Coin Values and PCGS have an unqualified 1934 entry which I interpret as the medium motto. The Red book (2008) only lists the DDO, heavy, light variants, but it also does not list the 1934-D heavy that Coin Values and PCGS lists. Go figure
I think it's going a bit overboard to include "medium". It's sort of like the 1922 cent with D, weak D and no D. Either the D shows or it doesn't. Why should a later die state be treated differently? Especially when you have to hold the coin at a certain angle with the light hitting it at just the right angle to be able to see a little bump about where the D must have been to call it a weak D? For the Quarter, either the motto is as strong as the rest of the coin overall, or it's noticeably weaker than the rest of the coin overall. Wear shouldn't enter into the determination.
The reason for light, medium and heavy is that they came from three different hubs. The light came from the hub used in 1932. The medium came from the same hub used in 1935 and the heavy came from the same hub used in 1936 and 37. Hope that helps.
Yes. 1934 was a great year for varieties. The light motto is probably worth a bit more than the others but I lost track of the values years ago. There was also a DDO for 1934 that is worth watching for.
Actually, I was questioning your implication that the same hub was used in 1932 and 1934; then another hub in 1934 and 1935; and finally a third hub in 1934, 1936 and 1937. Was that what you were saying? Where did you find that information?
My post was from memory but I'm sure you can find the information in Breen, CPG or a Google search. There are probably other books on Wash. quarters by now. As I said, I don't keep up with this any more. A PCGS forum search will bring up many threads on the topic. There is nothing new about this topic. It's really old news.