...Long
before most commoners had the idea even remotely, he [Pythagoras] was
fully aware that the universe itself is a mass of mathematically ordered
processes going on apparently forever, and that all things are based upon
one pattern but differ in the number of their parts and the magnitude of
their mass. Thus mathematics became involved in weight, in all of our
calculations concerning the orbits of planets, in the seasons and
everything that we know. Wherever there is an orderly sequence there is a
mathematical factor. We number the days of the month, the days of the
week. We number the days of the year and we number the number of years
that make up the great Platonic year. All these things are mathematically
ordered.
Music is
also ordered. Tonal harmonies had to be according to musical modes. There
were seven modes of music corresponding to the planets, each dominated by
mathematics. There are many types of music such as martial music, sacred
music, romantic music, etc. If you could see this music, as Pythagoras
pointed out, it is not simply sound; it is architecture, the music
patterns are forms in space. They are harmonic forms. If you could see
them in their full beauty and magnitude you would see tremendous,
mysterious buildings rising in a mist according to the tone of the music.
It is said that while Beethoven was looking at the skyline of the Alps
once, he realized these peaks were harmonic.
Pythagoras,
following the Egyptians, pointed out that the greatest healing agent in
the whole world is harmony. Sickness is inharmony. It arises from conflict
in function or conflict between the person and the body. It is an
inconsistency, a discordant state resulting from ignorance, perversion, or
the transference of wrong attitudes in the function of the body. To
Pythagoras, health was harmony, and harmony was bringing all things into
order, into proper relationships, and this was possible by means of
mathematics. Mathematics could determine inharmony and gradually transmute
inharmony. It knew what constituted a constructive composition by its
mathematical formula and also what was not a constructive composition by
the asymmetry or discords that were built into it. It was Pythagoras,
therefore, who was the first to decide the intervals which were discordant
and he came to the conclusion that the intervals most likely to be
discordant are the intervals of the even numbers as opposed to the
intervals of the odd numbers, which were the constructive force. This
odd/even pattern goes back to numerology with him.
Pythagoras also
found that beautiful music to honor the gods required a different type of
composition for each of them, so that their mood might be experienced
within the sensitive field of the human magnetic structure in a manner to
convey the quality of the deities themselves. This led immediately to the
gradual forming of these sound patterns into structures and these
structures, in turn, became the basis of sacred architecture. This
architecture was a completely mathematical formula which continued on down
through the Vetruvian School in Rome and for a long time dominated the
construction of buildings in nearly all parts of the world.
If the
individual is left alone, with nothing done to over-influence him--if he
is a natural being, naturally maintained in order, his common sense and
natural, intuitive intention expresses itself with a reasonable degree of
normalcy. Primitive peoples, or those who have not been influenced by
sophistication will nearly always live, think, and build harmonically.
They will be in harmony with the development which they themselves have
attained. But when the architectural aspect comes to be over-influenced by
fashions, discordant circumstances, the determination to have a greater
profit from the structure, and buildings are built not to perfect emotions
but to produce material profit for the builder, then the quality of the
architecture declines...
-Manly P. Hall
ON THE PYTHAGOREAN
PHILOSOPHY OF NUMBERS
Invitation to show: Richard Gere
Photographs
