I've recently had a discussion with other furnituremakers and woodworkers about the "golden mean" and "golden rectangle." I'm still looking, but I've been led to understand that the concept is one that was superimposed on designs of earlier times by Victorian English writers seeking to explain what they were seeing.
Now RATIOS...
If you look at Greek architecture, for example, there are many ratios evident in the design of a single structure. Colonial furniture design was often pretty much a series of ratios given to a journeyman by a master. For example, a highboy might be determined to be as tall as the height of the top of the windows in the room it was destined for. Then the ratio of height to width would be stated, the ratio of width to depth, and so on. Drawers might be similarly scaled. An essentially illiterate journeyman could proceed with this information. Field measurements could be carried back to the shop on a stick. When I was doing my first layout work in the 70's, my boss brought me measurements that way, not numbers off of a tape and written on paper.
I've begun to use dividers and "sectors" to lay out furniture. YEARS ago, I was taught to do all my layout using "story sticks," and still do that. NONE of the craftsmen (or the owner) in the shop where I now work part-time/semi-retired knows how to do this, so I get much of the new layout work.
A "sector" is a simple device used in many building trades. In my situation, mine is a shop-made device. I chose two stable and straight (I made 'em that way) maple sticks about 1 x 1.5 inches and maybe two feet long. Can't recall--not important. The two are joined at one end by a brass hinge screwed into the end grain, so they open and close like alligator jaws. Along the length of the two sticks are incised lines squared around each piece, and stepped off equally along the length with dividers starting at the pivot point of the hinge. I think my first has thirteen marks, done just because. Thirteen colonies maybe. Whatever. I marked each line with Arabic numbers, but a pic of an old one had the numbers in Roman numerals, probably because they could be whacked into the wood with a chisel. All straight lines. Quick. Time is now, and was then, money.
So let's say I want a 4:5 ratio, and I know the longest line. I open the sector and place the marks for either 5 or 10 (doubling 5) at the ends of that line. I then use my dividers to pick up the length across the sector at 4 (or 8 if I used a double). The dividers carry that measurement to my layout or directly to the stock being worked. A paperless shop at a time when paper was too expensive to use and toss.
Since starting to explore this, I've made longer sectors to measure longer lines, and have made my own dividers from wood, using metal points. Accuracy is repeatable and limited only by the craftsman's care and the sharpness of the points and width of the lines marked out with blades. Only weird thing is doing this pre-tape measure stuff in a shop that's full of rulers. Before about 1830 much work was done this way. No need to understand fractions, adding, subtracting, dividing... What happened about 1830? Machines. Craftsmen started to make the shift to being machine operators, and machines demanded numerical measurements. Workers had to be educated differently to use arithmetic.
So anyway, the Golden Whatever is an interesting academic exercise, but I'm finding it much more interesting to work with ratios, and using things like ratios in the human body or the Fibonacci sequence. None of it requires a tape or a calculator. Wish I'd started this journey when I was a lot younger.
This is all pretty new to me, and pretty much based on my opinion. Ignorance is the mother if invention sometimes. Toss it if you want. It's worth what I've charged you, I expect. Just my new/old way of viewing my work. I'm wondering what sort of academic discussions can come of examining original guns with an eye to exploring ratios. Probably already been done somewhere, huh.
