Uneven Sechach-Sechach of different heights:[1]

Less than three Tefachim between the higher and lower Sechach [Figure A]:[2] If the Sechach was uneven, with some of it being going slightly upwards and some of it going slightly downwards, then it nevertheless remains valid. [For example, if a Sukkah is made with two frames to support the Sechach, an upper and lower frame, and between every beam of Sechach on the lower frame there is empty space, and above that empty space is a beam of Sechach which is supported by the upper frame. See figure A.] This applies even if this lack of symmetry of the Sechach causes there to be more sunlight than shade in the Sukkah when the sun shines at it from an angle.[3] This, however, only applies if there is not three Tefachim of space [23.5 cm.[4]] between the upper and lower Sechach.[5] If, however, there are three Tefachim between the upper and lower Sechach then at times they do not join eachother, and the Sukkah is invalid, as explained next. The measurements followed in this law are a tradition of Moshe from Sinai.[6]

More than three Tefachim between the higher and lower Sechach [Figure B-D]:[7] If there are three Tefachim between the upper and lower Sechach then they do not join eachother, and it is not considered Sechach at all.[8] [Meaning, that we do not view the two Sechach’s to be part of the same Sukkah, and hence in the above example where the upper and lower Sechach switch off every other beam, like in a zigzag, then the entire Sukkah is invalid, as it does not contain enough valid Sechach on either level individually. See figure A. Now, if the higher and lower Sechach were on separate sides of the Sukkah with all the lower Secha being on the right side and all the lower Sechach on the left side, it would possibly be viewed as two Sukkahs with each required to have its own dimension of 7×7 Tefachim and three Kosher walls, otherwise both sides are possibly invalid.[9] See Figure D] If, however, the upper Sechach has the dimension of a roof which is a 1×1 Tefach dimension or more[10], and it hovers directly over the empty space between it and the lower Sechach in a way that if it were to be lowered down exactly to the space under it and be even to the lower Sechach then it would fit between the space and no part of the upper Sechach would actually touch the lower Sechach[11], and the space between the two beams of the lower Sechach is equal or more than the width of the upper Sechach[12], then it is valid even if there is more than 3 Tefachim between them.[13] [See Figure B] However, if the space between the two beams of the lower Sechach is less than the width of the upper Sechach, or if the upper Sechach is not directly parallel to the space under it and would thus touch the lower Sechach if it were lowered to its level, then if there is a three Tefach distance between the higher and lower Sechach, then the two Sechach’s are not viewed as attached [and is possibly invalid as explained above, depending on the arrangement of the upper and lower Sechach in the Sukkah and if an area of 7×7 Tefachim with three walls will remain].[14] [See Figure C-D] The measurements followed in this law are a tradition of Moshe from Sinai.[15]

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[1] Admur 631:6-7

[2] Admur 631:6; Michaber 631:5; Mishneh Sukkah 22a

[3] Admur ibid; Rama ibid

The reason: As since if the sun were to stand in middle of the sky on top of the heads of all people, it would have more shade than sunlight, therefore it should not be invalidated simply due to sunlightthat comes from an angle. [Admur ibid; Tosafus Sukkah ibid; Tur ibid]

[4] See Shiureiy Torah p. 249 that an Ama is 47 Dochakos [as opposed to 48 for a regular Tefach], and accordingly a Tefach Dochakos is 7.83 cm [i.e. 1/48 of a cm times 8, deducted from 8 cnetimeters]  and by the Shiur Sukkah of 7×7 one should measure with the stringent approach of an Ama Sochakos, and the same would apply here Lechumra to measure the four Tefachim as Dochakos. See also M”B 633:2 and Shaar Hatziyon 633:2 that by Sukkah we follow the stringent approach in the dimensions, either Dochakos or Sochakos, and by the 7×7 dimension we follow Sochakos, and the same would apply here by the 20 Amos dimension; See also Midos Vishureiy Torah pp. 48-57 regarding Ama Sochakos and Dochakos; Piskeiy Teshuvos 633:1 writes that its 31.2 according to Grach Nah, when taking into account the Dochakos according to Chazon Ish, as he explains there in footnote 2

Other opinions-Chazon Ish: According to the Chazon Ish, the measurement is 37.68 cm following the 9.42 measurement of Tefach Dochakos. [See Piskeiy Teshuvos ibid]

[5] Admur 631:7; Michaber ibid; Abayey Sukkah ibid

The reason: As any area which is less than three Tefachim apart is considered attached due to the rule of Lavud, and they therefore join each other to be considered like a single Sechach. [Admur ibid; Tosafus Sukkah ibid]

[6] Admur 631:7

[7] Admur 631:7

[8] Admur ibid; Michaber ibid; Abayey Sukkah ibid

The reason: As any area which is less than three Tefachim apart is considered attached due to the rule of Lavud, and they therefore join each other to be considered like a single Sechach. If, however, there are three Tefachim between the upper and lower Sechach then they do not join eachother, and it is not considered Sechach at all. [Admur ibid; Tosafus Sukkah ibid]

[9] See Piskeiy Teshuvos 631:3 and footnote 7 who discusses this matterand whether we can still apply the rule of Dofen Akuma.

[10] Admur ibid; Michaber ibid “Tefach or more”; Rava Sukkah ibid; Rashi ibid

Must each individual piece of Sechach have a Tefach by Tefach: Some Poskim rule that each individual piece of Sechach in the upper level must have a 1×1 Tefach dimension for us to view it as if it descends below, and it does not help for it to simply have a Tefach by Tefach all together. [M”B 631:8 in name of Ran; Kaf Hachaim 631:15]

[11] Admur ibid; Michaber ibid; Rambam Sukkah 5:21

Explanation: Some Poskim explain this to mean that the lower Sechach has space between each of its beams of Sechach and the upper Sechach is parallel to this empty space and if it were to descend it would close up this empty space between the two beams of lower Sechach. [Kesef Mishneh on Rambam ibid; Shulchan Gavoa 631:8; M”B 531:9; Kaf Hachaim 631:29]  However, according to Admur ibid who writes that it is valid even if there is more space between the two beams of the lower Sechach than the width of the upper Seach which is hovering over it, then it nevertheless remains valid, and it is only if there is less space that it would be invalid.

[12] Admur ibid; Based on Rama ibid; Ran Sukkah 10b; Lechem Mishneh on Rambam ibid

Other opinions: Some Poskim rule that if the space between the two lower beams, is more than the space of the higher beam, then it is invalid. [Kesef Mishneh on Rambam ibid; Shulchan Gavoa 631:8; M”B 531:9; Kaf Hachaim 631:29] See previous footnote!

[13] The reason: As we view the upper Sechach as if it descended below and is resting in the area of space under it [and it is hence considered as if there is no height difference between it and the lower Sechach, and it hence remains valid]. [Admur ibid; Michaber and Rambam ibid; Rava Sukkah ibid] This concept is called Chavut Rami. [Kaf Hachaim 631:16]

[14] Admur ibid

The reason: As in such a case we do not view the upper Sechach as if it has descended below and is resting in the area of space under it [and hence we must invalidate it due to its three Tefach distance and lack of Lavd,]. [Admur ibid]

[15] Admur 631:7; See Admur 612:1; Yuma 80a; Sukkah 5b