rating on it as well.