The Sacred Geometry Used in the Structures
Certain naturally occurring shapes and forms are mysteriously pleasing to the human eye. Examples are the graceful swirl of a nautilus shell, the crystalline structures of the mineral kingdom and the remarkable patterns found in snowflakes and flowers. However, it is not only the subject matter of these forms that captures our attention. Equally important are the proportional arrangements of the individual parts comprising the total form. The same is true with different forms of art such, a good example being classical painting. In Europe during Medieval and Renaissance times a number of painters are known to have laid out the initial design of their paintings according to particular geometric formulas. Sculptors and painters in the Islamic world did the same. The positioning of elements within the frame of a painting was considered as important as the subject matter itself. European classical painters are said to have inherited these positioning formulas from the mystery schools of the Greeks and Arabs who in turn had gotten them from the ancient Egyptians. But where did the Egyptians get this knowledge?
The Egyptians and other cultures of antiquity derived these geometric formulas by keen observation of the natural world. We call this branch of knowledge sacred geometry and find its influence not only in painting but also in certain styles of religious architecture. Paul Devereux discusses this subject:
The formation of matter from energy and the natural motions of the universe, from molecular vibration to the growth of organic forms to the motions of planets, stars, and galaxies are all governed by geometrical configurations of force. This geometry of nature is the essence of the sacred geometry used in the design and construction of so many of the world's ancient sacred shrines. These shrines encode ratios of creation and thereby mirror the universe. Certain shapes found in ancient temples, developed and designed according to the mathematical constants of sacred geometry, actually gather, concentrate and radiate specific modes of vibration. For example, a particular structural geometry and precise directional orientation of a pyramid shape completely alters the electromagnetic properties of the space contained within the pyramid. Three dimensional structure and vibration are absolutely, though mysteriously connected. This is well known to makers of musical instruments. It was also known to the makers of ancient temples. Certain shapes resonate to cosmic frequencies too fine to be registered on the electromagnetic spectrum. The fineness of the vibration is the key to their powerful effect. It is similar to the concept behind homeopathy where the slighter the application the greater the response. (12)
Fundamentally, sacred geometry is simply the ratios of numbers to one another: 1:2, 2:3, 4:5. When such numerical ratios are incorporated into three-dimensional form we have the most graceful and alluring architecture in the world. When those very same ratios are expressed in the domain of sounds they yield the transcendental and transformative music of Indian ragas, Tibetan overtone chanting, Gregorian chanting, African drumming, and the masterwork of Bach, Mozart and other European classical composers. Goethe once said, "Architecture is frozen music." By this statement Goethe was describing the relationship between musical ratios and their application to form and structure.
While not all the forms found in geometry and nature are harmonic in nature, those that we find most beautiful to the eye do indeed adhere to harmonic series. In particular, forms that express ratios based upon the octave (2:1), fourths (4:3), fifths (3:2), and thirds (5:4) create forms that are visually harmonious. The knowledge of how to use these harmonic ratios to create architecture was basic to the ancient mystery schools of Egypt and Greece. Pythagoras, who got his knowledge of these matters from thirty-three years of wandering and studying in Mesopotamia and Egypt, was especially influential in introducing this sacred geometry to the Greeks, and thereby to Western civilization.
One sacred geometrical proportion, known as the Golden Mean or the Golden Section, was immensely important to ancient architects. The Golden Section is a geometric proportion in which the ratio of the whole to the larger part is the same as the ratio of the larger part to the smaller. Thus a:b = b:(a-b). The Golden Section often involves proportions that relate to the ratios found in the major sixth (3:5) and the minor sixth (5:8). Atomic physicists, chemists, crystallographers, biologists, botanists and astronomers have found these same ratios to be the underlying mathematical framework of the universe. The ratios are also present in the human body and mind, perhaps accounting for the profound and transformative effects of sacred architecture and sacred music upon the human organism. An ancient Hindu architectural sutra says "The universe is present in the temple in the form of proportion." Therefore, when you are within a structure fashioned with sacred geometry, you are within a model of the universe. The vibrational quality of sacred space thus brings your body and mind into harmony with the universe.