Hi Steve,  When sound hits a wall (or floor or ceiling) one of three
things can happen: (1) the sound can pass through the wall and into
the adjacent space; (2) the sound can reflect off the wall like a pool
cue (it will reflect off at the same angle that it hit the wall, but
in the opposite direction); (3) the sound can be absorbed by the wall
and its energy converted to an extremely small amount of heat.

The high frequencies and the low frequencies and every frequency in
between will behave differently.  The high notes may be reflected and
the low notes may pass through.

Let's assume for a moment that the sound definitely reflects (similar
to a concrete wall in acoustic character even though your wall is not)
and we are talking about low frequency bass notes.  We will get twice
"as much" bass from setting the music box on the floor as opposed to
floating it in mid air.  This is because the some of the low note will
reflect off the floor and add back into the sound already headed toward
your ears.  The two sine waves add together and get twice as tall in
pressure (but only for the bass notes).

If you take this a step further and place the box at the edge of
both the wall and the floor, another reflected wave adds in and you
get more bass.  If you take this one step even further and place the
box in the corner between a two walls and the floor, another reflected
wave adds in and you get yet even more bass.

So if you move your box to a corner and don't notice more bass, it
is most likely the sound is going through the wall and not getting
reflected back.  You can also confirm this by listening to see if you
can hear it on the other side of the wall.  This is the case where
adding a marble slab may help you punch up the bass.

Reflections from the walls can also kill your bass for certain notes.
If you have the box sitting out away from the wall, there will be a
note's wave that reflects off the wall and comes back out of phase with
the wave already head toward your ear and will completely cancel it
out.

Changing the distance from the wall will change the note that gets
cancelled out.  You could try putting the box up against the wall and
slide it side to side in different positions.  You may also be getting
a reflection off the side walls that will change depending on
horizontal position along the wall.

A third thing that happens is that rooms themselves have resonances
as if the room shape were one large organ pipe wanting to sound a
particular note.  The notes that your room wants to sound depend on
the ratio of the height to the width to the length of the room.
Certain ratios will produce nicer patterns of room modes and others
will create less pleasant ones.

While you can't change the dimensions of your room, changing the
position of the box and changing the position of your ears could
produce very different listening experiences.  Room modes, as these
room notes are called, are really loud at some places in the room and
almost silent in others.  Having room modes at all depends that the
sound is reflecting off the walls and not going through the walls.

What about the wall _absorbing_ the sound?  In order for the wall to
absorb the sound without it passing through, it must be at least as
thick as 1/4 the wavelength of the note being absorbed.  Middle A (440
Hz) is 3/4 meter long, so the wall would have to be 0.20 meter thick to
have any chance at absorbing it and the bass notes would be impossible
to absorb for any normal wall.

This means the only effect the carpet has is to make the room less
bright.  The carpet is absorbing sounds in the range of the sizzle of
a cymbal crash and is deadening the upper harmonics of any lower notes.
Bass notes are so physically large they pass right through carpet as if
they never saw it in their way.

Perception, however, is a psychological thing and a less bright room
could give you less of a sense of envelopment and energy that isn't as
enjoyable.  But, you specifically said bass, so I'm mostly writing
about low frequency behavior.

Regarding the reader's comment about the floor being a sound board,
this may very well be the case that the floor of the old room was
physically coupling and resonating along with certain notes in a way
that was pleasant.  You could somewhat test this putting the box back
in the old room and isolating it from the floor with some stacked
folded blankets where the vibrations cannot get through to the floor
and seeing how it sounds.  No change means the floor probably isn't
helping you.

It is possible the floor is sympathetically resonating with some notes
without being directly coupled, but highly unlikely.  It is especially
unlikely that the old floor is resonating with the bass since it would
need to have quite a bit of freedom in its structure to flex in order
to do that.

I would advise against intentionally designing a resonating board for
the new space without consulting a music instrument maker.  The design
of a sound board that couples well and resonates evenly across all
notes is a delicate art.

Best regards,
Dave Theis