a common space for harmonic overtones Cyan Blue: "12 TET"
(twelve-tone equal temperament), which has been dominating our
music culture for the last 100 years or so. The even division
(like hours of a clock) of the octave circle looks extremely
pleasant to the eye but what is visually pleasant may not be
harmonic to the ears - just think of the paper A format which is
very harmonic to the eyes but in music the proportion 1:
squareroot 2 is extremely dissonant. The axises are found at
0-100-200-300-... etc. cent. The Point is that the reference of
purity for the ears (and music theorists) and overtone freaks
naturally are the intervals from the harmonic series (systemized
in 'just tuning' -green) and the thirds and sixths of 12-TET are
far from pure. We have actually made a musical convention which
has sacrificed the experience of just thirds and sixths. Magenta
Red: Pythagorean tuning, generated by perfect fifth intervals (6
up and 5 down from the fundamantal). It is symmetrical (apart
from the tritone) around