Middos, Chapter 4, Mishnah 4. This chapter is devoted to the Heichal and the structures built around it, and our mishnah continues the description of the ta'im, the cells that surrounded the Heichal on three levels. Having learned how many cells stood on each level and in each direction, the mishnah now tells us something surprising: the cells were not all the same size. The higher the level, the wider the room.
The reason is a matter of construction. The wall of the Heichal was not a straight vertical face from bottom to top. At each level it was set back, drawn inward by one amah, and that setback created a ledge running along the wall. The ledge served a purpose: the ceiling beams of the level below rested upon it. And once the wall had stepped back by an amah, the room built above that ledge gained an extra amah of floor space. In other words, every ceiling in this structure was wider than the room beneath it, and every room was as wide as the ceiling on which it stood.
The three measurements
"Hatachtonah chamisha": the cells of the bottom level were five amot wide. Above them the wall of the Heichal was indented one amah, and that ledge carried the beams that formed the ceiling of those lower cells.
"Veroved shisha": the ledge measured six amot. It did double duty, serving from below as the roof over the cells of the bottom row and from above as the surface on which the next row was built. "Ve'emtza'it shisha": the middle cells stood on that six amah surface, and so they too came to six amot in width.
"Veroved sheva": at this height the wall of the Heichal drew back a further amah, so the next ledge widened to seven amot, capping the middle row of cells and carrying the row above it. "Veha'elyonah sheva": the topmost cells, resting on that seven amah surface, measured seven amot across.
The source in the pasuk
The mishnah does not leave these numbers as a bare tradition. It roots them in Scripture. "Shene'emar", as it is stated: "hayatzia hatachtonah", the lowest story, "chamesh ba'amah rochbah", five amot in its width; "vehatichonah", the middle one, "shesh ba'amah", six; "vehashlishit", the third, "sheva ba'amah rochbah", seven. The verse in Melachim is speaking of the chambers ringing the walls of the first Beit Hamikdash, and it records exactly this rising sequence of widths. The ta'im of the second Beit Hamikdash were built on the same plan, and the pasuk yields not only the three figures but also the stepped wall that produces them.