These two folding illustrations show how space
might actually look, like folded papers, by applying theories of intervallic
A folding in half equals the octave.
A folding in thirds equals the fifth.
A folding in fifths equals the
Since multiplying by its powers does not affect the placement of the tones,
there are basically only eight concave and eight convex folds within an octave.
All the higher intervals of relative pitch such as , are clustered around all
intervals for D.
The isometric grid formed by the folds in the upper right are obviously
formed by folding diagonally across rather than vertically as in the other
drawing. The limits of the folding into ever smaller diagonals is always six.
The isometric lines show the generation of the familiar axes of multiples
of 2, 3 and 5 and their combinations.
Also each fold line (darker) measures
alternatively a diagonal and a side of ever diminishing squares.
Web Pages Updated by: Kristi Borst. Ad·Mark·Com