May the straps of the Tefillin that are wrapped around the arm touch each other or overlap?

Touching on sides: The wrapping of the Tefillin straps around the forearm [between the bicep/upper arm, and the wrist] is done due to custom, and not due to a Halachic requirement.[1] Accordingly, there is certainly no prohibition, or invalidation, involved if the straps of the Tefillin that are wrapped around the forearm touch each other by the sides. Furthermore, there is also no recorded source, neither in Halacha or Kabbalah, which mention an adherence of being careful that the straps should not touch each other, and to thus make a space between each one.[2] [Nonetheless, it is a widespread worldly custom to be particular upon wrapping the straps around the arm that the straps remain a distance from each other, and do not touch by the sides.[3] This was likewise the witnessed custom of the Rabbeim.[4] It is unknown as to why the custom is to do so.[5] If later on during Davening, the straps become loosened and touch each other, the custom is to refasten them in a way that they are distanced from each other.[6] During Shacharis, the Rebbe was witnessed to undo and refasten the straps at a distance from each other, if they became loosened and began touching each other.[7] Practically, Minhag Yisrael Torah Hi, and one is to initially adhere to this matter.[8]]

Overlapping: In addition to there being no issue with the straps touching each other by the sides, without there being a space between them, there is also no prohibition of Chatzitza, or other invalidation, involved if the straps of the Tefillin overlap each other, such as if one of the lower straps is wrapped partially over an upper strap.[9] Accordingly, many Sefaradim are accustomed to wear Rashi and Rabbeinu Tam Tefillin simultaneously, and to specifically have the Rashi straps bound on top of the Rabbeinu Tam straps, on the arm.[10] Nevertheless, some Poskim[11] rule it is initially proper to be stringent and not have the straps overlap each other, due to the issue of Chatzitza.[12][13] Practically, as stated above, the Minhag Yisrael is to initially space the forearm straps away from each other, and certainly to avoid having them overlap.

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[1] Admur 27:12; Michaber 27:8; M”A 27:13; Kisvei Arizal, Peri Eitz Chaim Shaar HaTefillin 10

The reason: See Peri Eitz Chaim ibid that the seven straps represent seven Naaros.

[2] There is no recorded source amongst the Poskim, or Sefarim of Nigleh or Nistar, which require that the straps of the Shel Yad Tefillin on the arm be surrounded by skin, and that they not be allowed to touch each other on the sides; There is also no reason or basis to find issue with the straps touching each other, even by the other parts of the arm. See all Sefarim quoted below which direct the Rashi’s to overlap the Rabbeinu Tam straps, and thus certainly the touching of the sides would not pose any issue either.

[3] I have not found any discussion on this custom in Sefarim

[4] See Ishkavta Derebbe p. 31 footnote 19

[5] See Ishkavta Derebbe ibid “I do not know, and have not heard the reason of the custom of the Rabbeim to at all make space between the straps wrapped on the forearm.” However, perhaps the following suggestions can be made: 1) The straps all represent parts of Hashem’s name, as written in Peri Eitz Chaim ibid, and just as the letters in a Sefer Torah may not touch each other, so too the straps. [See Ishkavta Derebbe ibid for a similar explanation regarding why we leave a space between the sets 2 and 4 of the straps] 2) The straps each represent a different level of “Naarah”, as writes the Arizal ibid, and these Naaros are to be separate from each other.

[6] This, however, seemingly was done in order to properly fasten the straps on the arm, and not merely because of a touching issue.

[7] See here: https://www.youtube.com/watch?v=P2WbWz3YkVc

[8] Many of the customs, and even Halachos that we keep regarding Tefillin are “customs” with no source in the Talmud. See for example Rashba 827, brought in Rama 27:4; and M”A 27:5, regarding Chatzitza, that the Rashba gave a final ruling based on the custom he saw done.

[9] See Rama 27:4; Admur 27:7; Taz 27:4; M”A 27:5 that there is no Chatzitza invalidation by the straps of the Tefillin [Rama ibid], especially if they are by the forearm [Admur and Taz ibid], and especially if it is only a small amount [M”A ibid]; See Admur 651:5; Rama 651:1; Tur 651; Sukkah 37b that we never apply the rule of Chatzitza by Min Bemino, which is two items of the same species. The same applies regarding Tefillin. [Revid Hazahav, brought in M”B 27:14; Shulchan Hatahor 27:2; Maharsham 4:137] Accordingly, even if the law of Chatzitza would apply to these straps, leather would not be viewed as a Chatzitza between the straps/Tefillin and the skin; See all Poskim in next footnote regarding wrapping Rashi over the Rabbeinu Tam straps; See Piskeiy Teshuvos 27 footnote 90; 34:3

If the straps have loosened: If the straps have become loosened and have fallen downwards, on top of one of the lower straps, then seemingly it is to be fixed and fastened, otherwise it may not be considered strapped around the arm. Vetzaruch Iyun

[10] See Arizal in Peri Eitz Chaim Tefillin 10; Ben Ish Chaiy Vayeira 21; M”B 34:5; Yabia Omer 1:3; 5:5 Vayeishev Hayam 4:3 [of Rav Yaakov Hillel]; Piskeiy Teshuvos 34:3

[11] See Shraga Hameir 6:80 [See there that he rules it is better for one with a cast to wrap a minority of the straps over the cast, which is a real Chatzitza, then to wrap all the straps on top of each other, in the area of skin that precedes the cast; However, he records the M”A 27:5 that there is no Halachic issue in having only have a small part of the straps overlap each other.]

[12] The reason: As some Poskim rule that by Tefillin even Min Bemino is a Chatzitza. [Birkeiy Yosef 27:1 who compares it to Bigdei Kehuna; Levushei Serud 27; M”B 27:10 and 14 that initially one is to be stringent like this opinion; See Machatzis Hashekel 34:5; Shut Hastam 50; Rav Poalim 3 Sod Yesharim 8; Doveiv Meisharim 2:37; Piskeiy Teshuvos 27 footnote 90; 34:3] Likewise, some Poskim rule that even the straps should not have a Chatzitza under them. [Peri Megadim 27 M”Z 4; Doveiv Meisharim ibid; Cheshev Haeifod 1:21; Teshuvos Vehanhagos 2:26; Piskeiy Teshuvos 27:9]

[13] See Rama 27 that there is never Chatzitza by the straps; M”A