Instead of trying to change your door, why don't you try deadening your hallway. Hang some decorative burlap on the walls. Get creative. If the hallway is big enough, a few plants might help out, too. Place a few rugs on the hallway floor. As it is, I have trouble with the idea of sound leaking out from under your doorway, especially the mids and highs. Of course, bass freq will go right through your walls.
Here are some suggestions in the order of being effective (and most likely the most costly first)
1. Change the door and frame to an outside door with a wooden threshold and insure there is good weather stripping.
2. Change the door to solid core, weather strip the entire door, add a threshold at the bottom and use one of the rubber gaskets on the bottom of the door to seal the bottom.
3. Change the door to a solid core door and weather strip,
4. Add layers of sound absorbing material to both sides of the door (this can be done to any, but will not have much benefit on solid core doors).
The other aspect to consider is that having mass and an airgap makes the best sound barrier. Studios use 2 doors with an air gap in between in critical areas. If you have a location or way of adding another door with an airgap (need only be 6 inches), you can make great strides.
Another approach could be to put a carpet runner in the hallway that extends under the door, and maybe a decorative textile hanging (with some thickness and weight to it, not a linen) on the listening room side of the door itself.
How about hanging a heavy drape over the door? Push it aside when your done.
I used sounddeadening doors. Heavy wood core with tremendous fire rating. Rubber gasketing around the frame with a base that drop seals when the door closes. Really tighten up the room. You can reach high sound levels and these can not be heard outside the room. I don't really believe treating the hall would be helpful at all.
The exterior door is the way to go. Just make sure you use a threshold with a seal.
The exterior door with seals all the way around it the way to go. No offense but I do not believe some of you have any experience with sound reduction. Drapes would to nothing for something like this. To block sound, you have to stop air transmission and that mean seals and that means mass. The heavier the door the better. Even a metal door with seals is better than an interior door without. When the door is installed, also caulk around the perimeter of the frame before you put up the trim. If you do not, your sound proofing is only as good as the thickness of the trim,which usually is not thick, that you install.
No offense taken -- the light-duty suggestions aren't supposed to hermetically seal off the room, just cut down HF reverberation a bit, in keeping with CWL's expressed wish for ideas that A) are inexpensive and B) keep the present door intact. I agree that this approach can't be of greater than middling effectiveness, but I don't think more is possible unless those two preconditions were to be removed, in which case have at it. But I can't really tell whether his main priority is alleviating a residual annoyance inside the listening room, or making the rest of the house quieter...
An exterior door is the solution on the cheap side. That is what I did for my dedicated listening room.
Lowest tech solution which doesn't require rediculous dollars to solve a simple problem - a long pillow/beanbag to lay at the foot of the door to block the air/sound flow. It could be filled with beans, etc. something not too heavy but dense enough to block sound. Any seamstress worth her salt could easily sew it for cheap using the exact dimensions necessary for your door. You can have the fun of entering "no man's land" the fabric store to pursue the proper fabric...
You could compliment this system with a rubber seal on the floor, if you wish - something economical from home building center ie. Home Despot.
There, I just saved you hundreds.
Another vote for an exterior door. I bought one with a small double-pane window so that one may see to the other side which was an important consideration for my wife. It is best solution I have found. Caulk well as mentioned above.
I am actually building a Rives designed studio right now. Though I do everything in overkill mode, I can share some light on your situation.
Yes, use solid core exterior doors. Also perimeter gaskets/seals by Pemko and Zero International should be the minimum. You can add mass by applying drywall to each side of the door with a layer of Green Glue. Communicating doors will add the air space that is needed. I am doing that to an exterior door. Doors by Overly and other's are a bit pricey. You can do just as good, or even higher STC ratings by the methods described above.
Douglas_schroeder's suggestion was going to be mine. There are also various sand-filled fabric tubes/socks that people use to keep the cold from coming under their doors that you can probably find in a Miles Kimball catalog or the like and would be quite effective, if you don't want to support your local seamstress.
Thank you everyone - wow this topic seems to be of greater interest than I expected.
Advice along the lines of the sand filled sock and the gasket is what I have been hoping to find.
I cannot change the door to this room - it is already a heavy, exterior type door with panels and moldings. Nor can I change the decoration or surfaces in the hallway.
The main issue is the gap underneath the door, and I was hoping to avoid the mechanical gap sealing device that I have seen for studio doors.
So please keep the suggestions coming and I will hope for a greater than "middling" solution for less than a middling price.
Well yeah, if that's all you can do, the first thought into my head before I posted originally was simply to stuff a bath towel up under the door and maybe install a gasket -- but after perhaps experimenting with a towel, I like Russ' sandtube suggestion as being a bit more elegant. However, for more efficacious results I still think you also need to consider treating the listening room side of the door with some kind of sound-blocking/absorbing material, which your list of prohibitions doesn't seem to rule out.
If you want to save money, why don't you just buy some weather stripping from Home Depot and a threshold? You could at least try this before spending more money on a new exterior door first. You can even make a threshold yourself and use weather stripping on the edge where the door shuts against it.
You could just try a door sweep. They are used on the bottoms of exterior doors to seal the door to the threshold. They are adjustable up and down and they are easily cut to length if necessary. If you are not familiar this link will give you an idea of what they are.
For a few bucks and 5 minutes it may be an easy remedy.