Palladio’s seven rooms

The rules it illustrates

Ratios from the musical consonances. Proportion rooms and façades by the same ratios that make musical consonances: 1:2 (octave), 2:3 (fifth), 3:4 (fourth), and their compounds.

The seven most beautiful room shapes. Make rooms round, square, or with a length equal to the diagonal of the square, to a square and a third, a square and a half, a square and two-thirds, or two squares.

The height of a vaulted room. Make the height of a vaulted room the arithmetic, geometric or harmonic mean of its length and breadth.

The square room as a cube. Make a simple square room as high as it is wide, so that it encloses a cube; for oblong rooms the double cube (twice as long as it is wide and high) is satisfactory in almost any circumstances.

The heights of flat, coved and vaulted rooms. If a room is no longer than twice its breadth, make it as high as it is broad; make a coved room higher than a flat one, with a cove a quarter to a fifth of the whole height; take a vaulted room to the crown at half the sum of its length and breadth.

The three means. Between two numbers a and b, find the arithmetic mean (a + b)/2, the geometric mean √(ab) and the harmonic mean 2ab/(a + b); use them to find a third dimension that belongs to the other two.

Linked rooms in a plan. Let the rooms of a house share dimensions, so that the length of one is the breadth of the next and each stands to its neighbours in the ratios of the scale; the whole plan then forms one proportional system.

Where it appears in the book

In the styles Palladian.

In the chapters Proportion and Number.