This is just like a musical chord, in which you have three different notes that combine to create a single harmonious whole. The idea that you need three chords in a note comes from consensus -  most people respond to certain combinations of three notes positively. In this regard, two notes together, even if consonant, sounds incomplete. This was noticed by the ancients and is accepted even in modern music schools. Christians saw this as a natural inclination to respond to beauty, which points to the beauty of God, who is Three Persons.

The building above is the material representation of a large orchestra in which every instrument is identical and they can play only one note. It creates a design as dull and monotonous as that orchestra would sound!

We also discuss the importance of the number eight. Christ is traditionally referred to as the Eighth Day of Creation. Raphael, therefore, used an octagonal design for his painting of the crucifixion. As a principle of beauty, this connects to the octave in music and to octaves in the liturgy. 

Trace a line from the head of an angel, to its feet and then connect the four heads of the figures below, up vertically to the feet of the other angel, and then to its head and back to the beginning. You trace an octagon.

I mention the dissonance of Schoenberg's music. Here is something for you to listent to..urgghh! I once went to a concert at the Barbican concert hall in London where they put a Schoenberg piece in there amongst the rest that I actually paid to listen to. As the first violin stood up and played the note to allow the orchestra to tune (which you will see happen in this video), the person I was with turn to me and quipped: 'The idea with Schoenberg is that everyone makes sure that they are out of tune with that note.'

While we are talking about the bad stuff, here is an example of Bauhaus architecture from the same period. 

Finally, we refer to a design called the Tetractys that is the symbol of cosmic beauty used by the Pythagoreans of ancient Greece. The first four numbers, 1, 2, 3, 4 are represented in a triangle.