I realize that there are many people already who repair their rolls and
use archival tape to do it with.  Nothing wrong with that at all.  It's
the best tape to use.  However, I thought I might mention a few things
that you can do with either Scotch "Magic" (frosty) tape or archival
tape.

The two biggest problems with Scotch tape is thickness buildup on the
roll, and adhesive bleedout along the edges of the tape, and sometimes
in a line across the outer surface of the tape, too.  Here is a good
way to take care of both problems.

For most tears, you don't use longs strips of tape, but short ones.
You never put tape on the underside of a roll except at the leader,
always on the top.  But before you apply any tape at all, lay a 6"
length of tape down on a piece of exposed cutting board surface,
like a rotary cutting mat, and using a ruler, make a series of slices
through the tape with a #11 scalpel blade or Xacto knife, about 1/8"
apart, giving yourself thin tape strips that measure 1/8" wide and 6"
long.  In many cases, I will also cut another strip of tape into 1/16"
strips.  Do that on a dark mat so you can see your pieces well.  They
come in blue and grey and green, to my knowledge.  With the thinnest
ones, you can make little "stitches" across chain bridging tears and
the like.

The second trick, if you will, is to always talcum your repairs.
I don't mean to inundate the area, but a little makeup brush that will
lightly dust the talcum powder is plenty.  It coats any edge adhesive
and prevents adhesive bleed, which could, after awhile, stick
successive layers on the roll together and tear the roll up.

The advantage of making thin tapes strips should be clear: the tape
buildup has less to do with tape thickness and more to do with overall
amount of tape, added up between the layers of paper.  And when you
stitch the paper together, you aren't fully fixing 100% of the tears,
but you don't need to.  The stitches are stronger than the paper and
will hold for many years.

There are many little tricks you can use to fix the really terrible
rolls, but regardless how bad they are, if you begin with these tips
and use them on any roll you repair, it will always work better and
your repairs will be almost invisible.

The most important thing about a roll is the width and trueness of the
two edges.  When you are trimming what used to be a long, torn edge and
you have restored it with new blank roll paper, getting an exact edge
will be a problem unless you are very careful with how you cut.  So you
have to leave enough of the original edge to parallel-cut to, even if
it means shortening your new paper edge at intervals not exceeding the
length of the roll repair table or surface and the straightedge you are
cutting with (using just simple tools one would have around the house
with the roll repair table.)

Craig Brougher