My tzitzit are tied according to the standard method used for tying white tzitzit with 5 knots and 7-8-11-13 wraps between knots. Are my tzitzit kosher or pasul?

The 7-8-11-13 method is a custom to be used when using white strings only. This
method is not really dealt with on our website because no one discusses tying like this
with tekhelet. Indeed, R. Shachter believes this method was designed to make up for the
fact that no tekhelet was available.

Furthermore, even if one wants to tie like this, he should really have one white wrap at
the top and one white wrap at the bottom (as shown at the bottom of our tying tools page:
https://www.tekhelet.net/diagrams/TyingDiagramSeriesHomePage.htm). This is of
critical importance because the gemara (Men. 39a) states explicitly that one must start
and end with the color of the kanaf.

Regarding the validity of the tzitzit if one has already tied his tzitzit 7-8-11-13, without
the white wraps at the beginning and end – the question is not a simple one. The gemara
derives the rule that one must start with the color of the kanaf from the pasuk “venatnu al
tzitzit hakanaf” the tzitzit (non-tekhelet strings) are to be like the kanaf. Clearly there is a
derabannan requirement to do it properly, but if the gemara is saying that the requirement
comes from the pasuk, then perhaps this is a d’oraita requirement. After quite a bit of
research, I have found one source which specifically addresses your question: Shita
Mekubetzet (Men. 38a, #3) explains that it is a “mitzvah” to start with white, however
starting with tekhelet does not “me’akev”. So this is a heter, however be aware that this
is a rather “novel” approach to the gemara in which the pshat seems to be talking about
whether one needs to “insert” the white into the hole before the tekhelet or not.

– Mois Navon.