Source for tzitzit according to Sefer HaChinuch

Question

I'm looking for the source in Sefer HaChinuch that discusses the author's method for tying tzitzit. Can anyone point it out for me?

Answer 1

Chinuch mitsva 386 :

• כן אמרו (מנחות לט א) שכורכין חוט התכלת על הלבן, שהנפש היא העליונה והגוף תחתון. ‏

  They (the sages) said that they wind the sky blue thread around the white, because the soul is at the top and the body at the bottom.

  ואמרו שעושין ממנו שבע כריכות או שלש עשרה לרמז הרקיעים והאוירים שביניהם, ‏

  And they said that we make with it (the blue sky thread) seven [sets of windings] or thirteen, to refer to firmaments and the spaces between them.

  וכמו שאמרו (שם) תנא הפוחת לא יפחת משבע, כנגד שבעה רקיעים, ולא יוסיף על שלש עשרה כנגד שבעה רקיעים וששה אוירים שביניהם. ‏

  as they said not less than seven and not more than thirteen [sets of windings] proportionally to the seven firmaments and the six spaces between them.

  כיצד עושין הציצית? מעבירין ארבעה חוטין בכנף הבגד, שהן שמנה ראשי חוטין כשהן תלוין בכנף, ‏

  How to make the Tsitsit, putting 4 threads in the corner of the cloth, the 4 threads have 8 extremities of thread hanging from the corner.

  ואין תולה אותן סמוך ממש לשפת הבגד, ‏ ולא רחוק אלא סמוך כשעור גודל מראשו עד הפרק הראשון, ‏

  But they are not hanging from the garment edge, but from a distance equal to the length of the distal phalanx of the thumb,

  כדאמר רבי יעקב אמר ‏ רבי יוחנן בגמרא (שם מב, א), וצריך להרחיק כמלא קשר גודל. ‏

  as said Rabbi Yaakov in name of Rabbi Yochanan in Gemara (Menachot 42b), he need to take it away as a thumb phalanx.

  ועושה אחד מהם גדול כדי שיכרך בו האחרים, וקושרן בחמשה מקומות קשר כפול (שם לט, א בתוס' ד''ה לא). ‏

  One of the threads must to be longer to wrap it around others.

  ובין קשר וקשר עושה שלש חליות, ובאמצעות הקשר האחרון עושה ארבע חליות שנמצאו בין כלן שלש עשרה חליות. ‏

  And between two knots, he makes three Chuliot, and in the last inter-knots space, he makes four Chuliot. The total there are thirteen Chuliot.

• About the definition of Chuliot (little tubes), see Gemara Menachot 39a:

  וכמה שיעור חוליא תניא רבי אומר כדי שיכרוך וישנה וישלש ‏

  What is the minimum length of a Chulia? - It was taught: Rabbi says, [In a Chulia] the thread must be wound once, twice and a third time.

  The number of wraps of each set of Chuliot (windings) is called A, the number of Chuliot is B. We have (A X B) in a serie as this: (3 X 3) + (3 X 3) + (3 X 3) + (3 X 4) and 5 double knots: before the first set of 3, between sets and after the set of 4. A total of 13 Chuliot.

• Words definitions.

  1. "חוליה" is as the word "חלול" hollow, as hollow bone ("חוליה" = vertebra, which is hollow for the spinal cord) see also Radak Shorashim, "חלה". For us "Chulia" is a little pipe, made as a coil spring by the woolen thread, which at least three turns arround the seven threads (as said in Gemara above cited "the thread must be wound once, twice and a third time").
  2. Kricha is something which bind items as "כריכות ברשות הרבים" in the 2nd chapter of BM. It is a loop which bind 3 loops as this .
  3. So, in conclusion, the Shita is as the diagram bellow; one Kricha around each Chulia. Now we understand the Chinuch a couple of lines above the quoted passage. "ואמרו שעושין ממנו שבע כריכות או שלש עשרה " because after the bounded Chulia is called by metonymy Kricha. The link with the photo doesn't agree with this.

In the following diagram, "O" is the hole in the talit's Corner, "@@" is a double knot, " " is a Cricha which bounds the 3 turns or the 4 turns of a Chulia. "||| ||| |||" is 3 Chuliot, "||| ||| ||| |||" 4 Chuliot, ">>>>" are the 4 X 2 wool thread outgoing from the hole, "<<<" are the distal part of the 4 X 2 wool threads.

"O>>>> @@ ||| ||| ||| @@ ||| ||| ||| @@ ||| ||| ||| @@ ||| ||| ||| ||| @@ <<<<"

But in a website regarding Tsitsit I found an other interpretation of the Chinuch, which have probably drawn inspiretion from the Rambam, see here.

A noticeable difference between Rambam and Chinuch and Rambam is in my little view a sentence of the Rambam (Ahava, Tsitsit, 1, 7):

ולוקח חוט התכלת וכורך בו שתי כריכות בצד כריכה של לבן וקושר. ואלו השלש כריכות הם הנקראין חוליא. ‏

He explains clearly that a Kricha is a turn around the 7 threads, and a Chulya is a group of 3 Krichot (clarifiying the words of the Gemara stating the size of a Chulia). This sentence said explicitly that Cricha is a part of Chulya as a link of a chain. The Chinuch did not write that the Hulya is 3 turns, but told about 7-13 Krichot and further told about 13 Chuliot. This is perhaps a proof that each Chulia is surrounded by a Kricha as you can see in my diagram.

But I don't understand why the Chinuch skipped the rule of 3 wrapping for each Krichot.