Some time back I began studying the proportional forms common in the pre-industrial era. So many interesting things can be found when one looks beyond the inches and feet on a ruler.
Vitruvius laid out an amazingly broad series of proportions based on the human shape. Before him, Pythagoras developed a proportional system based on music.
Given the abundance of proportions described above, this third set is no less important for it’s lack in variety. There are only two ratios of Ecclesiastical Proportion. The first is drawn from Biblical Sources. Exodus, Chapter 25 verse 10 (King James) reads: “And they shall make an ark of shittim wood: two cubits and a half shall be the length thereof, and a cubit and a half the breadth thereof, and a cubit and a half the height thereof.”
In modern dimensioning, this would be a wooden chest that is 27″ high, 27″ wide, and 45″ long. As a whole number proportion two and a half to one and a half is 5:3. For many years it was believed that Churches were designed to this proportion. Being in confluence with the Vitruvian Perfect Number Proportion of 10:6, it is not difficult for this estimation to be readily accepted.
Colin Joseph Dudley performed an empirical study, however, and came to find that the proportion of church buildings and their contents was not, in fact, 5:3. In studying the architecture of two particular churches in England which were constructed and expanded between the 11th and 14th centuries, he discovered quite a different proportion was used in their design and construction.
In argument against 10 and 16 being perfect numbers, St Augustine of Hippo instead argued that 6 was indeed the perfect number. This refutation of Vitruvius’ assertions was made in “The City of God” written in the opening years of the Fifth Century. While confirming that 6 was indeed the perfect number, and 12 the double interval only required to assure certainty (while echoing the number of days in which the world was created and the number of disciples who followed Jesus), he did make one additional mention of mathematical interest. Augustine paraphrased Euclid in stating “In divining the square root of two, we may find God.”
While the square root of two is the solution that stymied Pythagoras’ Theorem of Right Triangles, a whole number expression of the irrational number that begins as 1.414 is readily handy. Dudley confirmed that the estimation of 7/5 was used to design the Cathedrals of Canterbury and Petersborough in England. Seven divided by five is 1.4, a convenient short hand for the square root of two. This proportion, when looked for is more readily applicable to Ecclesiastical Structures and Furnishings than the “almost” 2:3 or 3:5 believed so universal.
So yes, I am looking forward to George Walker and Jim Tolpin’s new book, “By Hand and By Eye.” I’d really like to see how much of my own research matches these two masters of design.
Later this week, we’ll be discussing cottonwood and how it works under the tool edge.