Last Shabbat I noticed that one of my tzitzit had become untied; does the fact that one of the corners is untied, or different from the other three make the tallit posul?
f one of your corners has become untied this does not poseil the talit as long as the minimum d’oraita requirements are fulfilled.
The d’oraita requirements are:
a) kesher elyon (there is a discrepancy as to whether this refers to the uppermost knot or lowermost knot) – (see Biur Halacha, Oreh Hayim 11:10, s.v. v’natko).
b) one chulya of three wraps (the Rambam believes that at least one of the wraps be tekhelet).
c) there should be gdil (wound) and anaf (hanging)
d) minimum total length (some hold there is no d’oraita req. others hold that the kdei aniva length is d’oraita – see Biur Halacha, Oreh Hayim 11:4, s.v. ain).
Therefore your talit is not pasul as long as you have the first knot next to the garment and then three wraps (with one or more being tekhelet) and then another knot, and that there is some hanging part of the strings, ideally k’dei aniva (between 4 – 4.8cm). Indeed, the Mishna Berura (Oreh Hayim 11:14:66) explains that if it was Erev Shabbat and one only had time to tie this minimum d’oraita amount, he can wear the tzitzit on Shabbat and say the bracha on them (though he must complete the tying after Shabbat for he has not fulfilled the d’rabanan requirements). The Mishna Berura in his Biur Halacha (Oreh Hayim 11:4, s.v. yoter) adds that if the tzitzit are not at least 12 thumbreadths in length there are stringent opinions that one’s tzitzit are in question and so though one can definitely wear them one should not say a bracha on them.
As mentioned, one cannot rely on this for any length of time when repair is possible for it does not meet any of the d’rabanan requirements.
The d’rabanan requirements are:
a) one must start with white and end with white.
b) one must have at least 7 chulyot.
c) the tied area must be at least 4 thumbreadths and the hanging part at least 8 thumbreadths (thumbreadth is 2 – 2.4 cm).
d) that the tied area to hanging part be in proportion of 1/3 to 2/3
– Mois Navon.