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Planetary Concordance

Finding Harmony Among the Planets' Motions

Assuming that the acquired data of planet positions and velocities is accurate, the information below shows the relationships between the motions of the planets such that the angular velocities are in proportions which correspond to musical intervals.  Actually, I'm a bit unsure about the accuracy because I'm finding that the positions that I calculated aren't in agreement with the ones in the online ephemeris with JPL.  


Notice how Saturn's position doesn't seem to be sitting on its own orbit; the outermost circle doesn't touch the red dot nearby.  The orbit trajectory is from Horizons on-line, whereas the particular moment for Saturn comes from the DE-406 off-line.


Ephemeris Report:
Date:12/25/2021 10:19:25
Julian Day: 2459574.180150463
Linear Units:Astronomical Units
Angular Units:Radians

  Velocity (x,y,z) Position (x,y,z) Angular Velocity (rad/day) Frequency (Hz)
Mercury (0.0097, 0.0224, 0.011) (0.3248, -0.1745, -0.1279) 0.0671 12930.235
Venus (-0.0202, 22.5271, 0.0017) (0.0517, 0.6587, 0.2927) 0.0282 5437.5374
Earth (-0.0174, -0.0011, -17.0089) (-0.0736, 0.9035, 0.3918) 0.0178 3425.0604
Mars (0.0116, -0.0066, -0.0033) (-0.9502, -1.1194, -0.4879) 0.0089 1714.102
Jupiter (0.0027, 0.0068, 0.0028) (4.6327, -1.648, -0.8192) 0.0016 302.9792
Saturn (0.0037, 0.0037, 0.0014) (6.9283, -6.4423, -2.9594) 0.00055 104.1623

Planetary Concordances: (within tolerance +/-0.1%):

Between Mercury and Venus, one octave plus one minor third.
Between Mercury and Earth, one octave plus one major seventh.
Between Mercury and Mars, 2 octaves plus one major seventh.
Between Mercury and Jupiter, 5 octaves plus one perfect fourth.
Between Venus and Earth, one minor sixth.
Between Venus and Mars, one octave plus one minor sixth.
Between Venus and Jupiter, 4 octaves plus one major second.
Between Earth and Mars, one octave.
Between Earth and Jupiter, 3 octaves plus one tritone.
Between Mars and Jupiter, 2 octaves plus one tritone.



Categories : mathematical, music

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