Recently, I have had hard deposits coming off of the back of my bottom
front teeth. They are an off-white/yellow colour, often with a black
mark that looks a little like the back of fish scales on one side.
They break in two with only a small amount of pressure from a
fingernail. Once these deposits come off, the tooth is fairly smooth,
except for occasional, tiny jagged pieces sticking out (that seem to
be deposits themselves). The gum beneath these deposits seems to be
recessed. When the deposit comes off, gum is quite soft for a few
days, then hardens as normal.

Are these deposits likely to be tartar, or pieces of teeth that have
broken off? Is the gum recession likely due to the presence of tartar,
or is the 'recess' more likely to simply be the gap the piece of tooth
used to fill?

No more details please! I think it is tartar, but that isn't important.
Just bite your teeth and get a dental hygienist to clean them.  He or
she will probably tell you what you already know, that you should have
been there a long time ago, and that the gums are a problem.  But it
will all get worse the longer you wait, and it may not be that bad
yet, and won't be really painful.
Just do it.

its tartar...