A Description of the Theory of Harmony and Proportion in Renaissance Architecture

Architectural Principles in the Age of Humanism by Rudolph Wittkower

Here is a book that is, in my opinion, an excellent source for people who are interested in understanding the basis of harmony and proportion. In the past, I have posted numerous examples of buildings that use traditional harmony and proportion, and contrasted them with the ugliness of modern architectural design (e.g. Monotony and Cacophony are the Twin Principles of Modern Design - Whatever Happened to Harmony?) As well as focusing in detail on the mathematical proportions used and described by men like Alberti and Palladio in architectural textbooks, there is a lot of context provided, and the author describes well the philosophical ideas behind the movement. 

Rudolph Wittkower (1901-71) was a German art historian who went to London when the Nazis came to power, and subsequently taught at the University of London. In this book, first published in 1949 with multiple subsequent editions, he contrasts the approach of architects from the High Renaissance period, who relied largely on musical theory for their mathematics, with those of the ancient Greek and the medieval period, the latter relying on geometric constructions based upon the triangle, the square, and the pentagon. As such, it is a good resource for someone who wishes to get a broad introduction to the subject. He also describes how the developing thought of the Enlightenment and its new understanding of what beauty is contributed to the gradual abandonment of the use of mathematically derived harmony and proportion, starting at the end of the 18th-century, and culminating in its almost total rejection in architectural schools by the mid-20th century.

As well as the main text, there are four appendices with talks given by the author, the last of which is particularly is recommended reading for a concise overview of the subject.

Those who are interested in going more deeply into the subject might be interested in taking my course, The Mathematics of Beauty which can be taken online, for audit or for credit, from www.Pontifex.University

Nostell Priory in England, built in the Palladian style, in Nostell near Wakefield in Yorkshire in 1733.