Standard alkaline cells start out a bit over 1.5v, and are considered dead by the time they drop to 1.0 volts. So a "9-volt" battery will run 6 to 9 volts over its working lifetime. NIMH and NiCd cells have a pretty flat discharge voltage of 1.2 volts, so even a 7.2v battery would be enough.
That said, you will get more headroom with more voltage. The circuit will behave reasonably well with up to 67 volts, which is the maximum rated screen voltage for the 3S4.
For what it's worth, I originally chose to use four batteries because they often come in packs of eight at good prices - you can get two complete sets that way. A second advantage is that the battery lifetimes are matched, about 200 hours for the D-cells and for the 9-v batteries.