Back in the Days, the measures of everything was One. In Antiquity, the four cardinal sciences or the Quadtivium-- Astronomy, Aritmethics, Geometry
and Music, together with the Trivium-- Grammar, Logic, and Rhetoric, made up "the Seven Liberal Arts". Seeing everything as a whole, human body
proportions was put in relation with the dynamics of sound and the dimentions of the Earth and the system of measurements in geometry and arithmetic.
This drawing shows a Monochord, a central instrument in Pythagorean music theory (the three top notes are placed incorrectly)
The ‘chamber tone’ in music for instance was (until Nazi-Germany standardised it to be A=440Hz) calculated to be A=432Hz based on Pythagoras’
calculations and tuning system. This tone is in perfect harmony with the Schumann resonance of 7.83Hz (“the hum of the Earth”). However, some
dedicated the 432Hz frequency with C instead of A, but that’s mere semantics.
This table shows the ratios of Pythagorean music theory
In modern “tone-dynamics”, the distance between the (chromatic) notes of the (12-tone) do-re-mi scale is given by multiplying the given frequency
by the twelfth root of 2. Thus an A# is defined as: 432Hz x 2^(1/12) ≈ 457.688. However, Pythagoras used a system of “perfect fifths” (quints)
at a ratio of 2/3, which match the modern system, but only fairly: “the Pythagorean system would appear to be ideal because of the purity of the
fifths, (but) other intervals, particularly the major third, are so badly out of tune that major chords [may be considered] a dissonance." [Benward &
Saker (2003), Gunther, Leon (2011)].
This table shows the modern root ratios
As an example of how astronomy and music is linked in Pythagorean music theory, look at the ratios below, using some core numbers of classical
astronomy (some might recognise some of these numbers from the Apocalypse of John and the Bible, which is not odd, these numbers reflect the science
of those days):
144,000 : 333.3333 = 432 (classical chamber tone)
144,000 : 444.4444 = 324 (a quart below the chamber tone)
144,000 : 500 = 288 (a quint below chamber tone)
216,000 : 666.6666 = 324
252,000 : 777.7777 = 324
216,000 : 500 = 432
These are only a few examples, I could go on to show the whole scale and put the different frequencies in relation with conceptual core-figures of
classical astronomy and geometry, but I'll let these few figures above speak for themselves.
I find this stuff extremely amazing and gives my every-day life a touch of the cosmos and the divine. The beauty of this is almost too perfect. No
wonder they were more religious back then
edit on 12-1-2014 by Utnapisjtim because: Typo: a missing A, how ironic