image from l'Association Chartres, sanctuaire du Monde
It seems that the knowledge of the Golden Mean was greatest at Chartres. It is the largest gothic span that was done up to that date; nobody knows how they calculated it, nobody knows how they had the audacity to think it would stand up, and it has not shifted in seven hundred years. The curvature of the huge interior is based precisely on a five-pointed star and therefore embodies the Golden Mean. The height above the ground has to do with the delayed action of the voice going out and coming back. So, it's the old Sufi saying -- if you ask "Where is God?" the response is, "Here I am." So the whole experience of the chanting rising to the vaulting and returning or coming back down is like the angels replying to you and yet of course it is yourself. It's an amazing experience. You can have that experience if you go very early in the morning and do some personal chanting. Then you can hear this delayed action. It is good to remember that it was constructed for Gregorian chanting; it was not constructed for the organ, or for orchestras; it was constructed for plainchant, and when plainchant is sung there the whole thing suddenly has life; it's staggering. That shape is not only the shape that your body is subtly drawn into, but of the way the sound is returned to you.
-- Keith Critchlow "The Golden Proportion" Parabola 16:4
more on the architecture of Notre-Dame of Chartres
