According to Torah law, there is no requirement for tzitzit to have 7-8-11-13 windings. The Torah says you must have one knot and one chulyah. There is a dispute in the poskim as the whether the knot comes before the chulyah or after, so we do both. The Mishnah Brurah explains that if you tie on double knot, wrap a few windings around (at least three) and tie a second double knot, you have fulfilled the mitzvah according to Torah law. He says this is what one should do if he finds himself stuck without tzitzit a short time before Shabbos begins. He then goes on to explain that there is also a requirement according to Rabbinical law to tie the tzitzit in such a way that you have one-third anaf (tied) and two-thirds ptil (loose).
Therefore when the Shulchan Aruch (11, 14) explains how to go about tying tzitzit, it makes no mention of how many windings there should be, and in fact writes that there is no set number of windings.
ואחר-כך יכררך חוט הארך סביב השבעה קצת כריכות וקושר שני פעמים זה על גב זה, וחוזר
וכורך; וכן יעשה עד שישלים לחמש קשרים כפולים וארבעה עוירים ביניהם מלאים כריכות.
אין שעור לכריכות רק שיהיו כל הכרוך והקשרים רחב ארבעה גודלים והענף שמונה גודלים
In fact we normally leave the tzitzit we tie for our customers one-fourth/three-fourths, because I believe if they saw one-third/two-thirds many would be somewhat alarmed and possibly disappointed. In the yeshiva world today, you often see students sporting very long tzitzit. I imagine many of them think this is very pious, when in fact it is actually a leniency.
It’s very difficult to get the windings exactly 7, exactly 8, etc. We try our best to do it within half a winding. If you are not experienced at tzitzit tying, this may be hard to discern. If you look at the tzitzit on one side, you may count 7 windings in the first section, but when you flip it around to the opposite side there are 6 or 8 windings, because there may be six-and-a-half or seven-and-a-half. (The way to count accurately is to note careful where the winding starts, note where the final winding ends and compare the location.)
Rabbi Mois Navon of the Ptil Tekhelet Association speaks of this issue as well. “The truth is that it is very difficult to get precisely three full winds when coming out of a double knot or going into a double knot,” he writes. He then argues that “the Gemara’s requirement that a chulya be 3 winds is a directive for action to be taken by the person wrapping and not necessarily a statement on how the final product is to appear. That is to say, the tier is required to wrap the shamash around the core strings three times, this may however result in a chulya looking like two-and-a-half wraps or even three-and-a-half, depending on where the string started or ended.”