My son and I were looking at the Tosafot tying photos from your detailed tying instructions; and forgive me for saying so, but it looks a little sloppy. Is this the way we should expect it to come out, or could it come out looking neater? I'd really like to get the Tosafot tying method, however, some of the other methods are much prettier to look at.
As you saw from the web pictures, the Tosafot tying method comes out the way it is shown. I am sorry if you don’t find it particularly attractive. If you read the Tosafot source (see “In his own words” in the tekhelet tying tools page) you will understand that this is the intended outcome.
Now, some other factors to consider when determining which method you would like to use to tie are: (1) Beauty (“Noy”) – there is an issue in tzitzit that they should be aesthetically pleasing; (2) All the various tying methods fulfill the Torah (d’oraita) requirements for tzitzit. So basically, what I am saying is that you could choose a different method for tying, while still using the 2 full strings of blue (which is what Tosafot held).
Another alternative is to tie like Tosafot but to always keep the blue together and the white together (as opposed to the way it is usually done, where the white and blue strands are mixed together). What this means is that when you are tying, you take the two blue halves from one side and hold them together with the two blue halves on the opposite side of the begged (similarly for the white), and then you begin tying. You can see pictures of how to tie this method at: http://www.tekhelet.net/diagrams/IturBlueWhiteMethod/page1.htm
I found this looks really quite nice, and would recommend doing this, if you are using Tosafot number of strings.
– Mois Navon.