The Rule of Three 
THE BEAUTIFUL N ECESSITY : 
BEING ESSAYS 
UI’ON ARCHITECTURAL ESTHETICS. 
THE RULE OF THREE . 1 
\AI ALTER PATER has said that all art 
V V constantly aspires towards the condition 
of music. This is perhaps because all art 
has its root in number, being in one of 
its aspects only a system of harmonious 
numerical ratios, of which music is the direct 
sensuous expression. Everything in its last 
and mystic symbol, popularly known as 
Solomon’s Seal, or the Shield of David. 
It appears that this, the equilateral triangle, 
taken singly, doubled, and in the form of 
the regular hexagon, is one of nature’s arche¬ 
types, or universal patterns, for it occurs in 
the snow-crystal, in the bee’s cell, in flower 
forms without number, and it can be traced, 
—though more obscurely—in insect and 
animal structure, and even in the body of 
man himself. 
It is not surprising that a figure of such 
significance in nature is of importance also in 
analysis is number; and geometry is the 
manifestation of number in space. The 
ancient Pythagorean precept, and the latest 
generalization of modern science meet here 
on common ground. 
When ideas enter phenomenal life they 
assume perforce a threefold aspect. They 
appear as cause operation and effect ; or 
they take on the three dimensions of length 
breadth and thickness. Of this number 
three, an equilateral triangle, the simplest of 
symmetrical plane figures, is the geometrical 
equivalent; and if this pair, one of the two 
symbolizing time, and the other symbolizing 
space, be represented by means of intersect¬ 
ing equilateral triangles, forming a hexagram, 
the resultant figure is that ancient, beautiful, 
i This is the first of a series of six essays by Mr. Bragdon, in which 
are elaborated those theories concerning art generally and architectural 
art in particular as set forth in his notable speech : “Mysticism and 
Architecture,” delivered before the Third Annual Convention of the 
Architectural League of America. The papers will appear in con¬ 
secutive numbers of House and Garden. 
art, for art is “ idealized creation,”—nature 
carried to a higher power by reason of its 
passage through a human consciousness. 
According to Schopenhauer, it is possible to 
resolve all music into two chords, the 
dominant seventh, and the tonic; one of 
longing and striving, and the other of rest and 
fulfilment. These are to be conceived of as 
the interlaced equilateral triangles of harmony, 
for three is the least number of notes of 
which a chord can be composed, as it is the 
least number of lines with which it is possible 
to enclose a space. The hexagram of color 
is more familiar consisting, as it does, of the 
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