When I look at most buildings designed in the traditional manner - this would be most built before the Second World War - it strikes me that the goal of the architect in his design is beauty, and that he seeks visual harmony through an appropriate proportioning of the parts in their different magnitudes. Generally, these were deliberately chosen to conform to a mathematical pattern whcih was believed to correspond to the pattern of the beauty of the cosmos, and which in turn participates in the pattern of divine beauty.In contrast, when I look at modern buildings built since roughly the Second World War, I discern just two simple guiding principles of architectural design. These are even spacing and random spacing. Neither, in my opinion, is a principle of beauty. The first, even spacing, generates visual monotony. The second, random spacing, generates visual cacophony.Harmony, monotony, and cacophony are the good, the bad, and the ugly of architectural form.The traditional design principle has its origins in the mathematics of the ancient Greeks, and in one form or another was used, unquestioned, as the standard mode of design in art and architecture in the West until the period around the end of the 19th century. At that point, artists, architects and musical composers began, quite deliberately, to reject the tradition, and with it all traditional forms. By the mid-20th century, it had not only been rejected but, with very few exceptions, all but forgotten.Does this matter? I think so, because I think beauty matters. The test for each of us to decide if it matters is to consider the buildings we would prefer to see, live and work in.Consider first this Georgian house built in 17th century England.What we see here is a classic manifestation of visual harmony in which, like a musical chord which is comprised of three different notes, each story has a different magnitude, and the combination is, to my eye at least, pleasing. That certainly was the intention of the architect in designing it this way.Contrast this with the following more recent building, in which every story is evenly spaced.I would characterize this using another musical analogy. It is a visual manifestation of a string quartet in which four identical violins play nothing but the continuous sounding of one note. However, clean and pure that note might be, however perfectly rendered, it quickly gets dull to listen to. It is, quite literally, monotonous.The building below is built on the same design principle but on a grander scale, so that the result is the visual equivalent of a vast Mahler-sized orchestra, but once again, consisting of only one instrument, say 100 violins, all playing the same note. It doesn’t matter how many times you replicate that note, it is still monotonous. If that monotone is blasted at us through a megaphone, which is the visual equivalent of what is happening here, it gets worse, because we cannot escape it, and it obliterates all else around it that might be beautiful. In this case, it becomes offensive.Here’s another example displaying a different design principle. Look at this building below.First of all, can you guess what its purpose is?Believe it or not, it’s a church. This random design is directed by uninformed intuition, the visual equivalent of cacophony. It is like the effect you would get if you had an orchestra comprised of many different instruments with each musician just playing notes randomly, and completely without any regard for what the others are playing. Here’s another church in the same vein.Does this look like a building made to house the worship of God expressed through the beauty of chant and polyphony? The piece of music that best corresponds to this design that I can think of is Stockhausen’s absurd Helicopter String Quartet.The traditional mathematics of beauty, in contrast, is an authentic analysis of the common human perception of the world around us, and is richer and more varied as a result. Furthermore, it is the basis upon which a Christian architecture is built. The mathematics of harmony and proportion came from classical sources, but was developed and enriched, just as instrumental music itself developed in the context of a Christian culture.The more that we try to be different, as a deliberate statement of originality, the more, it seems that everything looks the same. The ugliness of so much modern architecture, and art and music for that matter, confirms for me the truth of the principle that there is no order outside God’s order, only disorder.For those who want to know more about the mathematics of beauty, you can read my book,or for an even more detailed account, take the online class offered at www.Pontifex.University ’s Master of Sacred Arts program called The Mathematics of Beauty.