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| My first attempt at tabletweaving.  Note the curls where the cards changed direction. | 
Tablet or card weaving in a method of weaving narrow bands which  dates back at least to the second century A.D.  It was used extensively  in Scandinavia and spread throughout Medieval Europe.  Uses ranged from  the utilitarian – straps and woven borders on fabrics – to elaborate  brocaded bands used on church vestments.
The basic  procedure in tablet weaving is quite simple.  Cards, usually square, are  threaded through a series of holes placed in the corners.  The cards  are held under tension and turned while a weft thread is passed back and  forth.  The manner of threading and sequence of turning create the  pattern.  Incredibly complex and intricate patterns can be achieved with  this basic technique.
While the basic procedure is  quite simple, learning to table weave can present some challenges and  frustrations.  Foremost among these is tensioning.  My first band was  woven using the warping peg from my rigid heddle loom attached to a  small portable ironing board, which I was able to hold in my lap, which  one end propped on a TV tray table.  It is possible to table weave using  a back-strap loom, however I found it far easier to put my work down  and maintain even tension when returning to it using a more fixed  system.  I have since built a portable loom of my own design which meets  my needs quite well, and will build a period-correct loom in the future  as part of this challenge.
Warping cards can also  present challenges to a beginning weaver attempting to learn on their  own.  A number of books and websites discuss the continuous warping  method, which is infinitely easier than warping each card individually  (though not always appropriate), but regardless of your chosen warping  technique two fixed points are absolutely required to keep the warp  threads from tangling and to keep them even.  Currently, I use a warping  peg and a doorknob to warp my cards, which works well only so long as I  do not need to open the door.  As some point I will need to get or  build a proper warping board.
The weaving itself is  fairly straightforward.  Again, tension seemed to be the main challenge,  both in keeping the warps even and tights, and in keeping the weft  even.  Maintaining a consistent band width and a smooth surface took  some practice, but by the time I had completed my first practice band I  was able to do both fairly consistently and more on to more complicated  patterns.   It does help to use some kind of measuring device to check  your band width now and again, particularly  when using softer fibers  like silk or cotton.
Sources:
Crocket, Candace.  
Card Weaving.  Interweave Press, 1991.
Lewins, Shelagh.  The Ancient Craft of Tablet Weaving:  Getting Started (
http://www.shelaghlewins.com/tablet_weaving/TW01/TW01.htm)  Last accessed Nov. 18, 2010.
Gaslee, Sarah.  Basic Tabletweaving.  (
http://www.stringpage.com/tw/basictw.html) Last accessed Nov. 18, 2010.