The intimidating-looking formula on the right is the ‘room name + spatial arrangement’ description, with the addition of numerals that the floor area of each room.
For the sake of convenience, let us assume that the building is oriented so that the facade (the hiroma or omote side) faces south, though this information is not carried in the symbolic descriptions, as not relevant.
Starting on the left, we have first a capital ‘E’, for an engawa running the full width of the building; the width of this space is not described.
From the next part of the formula we can determine that there are six rooms: a rear zashiki with associated storage or alcoves, another zashiki, a facade-side engawa or other liminal space, a bedroom (nando), a dining-kitchen (daidoko), and the main room (omote).
Next, the ‘W’ before the plus sign indicates that there is a full-width earth-floored utility area (doma or niwa) at the opposite end of the main building to the full-width engawa (‘E’).
The two horizontal lines represent partition lines: the top line terminates at the ‘W’ and the bottom line terminates at the ‘O’ (which should be lower case); from the positions of the room symbols relative to these lines we can determine that there is a ‘column’ of three rooms non-adjacent to the niwa (the rear zashiki with rear storage/alcove, the ‘middle’ zashiki, and front en space), that the omote runs from this column to the niwa, that the combined length of nando and daidoko is equal to that of the omote, and that the daidoko is adjacent to the niwa but the nando is not, being between the daidoko and the rear zashiki.
The floor area of each room, measured in tatami mats, is indicated by the number suffixed to it. So the rear zashiki ‘z’ is ten tatami mats in area (jū-jо̄ 10帖), and so on.
Now for the difficult part: reconstructing the dimensions (length and width) of each room from the given floor areas. Let’s start from the column of three rooms on the left, the combined width of which must equal the width of the building, 5.5 ken.
We know that each zashiki is 10 tatami mats (10 jо̄) in floor area, and that the en space is 5 jо̄ in area. Keep in mind that a tatami mat is 1 ken (1.818m) long and 0.5 ken (0.909m) wide. We know that the rear zashiki has a storage closet (oshi-ire 押入), decorative alcove (toko 床), or the like at its rear, as indicated by the small ‘s’ above the ‘z10’. The depth (the width or transverse dimension) of this ‘s’ space is not given, but let’s assume that it is the standard 0.5 ken (0.909m). This leaves us with 5 ken of building width (oku-yuki 奥行, lit. ‘rear going’) to distribute across the two zashiki and the en space. Assuming that the layout is regular (seikei 整形) and therefore the transverse (vertical) partitions of these three rooms are aligned, it makes sense to also assume that each room is 2.5 ken (2.5 tatami lengths or 5 tatami widths) long; by dividing this length into the area of each room and then dividing the result by 2, we can obtain the widths of the rooms with reasonable confidence that they are correct. For each zashiki:
(10 jо̄ / 2.5 ken) / 2 = 2 ken
For the en space:
(5 jо̄ / 2.5 ken) / 2 = 1 ken
So the dimensions of the two 10-mat zashiki are 5 tatami widths by 2 tatami lengths, i.e. 2.5 x 2 ken, and the en space is 5 tatami widths by 1 tatami length, i.e. 2.5 x 1 ken.
Next, we know that the bedroom (nando) and kitchen (daidoko) are both 10 tatami mats in area, but again, assuming the layout is regular (seikei) and therefore that the longitudinal (horizontal) partition boundary between the nando/daidokoro and the omote is aligned with that between the two zashiki, the width of these rooms must be the same as that of the rear zashiki (2 ken) and its ‘storage’ space (0.5 ken) combined, i.e. 2.5 ken. Knowing the width (2.5 ken) and the areas (10 tatami mats or 10 jо̄ each) of the nando and daidoko, we can calculate their length by dividing the area (10 jо̄) by the width (2.5 ken, i.e. 5 tatami widths), which gives us 2 ken, or two tatami lengths. Therefore the nando and daidoko are both 2 ken long by 2.5 ken wide.
We know that the omote is 24 jо̄ in area. Its length must equal that of the combined length of the nando and daidoko, i.e. 2 + 2 = 4 ken, and its width must equal that of the combined zashiki and engawa space, i.e. 2 + 1 = 3 ken. Doing the area calculation
2(4 ken x 3 ken) = 24 jо̄
confirms that that these dimensions are correct.
As mentioned, there is a full-width engawa (‘E’) at one end of the main building, and an earth-floored utility area (niwa, ‘W’) at the other end. We know that, as the overall width of the building is 5.5 ken, these spaces must also be 5.5 ken in width, but their length is not given. We do know, however, the overall length of the main building (8 ken), and from our calculations of the room dimensions and orientations we also know that the total length of the rear zashiki, nando, and daidoko, and the total length of the front zashiki/en and omote: both sum to 6.5 ken. By subtracting this length from the overall length of the main building, we obtain a leftover length of 8 ken - 6.5 ken = 1.5 ken. It is impossible to know what share of this 1.5 ken is apportioned to the engawa and what to the niwa, but it is reasonable to assume a standard 0.5 ken for the engawa, leaving 1 ken for the niwa.
Next is the separate niwa building, the ‘W’ in ‘TH 8 x 5.5 + W 3 x 6’. We know from the ‘3 x 6’ that this building is 3 ken long and 6 ken wide, for a total area of 2(3 x 6) = 36 jо̄ (or equivalent, since this area is earth-floored so the tatami figure here is ‘virtual’). Comparing the width of the niwa building with that of the main building, we see that the former is 0.5 ken wider than the latter; whether because the distance between the external structural wall/posts lines themselves are more widely spaced, or because a 0.5 ken under-eave space to either the front or rear of the niwa is enclosed, we cannot tell.
Finally the, ‘m8’ after the ‘W’ indicates that within the niwa building there is a stable (maya) or similar (‘m’) and that it is 8 jо̄ in area, though its exact position within the niwa is not captured by the symbolic description.