SerendipinballwizardGaurav pointed to Pandora and instantly I knew he'd shown the way to something I'd been looking for a long while i.e. a way to "accidentally find music on purpose". Some cool matching of features can be visualised behind the scenes.
On the "Beatles station", a tune starts to play and it's so familiar. It's "Pinball Wizard" by "The Who" whose opening and a couple of interludes are the same as "jo sab karte hai.n yaaro.n" from "Jo Jeeta Wohi Sikandar". Sure enough, I2FS has a listing for this. Nice way to stumble upon such things.
I can now listen to Bix Beiderbecke as well (thanks to Trevor Chaplin), which is great.
And Pandora is a great name; hopefully with a more positive effect than the original.