שיטות שונות לקשירת גדיל הציצית במקום שיש פתיל תכלת

ByHillel Schwab

א. מספר חוטי תכלת

משנה תורה, הלכות ציצית א׳:ו׳

ויהיה אחד משמונה החוטים חוט תכלת והשבעה לבנים:

Mishneh Torah, Fringes 1:6

(6) How are the fringes attached? One begins at the corner of the garment, that is, at the edge of the woven cloth, and measures off a length not greater than three finger-breadths and not less than the length between the base of the thumbnail and the first joint. Four threads are inserted there and turned down in the middle, so that eight twined threads are pendent from the corner, The eight threads are not to be less than four finger-breadths long. If longer, even as much as one or two cubits, they are fit for use. The breadth of the thumb is the standard for all finger-breadths. One of the eight threads should be blue, and seven should be white.

השגות הראב"ד על משנה תורה, הלכות ציצית א׳:ו׳

ֿויהיה אחד משמונה החוטין חוט תכלת והשבעה לבנים. כתב הראב''ד ז''ל טעות הוא זה אלא השנים של תכלת והששה לבנים עכ''ל:

Hasagot HaRa'avad on Mishneh Torah, Fringes 1:6

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תוספות על מנחות ל״ח א

מתני' התכלת אינה מעכבת את הלבן. מצוה לתת ב' חוטין תכלת וב' חוטין לבן בציצית...

Tosafot on Menachot 38a

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https://www.tekhelet.com/tzitzit-tying-questions-2/

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ב. שיעור וצבע החוליות

מנחות ל״ט

רב חייא בריה דרב נתן מתני הכי אמר רב הונא אמר רב ששת אמר רב ירמיה בר אבא אמר רב תכלת שכרך רובה כשרה ואפילו לא כרך בה אלא חוליא אחת כשרה ונויי תכלת שליש גדיל ושני שלישי ענף

וכמה שיעור חוליא תניא רבי אומר כדי שיכרוך וישנה וישלש תאנא הפוחת לא יפחות משבע והמוסיף לא יוסיף על שלש עשרה הפוחת לא יפחות משבע כנגד שבעה רקיעים והמוסיף לא יוסיף על שלש עשרה כנגד שבעה רקיעין וששה אוירין שביניהם

תנא כשהוא מתחיל מתחיל בלבן הכנף מין כנף וכשהוא מסיים מסיים בלבן מעלין בקודש ולא מורידין

Menachot 39

The Gemara rejects this proof: Perhaps the sons of Rabbi Ḥiyya were referring to a case where one tied knots between the sets of windings even though there is no obligation to do so. And Rabba says: Learn from it that the uppermost knot in the ritual fringes is required by Torah law. As, if it enters your mind to say that it is by rabbinic law, whereas by Torah law it is sufficient to merely insert the strings into the hole without tying any knots, for what reason was it necessary for the Torah to permit placing wool ritual fringes on a linen cloak? It is obvious that it is permitted, since if one attaches a swatch of wool and a swatch of linen with a single connection, it is not considered a connection with regard to the prohibition against wearing a garment that includes both wool and linen. Rather, learn from it that the uppermost knot is required by Torah law. § Rabba bar Rav Adda says that Rav Adda says that Rav says: If a string was severed at its base, i.e., where it is connected to the garment, the ritual fringes are unfit. Rav Naḥman sat in the study hall and stated this halakha. Rava raised an objection to Rav Naḥman from a baraita: In what case is this statement said, i.e., that there is a minimum length required for the strings? That is only when the strings are initially affixed to the garment. But in the end, i.e., after the strings are affixed in an acceptable manner, its remainder and its severed strings are fit at any length. The Gemara clarifies: What is its remainder and what are its severed strings? What, is it not that when the baraita mentions its remainder it is referring to a case where parts of the strings were severed and parts of them remain, and when the baraita mentions its severed strings it is referring to a case where the strings were completely severed, and nevertheless the strings are fit for the mitzva? The Gemara responds to Rava’s objection: No, the tanna of the baraita is teaching one halakha, and the baraita should be understood as follows: The remainder of its severed strings are fit at any length. The Gemara asks: If so, let the baraita simply say: Its severed strings are fit at any length; why do I need the mention of its remainder? This teaches us that we require a remainder of its severed strings long enough to wrap them around the other strings and tie them in a slipknot. § Rabba sat in the study hall and said in the name of Rav: The string used for winding around the other strings is counted in the quota of ritual fringes, i.e., it is one of the eight strings on each corner, and there is no need to have an additional string for winding. Rav Yosef said to Rabba: Shmuel said it, and not Rav. This was also stated by another amora: Rabba bar bar Ḥana says: Rabbi Yoshiya of Usha told me that the string used for winding around the other strings is counted in the quota of ritual fringes. Rava sat in the study hall and said in the name of Shmuel: If one wound the majority of the white and the sky-blue strings instead of leaving the larger portion of the strings hanging loose beyond the windings, the ritual fringes are nevertheless fit. Rav Yosef said to Rava: Rav said it, and not Shmuel. The Gemara supports Rav Yosef’s version from that which was also stated: Rav Huna bar Yehuda says that Rav Sheshet says that Rav Yirmeya bar Abba says that Rav says: If one wound the majority of the white and the sky-blue strings, the ritual fringes are nevertheless fit. Rav Ḥiyya, son of Rav Natan, teaches this discussion like this: Rav Huna says that Rav Sheshet says that Rav Yirmeya bar Abba says that Rav says: If one wound the majority of the white and the sky-blue strings, the ritual fringes are nevertheless fit. And even if he wound only one set of windings, the ritual fringes are fit. But the finest way to affix the white and sky-blue strings is to ensure that one-third of the length of the strings is windings and two-thirds are loose hanging strings. The Gemara asks: And what is the measure of a set of windings? It is taught in a baraita that Rabbi Yehuda HaNasi says: It is such that one winds once and winds a second and third time, i.e., each set must contain at least three windings. It was taught: One who minimizes the sets of windings may not have fewer than seven sets, and one who adds to this number of sets may not have more than thirteen sets of windings. The Gemara provides explanations for these guidelines: One who minimizes the sets of windings may not wind fewer than seven sets, corresponding to the seven firmaments. And one who adds to this number of sets may not wind more than thirteen sets of windings, corresponding to the seven firmaments and the six air spaces between them. It was taught: When one begins to form the windings, he begins winding with a white string. This is because the verse indicates that one first inserts “the fringe of the corner” (Numbers 15:38), i.e., the white strings, which are of the same type as the corner of the garment. And when he concludes the windings, he concludes with a white string, in accordance with the principle: One elevates to a higher level in matters of sanctity and does not downgrade. § The Gemara relates: Rav and Rabba bar bar Ḥana were sitting together. A certain man was passing by wearing a cloak that was made entirely of sky-blue wool, on which he had affixed white and sky-blue strings, and the ritual fringes were composed entirely of windings, without any portion of the strings hanging loose. Rav said: The cloak is beautiful, but the white and sky-blue strings are not beautiful. Rabba bar bar Ḥana said: The cloak is beautiful, and the white and sky-blue strings are also beautiful. The Gemara asks: With regard to what principle do they disagree? The Gemara answers: Rabba bar bar Ḥana holds that since it is written in one verse: “You shall prepare yourself twisted cords” (Deuteronomy 22:12), and in another it is written: “And they shall put on the fringe of the corner a sky-blue thread” (Numbers 15:38), it teaches that the ritual fringes may be composed entirely of either twisted cords, i.e., the windings, or loose threads or strings. And Rav holds that actually, we also require loose strings in addition to the windings, and when that term “twisted cords” appears in the verse, it comes for the purpose of teaching the number of strings that are required. If the verse would have employed the singular term twisted cord, it would still indicate that two strings are required, as twisted means that two strings are wound around each other. Once the verse uses the plural term “twisted cords,” it thereby indicates that four strings are required. By using the terms “twisted cords” and “thread,” the verses indicates: Form twisted cords with the four strings that one attaches to each corner, and let the strings hang loose from them. § Shmuel says in the name of Levi: Wool strings exempt a garment made of linen, i.e., one fulfills the mitzva by affixing wool strings to a linen garment. A dilemma was raised before the Sages: What is the halakha with regard to whether strings made of linen exempt a garment made of wool? One can say that it is only wool strings that exempt a garment of linen, as since the sky-blue string, which must be wool, exempts a linen garment, white strings of wool also exempt the garment. But if one affixes linen strings to a wool garment, he does not fulfill his obligation. Or perhaps, since it is written: “You shall not wear diverse kinds, wool and linen together. You shall prepare yourself twisted cords upon the four corners of your covering” (Deuteronomy 22:11–12), which indicates that one may wear wool and linen together in order to fulfill the mitzva of ritual fringes, there is no difference whether one affixes wool strings to a garment of linen, and there is no difference whether one affixes linen strings to a garment of wool. The Gemara suggests: Come and hear a resolution to this dilemma, as Raḥava says that Rav Yehuda says: Wool strings exempt a garment made of linen, strings of linen exempt a garment made of wool, and strings of wool and linen exempt a garment in any case, i.e., all garments, and even garments made from silks [beshira’in]. The Gemara notes: And this last point disagrees with a ruling of Rav Naḥman, as Rav Naḥman says: Shira’in are entirely exempt from the obligation of ritual fringes. Rava raised an objection to the opinion of Rav Naḥman from the following baraita: Garments made from types of silks known as shira’in, kalakh, and serikin all require ritual fringes. The Gemara answers: The baraita means that there is an obligation by rabbinic law, whereas Rav Naḥman meant they are exempt by Torah law. The Gemara challenges this suggestion: If that is so, then say the latter clause of the baraita: And with regard to all of these garments, strings of wool and linen exempt them. This indicates that one may affix wool sky-blue strings and white linen strings. Granted, if you say that the obligation of ritual fringes for silk garments is by Torah law, that is why diverse kinds are permitted for them. But if you say that the obligation is by rabbinic law, how could diverse kinds be permitted for them? The Gemara answers: Say instead: Either wool or linen strings exempt silk garments, but one may not affix both wool and linen strings to the same silk garment. The Gemara comments: So too, it is reasonable to assume that this is the correct interpretation of the baraita, as the baraita teaches in the latter clause: Strings made from these silk fabrics exempt a garment of their type but do not exempt a garment that is not of their type. Granted, if you say that the obligation to attach ritual fringes to these garments is by rabbinic law, that is why they are exempted if one affixes strings of their type. But if you say that the obligation is by Torah law, then it should be only wool or linen that exempt these garments. The Gemara rejects this: If it is due to that reason, there is no conclusive argument, because one can maintain that other fabrics also fulfill the obligation of ritual fringes by Torah law, in accordance with the opinion of Rava. As Rava raises a contradiction: It is written in one verse: “And they shall put on the fringe of the corner a sky-blue thread” (Numbers 15:38). The term “the corner” indicates that the fringe must be from the same type of fabric as the corner. And yet it is written: “Wool and linen” (Deuteronomy 22:11), immediately before the verse states: “You shall prepare yourself twisted cords upon the four corners of your covering” (Deuteronomy 22:12), indicating that ritual fringes must be from either wool or linen. How so? Strings made of wool or linen exempt any garment, whether the garment is made of their type of fabric, or whether it is not of their type of fabric. Strings made of all other types of fabric exempt garments made of their type of fabric, e.g., silk strings exempt a silk garment, but they do not exempt a garment made from a fabric that is not their type, i.e., a garment made from a different fabric. The Gemara notes: And Rav Naḥman, who holds that silk garments do not require ritual fringes by Torah law, holds in accordance with the ruling stated by a tanna of the school of Rabbi Yishmael. As a tanna of the school of Rabbi Yishmael taught: Since the word garments is usually stated in the Torah without specification as to the material from which the garments are made, and the verse specified in one of its references to garments that it is referring to garments made from wool or linen, as it states: “And the garment in which there will be the mark of leprosy, whether it be a woolen garment or a linen garment” (Leviticus 13:47), it may be derived that so too, all garments mentioned in the Torah are those made from wool or linen. Other fabrics are not classified as garments by Torah law. Consequently, when the Torah requires strings on the corners of garments (see Numbers 15:38), it is referring specifically to garments made of wool or linen. Abaye said: This statement by a tanna of the school of Rabbi Yishmael diverges from another statement by a tanna of the school of Rabbi Yishmael, who holds that all fabrics are considered garments. As a tanna of the school of Rabbi Yishmael taught: From the fact that the verse states: “A woolen garment” (Leviticus 13:47), I have derived only that a garment of wool can become ritually impure. From where is it derived that garments made of camels’ hair, rabbits’ wool, goats’ hair, or the types of silk kalakh, serikin, and shirayin, are also included in this halakha? The same verse states: “Or a linen garment.” The word “or” serves as an amplification to include all types of fabric.

משנה תורה, הלכות ציצית א׳:ז׳

ולוקח חוט אחד מן הלבן וכורך בו כריכה אחת על שאר החוטין בצד הבגד ומניחו. ולוקח חוט התכלת וכורך בו שתי כריכות בצד כריכה של לבן וקושר. ואלו השלש כריכות הם הנקראין חליא. ומרחיק מעט ועושה חליא שניה בחוט של תכלת לבדו. ומרחיק מעט ועושה חליא שלישית וכן עד חליא אחרונה שהוא כורך בה שתי כריכות של תכלת. וכריכה אחרונה של לבן. מפני שהתחיל בלבן מסים בו שמעלין בקדש ולא מורידין. ולמה יתחיל בלבן כדי שיהא סמוך לכנף מינה. ועל דרך זה הוא עושה בארבע הכנפות:

Mishneh Torah, Fringes 1:7

(7) One of the white threads is taken up and wound once about the other threads close to the garment. It is then dropped. The blue thread is then taken and wound twice about the other threads close to the winding with the white thread. The threads are then tied. These three windings are called a section. A small space is left; a second section is made, the windings being done with the blue thread only. A small space is left; a third section is made; and so till the last division where the blue thread is wound round the other threads twice and the third winding is done with a white thread, because, as the winding began with a white thread, it should also end with a white thread, on the principle that things sacred may be elevated to a higher degree but may not be degraded to a lower degree. The reason why the winding begins with a white thread is that the corner of the garment shall have adjacent to it threads of the same kind of material. This is the method followed with the four corners.

השגות הראב"ד על משנה תורה, הלכות ציצית א׳:ז׳

והגאון רב נטרונאי ז''ל סידר אותו יפה סידור נאה מאד על דרך שאמרה ההלכה. וכמה שיעור חוליא כדי שיכרוך וישנה וישלש אתכלת קאי. ותנא דתנא הפוחת לא יפחות משבעה על הכריכות קאי שהן שלש מן התכלת וארבע מן הלבן מפני שמתחיל בלבן ומסיים בלבן. קושר תחלה סמוך לכנף קשר אחד בחוט לבן ובחוט של תכלת והוא שנקרא קשר העליון ואחר כך כורך שני חוטין אחד של לבן ואחד של תכלת עד שש כריכות והשביעית לבן לבדו וזהו שבע שאמרנו והן חוליא אחת ואלו הכריכות כולן על ששה החוטין המשלשלים והמשולשלים בכנף ובענין זה עושה ה' קשרים ובין כל קשר וקשר חוליא של שבע כריכות כאשר אמרנו, ונהגו לעשות חוליא אחת בשני קשרים סמוך לכנף ושתי חוליות בסוף הגדיל עם שלשה קשרים ובאמצע כורך בלא דקדוק בין מכונס בין מפוזר בתכלת ולבן עכ''ל:

Hasagot HaRa'avad on Mishneh Torah, Fringes 1:7

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רב עמרם גאון (גאוניקה עמ׳ 331)

…וכך היה גודל לאחר קשר התחתון חוליה אחת של לבן ועליה של תכלת וחוליה של לבן ועליה חוליה של תכלת ועליה חוליה של לבן ועליה של תכלת ועליה של לבן וקושר קשר העליון וזה הוא לא יפחות משבע ואם רצה להוסיף עד י”ג מוסיף כסדר הזה..

ג. כיצד משלבים את הקשרים

מנחות ל״ח ב

אמר רבא שמע מינה צריך לקשור על כל חוליא וחוליא

Menachot 38b

If we say that the individual omitted the mitzva of white strings and fulfilled only the mitzva of sky-blue strings, how is this possible? According to the opinion of Rabbi Yehuda HaNasi, the absence of either one prevents fulfillment of the mitzva with the other, and therefore in this case one would not fulfill any mitzva at all. The Gemara answers that Rav Yehuda said that Rav said: It means that he omitted a mitzva but nevertheless performed a mitzva. And what does it mean that he omitted a mitzva? It means that he did not perform the mitzva in the optimal manner because he did not insert the white strings first, but he did fulfill the mitzva of ritual fringes. The Gemara asks: This works out well with regard to the mishna’s statement that absence of the white strings does not prevent fulfillment of the mitzva with the sky-blue strings, which has been interpreted to mean that failing to insert the white strings before the sky-blue strings does not invalidate the ritual fringes. But what is the meaning of the mishna’s statement that the absence of sky-blue strings does not prevent fulfillment of the mitzva with the white strings? Rami bar Ḥama said: That statement of the mishna is necessary only in the case of a garment that consists entirely of sky-blue wool. In such a case, one is supposed to insert the sky-blue strings before the white strings. The Gemara notes that this was also stated by amora’im: Levi said to Shmuel: Aryokh, do not sit on your feet until you explain to me this matter: When the mishna states that the absence of the sky-blue strings does not prevent fulfillment of the mitzva of ritual fringes with the white strings, and the absence of white strings does not prevent fulfillment of the mitzva with the sky-blue strings, what does it mean? Shmuel said to Levi: That statement is necessary only in the case of a linen cloak on which one places ritual fringes, where there is a mitzva to insert the white strings first. What is the reason for this? The verse states: “And they shall put on the fringe of the corner a sky-blue thread” (Numbers 15:38). “The fringe of the corner” is a reference to the string that is the same type as the corner of the garment. In the case of a linen cloak, which is generally white, this is a reference to the white strings, and since the verse mentions “the fringe of the corner” before the sky-blue thread, the white strings must be inserted before the sky-blue strings. The mishna therefore teaches that if one inserted the sky-blue strings before the white strings, we have no problem with it after the fact, and the ritual fringes are valid. The Gemara asks: This works out well with regard to the mishna’s statement that absence of the white strings does not prevent fulfillment of the mitzva with the sky-blue strings. But what is the meaning of the mishna’s statement that the absence of sky-blue strings does not prevent fulfillment of the mitzva with the white strings? Rami bar Ḥama said to him: That statement of the mishna is necessary only in the case of a garment that consists entirely of sky-blue wool, where it is a mitzva to insert the sky-blue strings first, as the phrase: “The fringe of the corner” indicates that the first strings one inserts into the garment are those that are the same type as the corner of the garment. The mishna therefore teaches that if one inserted the white strings first, we have no problem with it after the fact, and the ritual fringes are fit. Rava said: Is it actually the color of the garment that determines the proper order in which one should insert the strings? Rather, Rava said: The ruling of the mishna is necessary only for a case of severed strings. The mishna teaches that if the sky-blue strings were severed and the white ones remain, or if the white strings were severed and the sky-blue strings remain, we have no problem with it, and the ritual fringes are fit. As the sons of Rabbi Ḥiyya say: Severed white or sky-blue strings are fit, and similarly, severed hyssop branches are fit for sprinkling the water of purification mixed with the ashes of a red heifer. The Gemara asks: What measure do severed strings need to be in order to remain fit? Bar Hamduri says that Shmuel says: The strings must remain long enough to tie them in a slipknot. A dilemma was raised before the Sages: When Shmuel says that severed strings must still be long enough to tie them in a slipknot, does that mean to tie all of the strings together in a slipknot? Or perhaps the strings may be even shorter, provided that they are long enough to tie each one individually. The Gemara concludes: The dilemma shall stand unresolved. Rav Ashi asks: If the strings are thick and cannot be tied in a slipknot, but if they were the same length but thin they could be tied in a slipknot, what is their status? Rav Aḥa, son of Rava, said to Rav Ashi: If the strings are long enough to be fit if they are thin, all the more so they are fit if they are thick, as the mitzva one fulfills with them is more recognizable with thicker strings. The Gemara cited the opinion of Rabbi Yehuda HaNasi, who holds that one cannot fulfill the mitzva of ritual fringes without both white and sky-blue strings, and the Gemara explained that the mishna can be interpreted in accordance with his opinion. The Gemara now asks: Who is the tanna who disagrees with Rabbi Yehuda HaNasi and holds that the sky-blue strings and the white strings are not interdependent? The Gemara answers: It is this following tanna, as it is taught in a baraita: Rabbi Yitzḥak says in the name of Rabbi Natan, who said in the name of Rabbi Yosei HaGelili, who said in the name of Rabbi Yoḥanan ben Nuri: If one does not have sky-blue strings, he nevertheless affixes white strings. Rava said: Learn from the sons of Rabbi Ḥiyya that one is required to tie a knot after each and every set of windings, and one cannot suffice with only one knot at the end of all the windings. As, if it enters your mind to say that one is not required to tie a knot after each set of windings, then that which the sons of Rabbi Ḥiyya say: Severed white or sky-blue strings are fit, and similarly, severed hyssop branches are fit, is difficult: Once the uppermost knot is undone, all of the windings on the entire corner will come undone, as there are no other knots holding the windings in place, and in that case the garment will not have valid ritual fringes.

מנחות ל״ט א

ואמר רבה שמע מינה קשר עליון דאורייתא

Menachot 39a

מדרש תנחומא, קרח י״ב

ציצית, שש מאות. שמונה חוטין וחמשה קשרים, הרי שש מאות ושלש עשרה.

Midrash Tanchuma, Korach 12

(1) The Seers (i.e., the prophets) were the ones who said the doubled letters, mantzepakh (mem, nun, tzadi, peh, and kaf, which are the letters that have a different form when they appear at the end of a word). [The doubling of kaf that is found in Genesis 12:1,] "Lekh lekha (Go for yourself)," hints to Avraham that he will father Yitschak at one hundred years [of age] (as the numerical value of these two words is one hundred). [The doubling of mem that is found in Genesis 26:16,] "ki atsamta memenu (as you have become more powerful than us)" is a hint [to Yitschak] that hints that he and his seed will be powerful in both worlds. The doubling of nun [that is found in Genesis 32:12,] "Hatsileini na (Save me)" [is a hint to] Yaakov, [that] he will be saved in both worlds. The doubling of peh [that is found in Genesis 50:24,] "pakod yifkod (He will surely remember you)" [is a hint to] Yosef, [that] He will remember you in this world, and He will remember you in the world to come. The doubling of tzadi [that is found in Zachariah 6:12,] "hinei eesh, Tsemach shemo, ou'metachtav yitsmach (behold, a man called Branch shall branch out from the place where he is,)" is [referring to] the messiah. And so is it stated (Jermiah 23:5), "vahikimoti leDaveed tsemach tsadeek (and I will raise up a true branch of David)." ["The leader of fifty" (Isaiah 3:3)] ("Sixty were the queens" [Song of Songs 6:8]). Twenty-four books (of the Bible), and add to them eleven of the thirteen [books of the minor prophets] - besides Yonah which is by itself - and six orders of the Mishnah and nine chapters of Torat Kohanim, behold ["The leader of fifty"] ("Sixty were the queens"). "[Sixty were the queens] and eighty were the concubines" (Song of Songs 6:8). Sixty tractates and eighty study halls that were in Jerusalem corresponding to its gates. "And maidens without number" (Song of Songs 6:8). The study outside. "Behold the bed of Shlomo, sixty warriors" (Song of Songs 3:7). [This] corresponds to the [number of] letters of [the priestly blessing,) "May the Lord bless you and keep you, etc." (Numbers 6:24-26). The Satan (HaSatan) has the numerical equivalent of the count of the days of the solar year, as he rules over all the year to slander, except for Yom Kippur. Rabbi Ami bar Abba said, "Avraham was missing five organs before he was circumcised and [before he] fathered. The [letter] hay (with a numerical value of five) was added [to his name] and he became complete and fathered, and he was called Avraham [corresponding to the complete set of organs, two hundred and forty-eight], the numerical count of his letters." [Regarding] Sarai, two Amoraim (later rabbinic teachers) differed. One said, "The [letter] yod [with a numerical count of ten that was taken from her] was divided into two, [to give] a hay to Avaraham and a hay to Sarah." And [the other] said, "The yod that was taken from Sarah raised a protest until Yehshoua came and had a yod added, as it is stated (Numbers 13:16), "and Moshe called Hoshea [...], Yehoshua." And it saved him from the counsel of the [other] spies. [The significance of the letters in the name,] Yitschak [is as follows]: Yod [with a numerical count of ten] corresponds to the ten trials [of Avraham]. [The letter] tsadi [with a numerical count of ninety, as] Sarah was ninety when he was born. [The letter] chet [with a numerical count of eight, as] he was circumcised on the eighth day. And the letter kof [with a numerical count of one hundred, as] Avraham was a hundred years old when he was born. Yaakov was called according to [the significance of the letters of] his [own] name: Yod [corresponds to] the tenth of his offspring going backwards, Levi. Count from (the last son), Binaymin to Levi - there are ten sons, and Levi was the tenth. And he gave him as a tithe to the Omnipresent to fulfill [what he said] (Genesis 28:22), "all that You give to me, I will surely tithe it to You." [The letter] ayin [with a numerical count of seventy corresponds to the number of offspring he took to Egypt], "with seventy souls" (Deuteronomy 10:22). Kof corresponds to the [number of the] letters of the blessing [that he received], "And may He give you [etc.]" (Genesis 27:28). Take away the name [of God] from there, and one hundred [letters] remain. [The letter] bet [with a numerical count of two] corresponds to two angels [that he saw on the ladder in his dream] rising. Yehudah was called according to [the significance of the numerical count of the letters of] his [own] name: Thirty, corresponding to the thirty virtues of the monarchy. There were six hundred and thirteen letters on the tablets - from "I am" (Exodus 20:2) to "to your neighbor" (Exodus 20:14) - corresponding to the six hundred and thirteen commandments. And they were all given to Moshe at [Mount] Sinai; and in them are statutes and judgments, Torah and Mishnah, Talmud and aggadah. "The fear of the Lord is his treasure" (Isaiah 33:6). There is no greater characteristic than fear and humility, as it is stated (Deuteronomy 10:12), "And now Israel, what does the Lord, your God, ask of you [besides to fear Him]." "The fear of" (Yirat) has a numerical value of six hundred and eleven; along with Torah and circumcision, behold that is six hundred and thirteen. [The numerical value of] fringes (tsitsit) is six hundred. [Add] eight strings and five knots, behold that is six hundred and thirteen. "[The man (David)] raised on high" (II Samuel 23:1) - [high (al)] has a numerical value of one hundred, corresponding to one hundred blessings. As on every day, one hundred men of Israel were dying. [So] David and ordained [the daily saying of] one hundred blessings. "And now Israel, what (mah) does the Lord, your God, ask of you" - read it as one hundred (meah), these are the hundred blessings. Once he ordained it, the pestilence ceased. "This is the law of the burnt-offering (olah), it is the burnt-offering" (Leviticus 6:2), [meaning] the yoke (ulah) of Torah and the yoke of repentance. "Two anointed ones" (Zechariah 4:14). These are David and Aharon who were anointed with the anointing oil, such that their anointing was for [all] the generations. With Aharon, it is written (Numbers 25:13), "It shall be for him and his descendants after him, a pact of priesthood for all time." With David it is written (Ezekiel 37:25), "and My servant David as their prince for all time." "Forgive all guilt and take the good (tov)" (Hosea 14:3). Israel said, "Master of the world, at the time that the Temple existed, we would offer a sacrifice and be cleansed. But now all we have in our hand is prayer." The numerical value of tov is seventeen. Prayer [consists of] nineteen [blessings]. Take away from them the blessing for the malfeasers that was composed at Yavneh, and "Let the sprout of David blossom," which they ordained for the sake of "Probe me, Lord, and try me" (Psalms 26:2). Rabbi Simon says, "'Forgive all guilt and take the good (tov).' The numerical value of tov in at-bash (matching letters based on how close they are to the center of the alphabet) is [the same as] soul (nefesh). Israel said, 'Behold the fat from us, from our souls. May it be Your will that it be atonement for us and "that we pay with the words of our lips" (Hosea 14:3).'" "And the Lord gave her conception (herayon)" (Ruth 4:13). [Herayon] has a numerical value of the [number of the] days of the nine months of birthing (two hundred and seventy one). The name of the angel that is appointed for conception is night, as stated (Job 3:3), "and the night [that it was] said, 'A man was conceived." The measure of the water of a mikveh (ritual bath) is forty seah corresponding to the [forty mentions] of well, written in the Torah. And [the volume of] how many eggs is the measure of the mikveh? Five thousand seven hundred and sixty. And a seah is a hundred and forty-four eggs. Forty-three and a fifth eggs is the measure of [what is required for] hallah [tithe]. And from where [do we know] that a mikveh requires forty seah? As it is written (Isaiah 8:6), "Since this nation has rejected the waters of Shiloach that flow gently (le'at)." The numerical value of le'at is forty. Behold the measure of a seah is a tefach by a tefach with the height of [sixteen] tefach [and a fifth]. And one who separates the measure of the hallah [tithe] must separate [one part in forty three] and a fifth [from Torah writ like the numerical value of hallah]. Forty lashes (which are actually thirty-nine) is from Torah writ, as it is written (Exodus 35:1), "These (eleh) are the things which the Lord commanded." [The numerical count of] "eleh" is thirty-six; "things" (being plural) is two; "the things" [indicates an additional] one - behold, forty minus one (thirty-nine). "He shall strike him forty, he shall not add" (Deuteronomy 25:3), corresponds to the forty curses received by the snake, Chava, Adam and the ground, and the sages lessened one, because of "he shall not add." A Sanhedrin is twenty-three, so [that it is possible for] those advocating innocence to have one more (than twenty), and those advocating guilt to have two more. It is best for the two to come and push off one. The numerical value of anathmea (cherem) is two hundred and forty-eight. And Shmuel said, when it takes force it takes force on [all] two hundred and forty-eight organs, and when it leaves, it leaves from two hundred and forty-eight limbs, as it is written (Habakuk 3:2), "in anger, remember to have mercy (rachem, which is made up of the same letters as cherem)." It is written,"tirash," but we read it [as] tirosh. [If] he merits, he becomes a rosh (leader); [if] he does not merit, he becomes a rash (poor person). Our rabbis, may their memory be blessed said, "A man is recognized by three things: by his purse, by his glass and by his anger. Tavel is Ramaliah. Seshach is Bavel (Babylon) [according to] its numerical value of in at-bash. The numerical value of Gog and Magog is seventy, as they are the seventy nations [of the world].

שולחן ערוך הרב אורח חיים סימן יא

סעיף ל נוהגים לכרוך באויר הראשון ז’ כריכות ובשני ח’ ובג’ י”א וברביעי י”ג כריכות שעולים כולם למספר ל”ט כמנין הוי”ה אח”ד...

סעיף לא יש נוהגין לכרוך הכריכות שבכל אויר חוליות חוליות דהיינו לאחר שכרך ג’ כריכות הראשונות ירחיק מעט ויחזור ויכרוך ג’ פעמים באותו אויר עצמו ואח”כ יכרוך א’ מאויר הראשון ויצרף לזה ב’ מאויר השני וירחיק מעט ויכרוך עוד ג’ פעמים וכן יעשה עד כלות הל”ט כריכות בי”ג חוליות קטנות וכן היו עושין בזמן שהיה תכלת:

^^ זו שיטת האריז״ל וכן הוא מנהג חב״ד. אמנם יש שיטות שוות ברעיון אבל שונות במראה לבן איש חי ולחסידי ברסלב.

ספר החינוך שפ״ו:ה׳

...ועושה אחד מהם גדול כדי שיכרך בו האחרים, וקושרן בחמשה מקומות קשר כפול (שם לט, א בתוס' ד''ה לא). ובין קשר וקשר עושה שלש חליות, ובאמצעות הקשר האחרון עושה ארבע חליות שנמצאו בין כלן שלש עשרה חליות.

Sefer HaChinukh 386:5

(5) How are the fringes made? (Mishneh Torah, Laws of Fringes 1:6) Four strings are passed through the corner of the garment, such that there are now eight ends hanging from the corner. This is not done precisely at the corner, but [a half-]thumb's distance from the edge, as Rabbi Yaakov said that Rabbi Yochanan said in the Gemara (Menachot 42a), "It must be one large joint away." One of the strings should be longer so that it can be used for winding [around] the others. Five double knots are tied (Tosafot on Menachot 39a, s.v. lo); and between each knot, he makes three rings (windings), and between the final knot, four rings, so that there are a total of thirteen rings. The strings are made long so that it be enough for two [thirds] of the length to be branching; meaning to say without the knots and rings, besides the knots and rings. This is the main [approach to the] ideal fulfillment of the commandment. But ex post facto, even one ring suffices, and so [too,] ex post fact, even if the strings of the fringes shorten, even if there is only enough to make a basic bow, it is fit (Menachot 38b). But if even one string is completely torn, it is disqualified.

הגאון רב אליהו מווילנא (יהל אור, פרשת פנחס רכ”ז ע”א)

ואמר ח"י קשרים כו' מכאן דאף בי"ג חוליין רק ה' קשרים והוא בד' חוליין קשר א' וזאת קשר האחרון והוא שמא די"ב בחוליין, ג' פעמים ד' -- בחיות ושבטים ותקופות וכיוצא. וכן בכל קשר בכריכות.

תוספות על מנחות ל״ט א

קשר העליון. ...וכן נוהג רבינו תם לעשות אותן ה' קשרים ב' בסמוך לטלית וג' סמוך לפתיל משום מעלין בקדש ולא מורידין כדאמרינן שמסיים בלבן ועל כל קשר שני קשרים כדי שיהא קשר של קיימא מיהו לא מצינו שום סמך בהש"ס מפורש מה' קשרים ויש לומר דהא דאמרינן צריך לקשור על כל חוליא וחוליא היינו אחת של לבן ואחת של תכלת שהן שתים והשתא כשאין פוחת משבע עושה ה' קשרים סמוך לטלית קשר אחד ואחר כך שתי חוליות אחת של תכלת ואחת של לבן קשר אחד עד שמסיים שש חוליות הרי ארבעה קשרים ואחר כך עושה חוליא שביעית של לבן כדי שיהא מסיים בלבן ואחר כך קושר אח' הרי ה' קשרים ויש מפרשים לא יפחות משבע כריכות בין כל קשר וקשר:

Tosafot on Menachot 39a

...

הרב צבי שכטר שליט״א (גנות אגוז)

…אך בזמן דאיכא תכלת, שאז צריכים לדקדק היטב בכריכות, אשר זהו הדין של פתיל הנזכר בקרא, אז מסתמא צריכים לנהוג כדעת רוב הראשונים לעשות לכה”פ ז’ חוליות, ולעשות בין כל חוליא וחוליא קשר גמור של קשר ע”ג קשר, (כמנהגנו בזה”ז, דמ”ט נשנה את זה), ובכל חוליא יהי’ מינימום של ג’ כריכות (וכמבואר שם בגמ’ לעיל – וכמה שיעור חוליא, כדי שיכרוך וישנה וישלש.) ובודאי אם יעשה ז’ חוליות, ובכל אחת ז’ כריכות, יצא בזה לכו”ע...