Easiest way to regulate a 12 V battery to regulated 12 V?
What a regulator actually does is to smooth out variations in voltage to make a source look more like a battery. In a case like this, you don't have to worry about the source voltage changing much, so the main advantage of regulation is moot. 

Often equipment that's designed for low-voltage DC will actually accept a range of voltages. Sometimes it isn't, and really does expect a regulated supply. The problem here is, what's the range that the synth will find acceptable? Admittedly, applying regulation solves that problem by nailing the voltage down to something that's supposed to work, but the thing is, voltage regulation gets complicated when the source and the output voltages are closer than about 2 volts, because regulators need some headroom to work with. Automotive batteries nominally sit around 13.8V; worryingly high if your device wants a regulated 12V input, annoyingly low if you want to regulate it to 12V.

If you can measure the voltage from your present AC/DC converter, while it's connected to the synth, with the synth turned on, and that voltage is with say, half a volt of the battery's open-circuit voltage, you would probably be able to directly connect the battery, without a regulator.