A while back I noticed that a number of architect/builder’s sectors shown in manuscripts from the Renaissance era had the segmentation laid out along a diagonal line rather than along the inside edge of the legs. At first I thought this would limit the tool’s ability to directly (and therefore quickly) establish a whole number value across the width of a board. On reflection, I realized that you could simply transfer the wood’s width with witchcraft. I mean with a pair of dividers. (I must remember to turn off the automatic alliteration function in this word processor).
Let’s give this upgraded sector a shot, again using that handy little book as a product-placement prop.
Set your dividers to the width of the book.
Then spread the sector’s legs until the divider points fall on where the diagonal line crosses the sixth segment. If you make the sector in wood (you can use an old folding rule or make one from scratch) you can drill tiny pin holes at these locations to positively locate the divider points.
From here you’ll open up the dividers to span between the ninth intersections and then test the spread against the height of the book to discover the 6:9 (2:3) harmonic relationship: