I am aware of a debate about whether or not the first knot is necessary, it seems to be connected with whether or not more strings can be used. I don’t understand this, can you clarify? Also, concerning Techelet, since there isn’t a set method to the tying with Techelet, I ended up devising my own method, and I would like to be informed of any issues that there might be with this method If the first knot is necessary, then; double knot 10 turns double knot 11 turns double knot 9 turns double knot 13 turns double knot 26 turns using Rambam knot If the first knot is not needed, then; 10 turns using Rambam knot double knot 11 turns double knot 9 turns double knot 13 turns double knot 26 turns double knot In both cases, 5 knots and 8 string ends The number of turns comes up to 69, which is the same number of words in the commandment in Bamidbar.
Upper Knot: In tractate Menachot (39a) Rava said that the Upper knot is a Torah obligation. The Rishonim (leading Rabbis who lived approximately during the 11th to 15th centuries) disagree on the location of this Upper knot. Some say it is right near the corner of the garment (פירוש שני ברש"י המובא בתוד"ה קשר העליון). There is another opinion that it is the lowest knot at the end of the links (the part where the strings are wound around between two double knots), because one who ties only one knot does it at the end of the wound strings in order to prevent it from unraveling (רש"י ד"ה קשר עליון ובב"י סימן יא סעיף יד). There is yet a third opinion that it is the knot after the first link (רמב"ם הלכות ציצית פ"א ה"ז ובב"י שם). In practice, according to our custom - we tie five knots, one near the corner of the garment, one at the end, and a knot between all the links - we take into account all opinions. The Mishnah Berurah writes that even on Erev Shabbat (Friday) near darkness, although one can rely on the letter of the law that it is enough to have one link of three turns with a double knot at its end, it is better that he should also tie the first knot which comes before the first link as we are accustomed, in order to fulfill the Mitzvah according to the opinion of some authorities who hold that this is the knot our Sages were referring to as the one that is a Torah obligation. (שו"ע או"ח סימן יא סעיפים יג-יד ובמ"ב ס"ק סו). Adding Strings: There is a disagreement among the Rishonim whether one who adds additional strings to the Tzitzit is transgressing the prohibition of Bal Tosif (don’t add more Mitzvot or more details to a Mitzvah) or that it is permitted to add as many strings as he wants and he does not transgress Bal Tosif unless he adds strings of a different type. The Shulchan Aruch rules that if one added strings even from the same type it is invalid. The Mishnah Berurah quotes the Gra who agrees with the Itur that it is permitted to add as many strings as he wants as long as they are from the same type. The Mishnah Berurah adds that the Artzot Hachaim quotes another few great Rishonim who agree to this, therefore he concludes that if he completed making the Tzitzit already and cannot fix it, he can wear it but he should fix it at his earliest convenience (שו"ע או"ח סימן יא סעיף יב ומ"ב ס"ק ס). Techelet Nowadays: I would like to note that according to most of the great Halachic authorities Techelet (Biblical blue dye for Tzitzit) should not be used nowadays, as we have no tradition on this issue, and it may mislead and cause error to future generations who will think that there always was a tradition on this, and for other reasons as well. (ערוה"ש סימן ט סעיף יב, קובץ תשובות להגרי"ש אלישיב סימן ב, תשובות והנהגות ח"א סימן כט וח"ד סימן ה, אאמו"ר שליט"א בשם מורו ורבו הגרח"פ שיינברג שליט"א שאין להשתמש בתכלת משום שזה עלול לגרום לטעות לדורות הבאים כאילו יש בזה מסורת ויביא לידי מכשול, וע"ע מראי מקומות נוספים בפסקי תשובות סימן ח הערה 2). Method of Tying Tzitzit Nowadays: Nowadays that we do not have Techelet, the following is the method of tying Tzitzit according to the Ashkenazi custom: You thread four strings through the hole in the corner of the Tzitzit garment, while one of the four strings is longer then the rest. Then we have eight strings, four on each side. Take the four strings from each side and tie them over each other twice (a double knot). Wind the long string around the others seven times and tie again twice. Turn the long string around the others eight times and tie again twice. Turn the long string around the others eleven times and tie again twice. Turn the long string around the others thirteen times and tie again twice. In summary we have five double knots with the Tzitzit wrapped around between them according to the following numbers 7 8 11 13. The same should be done to all four corners. The meaning of the numbers is as follows: 7 & 8 stand for the sacred Name of Yud & Hey. Then 11 which combined with the above stands for the sacred Name of Havayah. Afterwards 13, which is the Gematria (assignment of numeric values to Hebrew letters) of the word Echad (one). All these together stand for the words “Hashem is one”. (שו"ע או"ח סימן יא סעיף יד, ומ"ב ס"ק ע). There are clear instructions in the Talmud and Poskim regarding the custom of tying Tzitzit in the days that we had Techelet. Number of Techelet Strings: There is a disagreement among the Rishonim whether at the time when Techelet was used, one had to put two white strings and two Techelet strings, or one Techelet and three white(ערוה"ש סימן ט סעיף ב) . The Mishnah Berurah (9, 7) quotes the Taz that in the times when there was Techelet one had to put two white strings and two Techelet strings. And so does the Aruch Hashulchan (שם) decide L’halachah. Method of Tying the Tzitzit: At the time when Techelet was used they would do seven links. Starting and ending with white. Three turns are considered a link. They would turn a white link and a Techelet link and tie. Then repeat and turn white and Techelet and tie. The same was done the third time. And at the fourth time he would turn with white only and tie. The reason for making seven links is compared to seven heavens in memory of Techelet that resembles the sea and the sea resembles heaven. (מנחות לט. טור וב"י סימן יא סעיף יד, פרישה ס"ק יט ודרישה ס"ק ד). The number of turns, links and knots is not an absolute requirement; it is just the most desirable way to fulfill the Mitzvah. (שו"ע או"ח סימן יא סעיף יד, ומ"ב ס"ק סה). Comments on Your Method: Here are some comments about the Tzitzit tying method you devised, although, as we have noted it is only for the most desirable way to fulfill the Mitzvah but according to the letter of the law what you are doing is permitted. 1. According to the opinion at the end of Tosfot in tractate Menachot (ד"ה לא יפחות דף לט.) explaining the Gemara, one should not do less than seven turns or add more then thirteen turns between the knots. Seven compared to seven heavens and thirteen compared to seven heavens and the six spaces between them. In the method you devised there are twenty six turns before the last knot. 2. The Mishnah Berurah (שם ס"ק סח) quotes the Magen Avraham who brings the Rosh who says that all the links should be equal because that is the ornamentation of Tzitzit. Therefore in the first space (link) he should make the turns far from each other and afterwards in every space closer. And in your method there is a big difference between the number of turns, so it is not equal and it spoils the ornamentation of the Tzitzit. 3. According to rabbinical law a third of the Tzitzit strings have to be wound around and two thirds hanging strings (מ"ב שם ס"ק סו). And according to your method it is necessary to ensure that this ratio is actually kept.