Accuracy in paper folding

No matter how carefully I matched edges, I was finding that the folded paper ended up like this -

or this -

Thanks to friends and the internet - and considerable practice - the situation is resolved. The trick? - making a template (a very accurate template, everything measured before and after cutting) and using it (aligned very carefully) to score the paper, folding the paper, and then using the template to score the next fold. Like this, where I'm about to make the third of three folds -

It's better to use a bone folder for scoring, than the blunt side of the knife ... it's all to easy to forget to check that it's actually the blunt side you're using!

I needed to fold my paper into 6.5cm wide sections, so made the template 13cm wide. That left a little extra (needed for gluing sections together). Once the three folds were made, I turned the paper over and brought the free edge up to the final fold - effectively folding the middle section in half. After that, it's easy to fold the other two sections in half too (separately!). Align the middle of the fold rather than one of the corners, but try to hold the edges steady as you make the crease - from the centre, with the bone folder.

My paper is "just" typing paper but it's been painted on one side with household emulsion and on the other with ink and wax, so its floppy character has changed somewhat, and those coatings made it a bit brittle. Perhaps because it was inexpensive paper out of a packet, it wasn't cut completely square - one of the reasons for the inaccuracies in the photos.

Some tips for accurate folding:
1. Check that the paper is cut accurately - compare the two ends.
2. Paper should be grain short (grain runs along the folds).
3. The first fold will guide other folds, so must be lined up precisely.
4. Fold one thickness at a time.

Scoring boards can be useful - but again, the paper must be aligned carefully and accurately.

Some videos here may be helpful with folding into 16 equal sections, and folding accordion pleats - and further videos are here; all are from a book called Folding Techniques for Designers, by Paul Jackson.

A commercial bindery advises:

Fold with the Paper Grain: Many folding issues can be traced to a layout that failed to consider the impact of wrong paper grain direction. Layout your projects so the most obvious outside folds are parallel with the paper grain direction. This is especially important if your project includes heavy, dark ink coverage, or is printed on a thicker stock brittle stock.
Eliminate Paper Stress: Folding projects that are poorly planned can create paper stress during right-angle folding and this can be a huge problem. The structure of paper is such that it is stronger under tension than under compression. When poorly designed folding sequences cause two panels to "fight," the top one under tension always wins, while the bottom one under compression always wrinkles.
Watch for Cracking: Paper fibers can break during folding, resulting in cracking which usually occurs on the first fold. Choosing proper fold plates, machines, and production techniques helps eliminate some of these problems.
Beware of Brittle Inks: Inks tend to be brittle and may crack when bent, exposing raw paper fibers underneath. The problem may be corrected by choosing fold plates and folding machines to minimize paper stress, or by adding moisture to the surface, which is known as a wet score. Sometimes simply slowing down the folder will do the trick too.

And here's a link to info on how to divide any size of paper into any number of folds - the general principle involves going from the approximate to the accurate - cutoutfoldup.com/411-fold-a-strip-of-paper-into-approximate-n-ths.php

Again slightly tangential, this TED talk asks if folding paper can take you to the moon - or rather, how many folds would it take to get to the moon - http://ed.ted.com/lessons/how-folding-paper-can-get-you-to-the-moon (check out the rest of the series too - one is about hyperbolic crochet).