Menachos Daf 39 מנחוס דַף 39

Rabbah says we can prove קשר עליון דאורייתא – the upper knot of tzitzis is a Biblical requirement (meaning, tzitzis must be tied to the garment with at least one knot): had the requirement only been Rabbinical, מאי איצטריך למישרי סדין בציצית – why was it necessary for the Torah to permit a linen cloak with woolen tzitzis (i.e., a derashah teaching to attach tzitzis, including the woolen תכלת, onto all garments, including linen ones, thus overriding the שעטנז prohibition)? If it is not required מדאורייתא to tie the tzitzis onto the garment, פשיטא – it is obviously permitted to use woolen tzitzis for a linen garment without tying it, because התוכף תכיפה אחת אינו חיבור – if one stitches wool to linen with a single stitch, it is not considered an attachment, and would not violate שעטנז!? Since the Torah needed to permit woolen tzitzis on a linen garment, it proves that they must be tied on with a knot, and would transgress the שעטנז prohibition.

Rabbah quoted Shmuel, though others quoted it from Rav: תכלת שכרך רובה כשרה – if most of the techeiles was braided (i.e., two-thirds of the tzitzis were braided and one-third loose), it is valid. Rav also said: ונויי תכלת שליש גדיל ושני שלישי ענף – the beauty of techeiles is to have one third braid and two thirds fringe. A man was once wearing a garment made entirely of techeiles, and its tzitzis were completely braided, with no loose threads. Rav said: יאי גלימא ולא יאי תכלתא – the garment is fitting, but the techeiles is not fitting, since it lacks loose threads. Rabbah bar bar Channah said: יאי גלימא ויאי תכלתא – the garment is fitting, and the techeiles is fitting. The Gemara explains that he holds that since the passuk describes tzitzis as "גדיל" – braid and elsewhere as "פתיל" – thread, we derive that tzitzis may be או גדיל או פתיל – either entirely braided or entirely loose thread. Rav holds that loose threads are always required, and the word "גדילים" teaches the number of threads required in tzitzis. The singular "גדיל" would indicate two threads (for a braid), the plural "גדילים" indicates four threads, and the additional term "פתיל" teaches עשה גדיל ופותליהו מתוכו – make a braided fringe and let loose threads emerge from within it.

Levi said: חוטי צמר פוטרין בשל פשתן – woolen threads release a garment made of linen from its white thread tzitzis obligation. The Gemara asks: does this only apply to white threads of wool, since the תכלת threads must certainly be wool despite being שעטנז with the linen garment, but פשתים – linen threads would not be permitted for a woolen garment? Or, since the prohibition of צמר ופשתים יחדו – wool and linen together is written near the mitzvah of tzitzis, it permits even פשתן threads in a צמר garment? Rav Yehudah says that either צמר or פשתן can be used for tzitzis in the opposite type of garment, and can be used for any other material. Rava posed a contradiction between pesukim: "הכנף" – the tzitzis of the corner implies that tzitzis threads should be made from מין כנף – the same type of material as the corner (i.e., the garment itself), but elsewhere the passuk specifies צמר and פשתים, implying wool and linen should be used for all types of garments. He concludes that צמר and פשתים can be used for all materials, and any material may be used as tzitzis in their own type of garment, but not for others.