Students, friends and mental health professionals have asked me how I became interested in researching old crap through books, paintings and by rebuilding vanished forms.
They expect an answer like: “Oh, I’ve always liked history” or some such. That’s not true. I hated history until college.
The real answer is this: In 1986 I read page 101 of Michael Baxandall’s “Painting and Experience in Fifteenth-century Italy” (Oxford). That did it.
OK, that’s an exaggeration. It was actually pages 95-101.
Starting on page 95, Baxandall begins a discussion of the “Rule of Three,” a common way to solve simple commercial math problems. Here’s an explanation by Piero della Francesca:
The Rule of Three says that one has to multiply the thing that one wants to know about by the thing that is dissimilar to it, and one divides the product by the remaining thing…. For example: seven bracci of cloth are worth nine lire; how much will five bracci be worth?
Today we might represent this equation as 7:9 = 5:X, but that’s a fairly modern way to represent the idea. Earlier merchants would line up the parts of the equation like this: 7 9 5 (result).
So why is this a big deal? Many in the merchant culture used this equation every day. It was so familiar that they made jokes that played upon the proportional relationships of numbers.
“The merchants’ geometric proportion was a precise awareness of ratios. It was not a harmonic proportion, of any convention, but it was the means by which a convention of harmonic proportion must be handled,” Baxandall writes.
Such as Leonardo da Vinci’s “Study of the proportion of a head.” Baxandall writes:
…Leonardo is using the Rule of Three for a problem about weights in a balance, and comes up with the four terms 6 8 9 12: it is a very simple sequence that any merchant would be used to. But it is also the sequence of the Pythagorean harmonic scale – tone, diatessaron, diapente, and diapason…. Take four pieces of string, of equal consistency, 6, 8, 9, and 12 inches long, and vibrate them under equal tension. The interval between 6 and 12 is an octave; between 6 and 9 and between 8 and 12 a fifth; between 6 and 8 and between 9 and 12 a fourth; between 8 and 9 a major tone. This is the whole basis of western harmony.
And so I was hooked. Was this true? Do these relationships show up all around us?
— Christopher Schwarz