Although musicians are often stereotypically in the iPhone demographic, there are Symbian-smartphone-owning musos too, which is why I'm always happy to welcome another musician's tool to the party. In this case KM Tuner, available in both free and paid-for versions. Yes, it's implemented in Java, but it's well done and provides real time tuning feedback, so worth a look!
Here's KM Tuner in action:
There are the usual Java permissions dialogs, though happily only on the very first 'run'; in action, you get real time analysis of a tone being played (check out the five decimal places), tuning indication and a pretty waveform.
If your note is within a fraction of a percent of a recognised open string for your instrument, you get a green indicator and line, otherwise it's red and you're out of tune!
KM Tuner works by doing successive short recordings and then analysing them. Yes, there will be short gaps of dead time between recordings, but I think this is acceptable for a typical tuning use case. As shown above, there are a few things you can fiddle with if the default doesnt work well for you; (right) a selection of instrument presets means that the notes will auto-snap to the right frequencies/strings, etc.
There's a simple, but graphical Help screen - very clear, and good to see.
I do have a number of small complaints about the applicaton:
some musicians might need more arcane tunings - for baroque instruments, for example
there's no manual string selection, so you're reliant on the software guessing which string you're tuning properly - in the case of a string which is some way out to start with, this can be a problem
there's no preset for a 12-string guitar (in my case)
there's no screen timeout override in place, so after a minute or so of tuning a problematic string you have to reach down and unlock the phone screen - yet again