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— The
Octave As Fractal Numeric Object — The Basic Symmetry of
I Ching
2005 © B.Svarog |
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This whole system
impresses with a perfect regularity‚ showing for any unprejudiced glance a
certificate of absolute mathematical strictness of the quint
system. It does not matter, that in the musical theory an appearance of commatic changed intervals, has served only for a greater
proof of "impracticability" of the quint
build more than three centuries. Music, as it is not
difficult to make sure, by its nature is close "to mothers" - subconscious,
laws of number and time‚ and nor to
a small extent is a result of agreements (convention) or collection of
arbitrary rules. It is another thing, that the internal need, developed by the European musical culture, was going
contrary with objective existing progressions of "real
harmony" or, better to say, only the "relations of I order"
were significant for its musical practice - namely those assigned by the first 12 steps. A comma was perceived as
undesirable ("13-th" in the quint circle)
and stimulated searches for a closed musical system (there the end in
accuracy may be coincided with the beginning). "To curve" was in the nature of
an Octave, the rationalism of the XVII century decided to unbend it. An utterance of Àlister Crawly is very
much to the point here: «For the
blindness to beauties and wonders of the Universe the mankind is obliged to their illusion
of rectilinearity". The dizzy success of temperation - of whole European
classics beginning from J.-S. Bach - has led to a
"partial àmnesia" about the
nature of numeric roots of music. "Having completely leveled in
rights" twelve intervals - simply by giving
them a value |
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