Electronic – How to convert 9 V DC to 5 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.

Olin's right about Microchip doing some nice switching regulators - I use the MCP1603 parts quite regularly. However these are buck regulators and don't have a 5V fixed option anyway. I just had a quick look on Farnell and didn't notice any MC parts that fit for this requirement. It may be worth a look on their website though.

The cheapest 5V boost regulator I am aware of that can work down below 1.8V at 500mA is the NCP1450 from ON Semi. It's £0.63 in qty 1, can source up to 1A, and can startup with low as 0.8V with no load. It comes in a nice and small 5-pin SOT-25 type package.
I haven't used it, but I saved it whilst searching for another regulator as it looked like a nice part. ON Semi make a lot of decent cheap parts in this category.