It's four-on-the-floor, and the same kind of arrangement (for shifting) went into production on the R12 and R17 models.
Here's a photo of my R12, with the hand shifter that passes through an H gate in the right kneepad:

We had a big write up of the bike and its rediscovery and restoration in
the Vintage club bulletin a couple issues back.
I was in Munich last summer and they had the R7 on display at the newly remodelled museum. Although it resembles the R17 (and, to a lesser extent, the R12), it's really a nearly clean sheet design. The frame is a bridge and the drivetrain hangs from it. BMW didn't do anything like that again until the K bikes came out in 1984.


