My iBook G4, OS X 10.5.2, says MuseScore 2.0.1 can't be open: not for this architecture?

MuseScore 2.0 only works on Mac Intel with Mac OSX 10.7 or higher. The last version available for PPC is MuseScore 1.1 https://musescore.org/en/download/musescore-1.1.dmg This version is very old...

I would be surprised if this is the first time you've encountered this issue—you'd be hard pressed to find any modern software that supports a system that old. For example, the current release of Firefox as of this writing is 38.0.5; the last version that would run on your system was 3.6.28. That's thirty-five major versions in between. It would be a shame to be unable to use a recent version of MuseScore or Firefox (or all kinds of other great programs). You can find a pretty good deal on Craigslist or eBay ($300 range) for an old white Intel MacBook that's capable of running the most up-to-date versions of OS X, and hence the most up-to-date version of MuseScore (though if you get the chance to choose between 10.9 Mavericks and 10.10 Yosemite go with Mavericks; it will be much, much more familiar coming from Leopard, while Yosemite would be difficult to adjust to, and Mavericks is as well-supported as Yosemite).

Hardly 35 major releases for Firefox - after 3.6.28 Firefox release numbers accelerated by a factor of about 10. But, yes, support for that Mac OS was dropped a long time ago by most software.