The zener requires only 1mA to work, and the LM329 works down to 0,6mA. I do not know how critical the voltage level on the syth is, it is quite difficult to tell how it works without the service manual. A synth will likely drift out of tune when something with poor stability would be used and I think the voltage will have to be tuned for a specific sound rather than voltage.
Creating the 5,333V from the 6V supply with a voltage divider would require an equally stable 6V supply, which this is not, because it seems to be fed from batteries that have a voltage that is dependent on quite a lot of circumstances, including their state of charge.
I still don't know what you're trying to do here. Do you have a synth of this type you are trying to repair, or are you trying to build a new one from scratch with the schematic? Given the specific part that was used, the designer seems to have gone for stability, else a cheaper part would have done. Please let us know what your intentions are, maybe with pictures and links to show what problems you are trying to solve.