Tying Tzitzit with Tekhelet

The Mitzvah of Tzitzit and Tekhelet in the Torah

(לח) דַּבֵּ֞ר אֶל־בְּנֵ֤י יִשְׂרָאֵל֙ וְאָמַרְתָּ֣ אֲלֵהֶ֔ם וְעָשׂ֨וּ לָהֶ֥ם צִיצִ֛ת עַל־כַּנְפֵ֥י בִגְדֵיהֶ֖ם לְדֹרֹתָ֑ם וְנָ֥תְנ֛וּ עַל־צִיצִ֥ת הַכָּנָ֖ף פְּתִ֥יל תְּכֵֽלֶת׃ (לט) וְהָיָ֣ה לָכֶם֮ לְצִיצִת֒ וּרְאִיתֶ֣ם אֹת֗וֹ וּזְכַרְתֶּם֙ אֶת־כׇּל־מִצְוֺ֣ת ה’ וַעֲשִׂיתֶ֖ם אֹתָ֑ם וְלֹֽא־תָת֜וּרוּ אַחֲרֵ֤י לְבַבְכֶם֙ וְאַחֲרֵ֣י עֵֽינֵיכֶ֔ם אֲשֶׁר־אַתֶּ֥ם זֹנִ֖ים אַחֲרֵיהֶֽם׃ (מ) לְמַ֣עַן תִּזְכְּר֔וּ וַעֲשִׂיתֶ֖ם אֶת־כׇּל־מִצְוֺתָ֑י וִהְיִיתֶ֥ם קְדֹשִׁ֖ים לֵאלֹֽהֵיכֶֽם׃ (במדבר טו)

(38) Speak to the children of Israel, and bid them that they make them fringes (tzitzit) on the corners of their garments throughout their generations, and that they put upon the tzitzit of each corner a thread of Tekhelet. (39) That shall be your tzitzit; and you shall look at it and recall all the commandments of the Hashem and observe them, so that you do not follow your heart and eyes in your lustful urge. (40) Thus you shall be reminded to observe all My commandments and to be holy to your G-d. (Bamidbar 15)

(יב) גְּדִלִ֖ים תַּעֲשֶׂה־לָּ֑ךְ עַל־אַרְבַּ֛ע כַּנְפ֥וֹת כְּסוּתְךָ֖ אֲשֶׁ֥ר תְּכַסֶּה־בָּֽהּ: (דברים כב)

(12) You shall make tassels (gedilim) on the four corners of the garment with which you cover yourself. (Devarim 22)

Principles Regarding Tying Tzitzit with Tekhelet

The number of Tekhelet strings on each corner

There are three opinions among the Rishonim with respect to the ratio of white strings to Tekhelet strings:

Rambam Half of one string (when folded becomes one of the eight strings) is Tekhelet. The Rambam understands the pasuk in Bemidbar in the following manner: put upon the fringe of each corner (= white) one thread of Tekhelet. Only the windings (ptil) around the white core (k’naf) must be Tekhelet (Hilchot Tzitzit 1;6)
Raavad and the Aruch, based on the Sifre in Shelach hold that one full string (when folded becomes two of the eight strings) must be Tekhelet (Hasagot, Hilchot Tzitzit 1;6)
Tosafot-Rashi Two full strings (when folded becomes four of the eight strings) must be Tekhelet (Menachot 39a and 41b “Bet Shammai”)

Issues regarding the windings (krichot)

Chulyot (links)

וכמה שיעור חוליא? תניא ,רבי אומר כדי שיכרוך וישנה וישלש, תאנא הפוחת לא יפחות משבע, והמוסיף לא יוסיף על שלוש עשרה. הפוחת לא יפחות משבע – כנגד שבעה רקיעים, והמוסיף לא יוסיף על שלש עשרה – כנגד שבעה רקיעין וששה אוירין שביניהם. (מנחות ל”ט ע"א)

And what is the measurement of a chulya (link)? We learned in a Braita, Rebbe says so that you can wind once, then again, and a third time. We learned in a Braita, one who minimizes should not have less than seven, and one who maximizes should not exceed thirteen. One who minimizes should not have less than seven – this is analogous to the seven heavens, and one who maximizes should not exceed thirteen – this is analogous to the seven heavens and six spaces between them. (Menachot 39a)

According to the Gemara, when tying tzitzit, there is a concept of chulyot (literally, links or vertebrae). There is an argument as to what the numbers seven and thirteen refer. Most Rishonim explain that these numbers refer to the amount of chulyot (each of which is made up of three twists as Rebbe states). Some Rishonim explain that each chulya can have between seven and thirteen twists, and they explain Rebbe’s three twists as referring either to the number of Tekhelet twists in each chulya (and the number seven includes both the white and the Tekhelet), or that Rebbe is talking about the absolute minimum required to fulfill the mitzva (bedieved deorayta), but the best method (lechatchila derabanan) should have between seven and thirteen twists.

Color of Twists

תנא, כשהוא מתחיל, מתחיל בלבן – ‘הכנף’, מין כנף; וכשהוא מסיים, מסיים בלבן – מעלין בקודש ולא מורידין. (מנחות ל”ט ע"א)

We learned in the Mishna, when one begins, he begins with white – “[the fringe of each] corner,” the same kind as the corner [i.e. the same color as the garment]; And when one concludes, he concludes with white – one always increases holiness and never decreases. (Menachot 39a)

There is an argument as to the explanation of this passage:

Rav Amram Gaon holds that the first chulya is white, the next is Tekhelet, and so on alternating white and Tekhelet for seven or thirteen chulyot. These chulyot of alternating colors are termed l’sayrugin.
Rambam holds that the first twist of the first chulya and the last twist of the last chulya are white, and all the other twists are Tekhelet.
Raavad holds that the twists of each chulya alternate between white and Tekhelet.

The knots

Kesher Elyon

ואמר רבה שמע מינה קשר עליון דאורייתא (מנחות ל”ט ע"א)

Rabbah says, this implies that the upper most knot is required from the Torah.(Menachot 39a)

Rashi (מנחות לט. ותוספות שם) brings down two possibilities regarding the placement of the uppermost knot:

Closest to the garment, in order to connect the strings to the garment
At the end of all the twists, which adds stability to the windings

Double or single knots

There is an argument as to the nature of the knots of the tzitzit. The Geonim (331 'גאוניקה ח”ב עמ) hold that a knot can be one string tucked under itself. Rabbenu Tam (מנחות לט. ד”ה לא) compares the knots of tzitzit to knots in other laws like Shabbat, and therefore requires a double knot. According to Rabbenu Chananel, the knot is made by looping one string around the rest, whereas The Mordechai holds that all the strings are used (by looping four around the other four).

Knots on each chulya

אמר רבא שמע מינה צריך לקשור על כל חוליא וחוליא (מנחות ל”ח ע"ב)

Ravah says, this implies that one must tie a knot after each and every chulya. (Menachot 38b)

Five knots

ציצית‚ שש מאות. שמונה חוטין וחמישה קשרים‚ הרי שש מאות ושלש עשרה.(תנחומא, קרח י”ב)

[The word] tzitzit is numerically equivalent to 600. 8 strings and 5 knots add up to 613. (Tanchuma, Korach 12)

The ratio of twists to strings

אמר רב הונא אמר רב ששת אמר רב ירמיה בר אבא אמר רב… ונויי תכלת שליש גדיל ושני שלישי ענף. (מנחות לט ע"א)

Rav Huna said in the name of Rav Sheshes in the name of Rav Yirmiyah bar Abba in the name of Rav: The most ornate Tekhelet ought be one third windings and two thirds hanging threads. (Menachot 39a)