Re: The Buddy Rich sound
A few prerequisites...
Buddy used drums made differently than they're made today. (fewer, thicker plies, and usually maple) Also, the vintage drums I've played (like "Radio Kings") have slightly larger diameters, so there's less of that modern "ka-wang!" overly-resonant sound. He used white coated Remo "Diplomat" heads mostly. To my ears, almost any drum set sounds a lot better in a big concert hall. (where we typically heard Buddy) Buddy typically carried a piece of 1/2" plywood with the band, on which the drums were always set up. (no carpet) And of course, his awesome technique made the biggest difference in the sound. But anyway...
i've heard Buddy play drums tensioned in a variety of ways, and have even followed equipment trucks back to the music store, when a local store provided drums for certain concerts, and tapped on them myself, using a pitch pipe as a reference. I would say that this was a waste of time. Buddy was a "normal" drummer, in that he didn't spend hours sitting at the set with a drum key in his hand. If the drums sounded "good", or even "ok", Buddy could kick a band and thrill us with the sound. He may have been a little more finicky during recording dates, but I can't even guarantee that, since the drums vary (quite a bit, sometimes) from one album to another.
Buddy typically tensioned his drums a little tighter than most people would think. Using pitch as an example for the top head tension: snare: a to c - (bottom head about a 4th to a 6th higher, say E to F# - (Toms, both heads the same) 9X13: d - 16X16(1) g - 16X16(2) c - Bass drum: a to c
Important...
Buddy often did not touch the drums for long periods of time. So, especially using "Diplomat" heads, the top head pitch would naturally go down, over time. There are recordings of Buddy where the drums are obviously loose, but still tensioned to about the same (5th) intervals. The pitch is NOT important... In fact, I'd say that you really don't want the pitch to be heard, because it can interfere with the music. It's just a combination of high, medium, and low tones, brought to life by a drummer who really knew how to play emotionally.