The Gretsch shell was a 3 ply, and then a 6 ply ... but neither shell had reinforcement rings. That great Gretsch sound. It was a mix of maple and gum.
Ludwig's were 3 ply, until 1976 ... when they went to 6 ply. 3 ply had reinforcement rings. 6 ply did not. Luddies were maple, poplar, mahogany ... or maple, poplar, maple ... on the 3 ply's.
Rogers shells (I'm sketchy, here) had thin shells with reinforcement rings, up until 1978. In 78, the XP8 shell was introduced. It was an 8 ply (the first all maple shell) stadium (no reinforcement ring) shell.
I've got no info. on Slingerland, but they followed the Ludwig/Rogers trend also.
The reinforcement ring not only added stability to the shell (help keeping in round), but was responsible for a warmer sounding tone. The bearing edges of these shells was also more rounded ... not as sharp ... as more modern designs.
It's really the sum of "several" ingredients that make vintage drums sound like vintage drums.All the companies went to the stadium shell as drummers started wanting/needing/demanding more projection from their tubs.
With the new heads available today, you can give almost any drum a warm, vintage tone. Back in the 60's/70's, there were way fewer head choices.
Also, at pretty much any period, "someone" was building 3 ply (or thin) shells with reinforcement rings.