The advice about tuning to the resonant note is sound but once you put the head and hoops and screws on, the over and undertones that can accompany those parts can become dominant. Always a fine tuning to accomodate the completeness of the package is required and then again and again, until it feels right.. Each drum you play will become a unique system and tuning will end up being second nature until you change heads and then it starts over but will take less time.
There will always be a debate about the character of bass drums. It revolves around boom or thud.I don't think setting a hard and fast rule about having damping rings makes sense because not all drummers want that degree of damping and some drums don't need it. If one wants an open toned drum, stay away from heavy,double, or heads with damping rings.
I'm a big fan of having mufflers on all heads, except of course the snare side.. Nothing will give you more latitude of sound and control over the sound of your drums. Up until about 1970, most well made drums came with at least one muffler but that design parameter quickly diminished until most drums came out with no mufflers..... Now, I think the original idea was to save money and offer a muffler as an option but there evolved this myth, that mufflers were bad in a drum , that they rattled or produced unwanted overtones and by the 90's, scores of used drums had them removed-----and there developed a vogue , in rock at least, for big open toned unrefined drumming, a la, John Bonham.
I have spent a considerable amount of time and effort , finding original mufflers and putting them back in drums. They become beautiful flexible musical instruments again. A little mechanical tightening and some heavy grease and the supposed tonal defects are what they are----a myth.
Trixon was unique, in that, up until the late 60's ,each drum had two mufflers and almost every bass drum came out with a huge rectangular muffler inside the front head and an adjustable strap muffler(so-called Pratt muffler) on the batter head and snares had an adjustable under the batter head and a flip on as well(i think some Ludwigs were that way too).You can use any head you want on a Trixon bass drum; you could probably use a yard litter bag and you could quickly tweak it to give a deep thud, that will flatten the carpet, a light boom ,a resonant boom or knock the curtains off the windows if you like.By adjusting the mufflers and the degree of openness of the beater stroke, you can attain boomy or thuddy notes with the same tuning. Trixon bass drums are the ultimate in kit bass drums, I have found non to equal them ---perhaps a Gretsch fitted also with a Pratt muffler can but unmuffled drums are totally coloured by the head and tuning, singly muffled drums less so. Heads with damping rings , really shouldn't exist. They came into being because the drums they were being fitted on were inadequate. It's a little like using a bent nail to keep a door closed because the latch is broken.
That said, I have recommended them as a remedial measure-----better than a blanket , I guess.