I'm interesting in finding songs based on attributes (minor key tonality, etc). These are things listed in the details of why Pandora picks songs, but using Pandora, I have to give it songs/artists.
Is there any way to get the Music Genome database (or something similar) so I can search for songs based on attributes (that someone else has already cataloged)
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You can use Gracenote's Global Media Database and search with Track-level attributes.
"Gracenote's Media Technology Lab scientists and engineers take things further by utilizing technologies like Machine-Listening and Digital Signal Processing to create deep and detailed track level descriptors such as Mood and Tempo."
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To add to above answers, Pandora's statement (as viewed using the above link in combination with the Internet Archive) was: "A number of folks also asked about the prospect for an open API, to allow individual developers to start building on the platform. We're not there yet, but it's certainly food for thought."
Given that this was seven years ago, I think their decision is pretty clear.
I don't think there is any way to access this proprietary data, something I asked them about long ago. It seems to me they want to protect this unique part of their system; after all, they've paid for the man hours to label each song. Even if Pandora releases a developer API, which they've hinted at, I doubt it will provide access to the Music Genome information.
Give Echo Nest a shot!