Wednesday, March 06, 2013

Pythagoras and the Music of the Spheres

These are the musings which began my search for a musical model for astrological aspect. It needs to be clearly noted that the musings here DO NOT lead to a musical model for aspect, but rather they form the basis for a fascinating exploration of “mood” for a person with astrological skills and computer programming knowledge. I have the astrological skills, I lack the programming capacity.

Pythagoras lived in ancient Greece, and is known as the “father of philosophy”. It is sufficient to say that he lacked the tools we have for planetary observation. Among the things he DID know were the positions of the planets by observation, and he could work out their speeds given several consecutive observations.

We know from Ptolemy, that the Sun was by far the most important body in the Zodiac in the ancient world (followed closely by the Moon). The ancient Greeks knew, as we know, that the Sun and the Moon are the only planetary bodies which never exhibit retrograde motion. The secondary motion of the Sun was, therefore, the standard by which everything else could be measured. We know that our Zodiac is the path of the secondary motion of the Sun through the course of a year. We NOW know that this secondary motion of the Sun is OUR BENCHMARK for the motion of our Earth through the heavens. The apparent secondary motion of the Sun is a mirror image of the actual secondary motion of the earth through the heavens. If we want to know where our earth is in the heavens, we need only find the Sun.

So, having established the secondary motion of the Sun as the most important motion in the Zodiac, what did Pythagoras do with that?

Again, we know from Ptolemy that all planets are described in terms of “applying to” the Sun or “separating from” the Sun.

For Mars, Jupiter, and Saturn, the cycle goes like this:
Conjunct Sun
Separating from Sun at a speed slower than solar speed (that is, the speed of separation is slower than solar speed...the Sun and the planet are both moving in the same direction, the planet is slowing down to eventually station).
Station to Retrograde (at the moment of station, the speed of separation equals exactly the speed of the Sun, as the speed of the planet is Zero)
Retrograde to Opposition (the speed of separation increases to a speed greater than Solar speed...the Sun moves forward while the planet moves backward)
Opposite Sun
Applying to the Sun at a speed greater than solar speed.(the Sun is traveling forwards and the planet is traveling backwards to meet it.)
Station to Direct (at the moment of station, the speed of applying aspect is exactly solar speed because the speed of the planet is zero.)
Applying to the Sun at a speed which is less than Solar speed. (both planets travel in the same direction, the Sun travels faster, which closes the gap. The planet moves at its fastest as it nears conjunction.)

To make the above list easier to understand
  1. Conjunction
  2. Separate slower than Sun
  3. Station
  4. Separate faster than Sun
  5. Opposition
  6. Apply faster than Sun
  7. Station
  8. Apply slower than Sun

It is my contention that Pythagoras, knowing these properties of planetary cycles, could calculate and anticipate musical proportions in these speeds.

Using the solar speed as his fundamental note, Pythagoras could readily (with some serious effort) proportion the speed of applying or separating as a musical proportion of solar speed. A planet at station would be seen as in “unison” with the Sun, in opposition it might be seen to be at its highest “interval” above the solar interval. In conjunction, it would be seen at its greatest “interval” below solar speed.

We need to note that a planet is at its greatest apparent speed when it is at conjunction with the Sun,(thus the speed of application is at a minimum) a position which cannot be observed due to the Sun’s light...however it was not beyond the ancient scholars to map the acceleration curve of the planet in question, and plot a projected speed and date for such a conjunction, and plot the expected deceleration curve for its re-appearance on the other side of the Sun.

With experience and observation, it is quite plausible that Pythagoras could calculate the “music of the spheres” and describe their ascending and descending scales as he saw the relative differences in their speeds of application and separation.

For Mercury and Venus, the cycle has extra parts.
  1. Conjunct
  2. Separate FASTER than Sun
  3. Maximum elongation (where the planet’s speed equals that of the Sun)
  4. Apply slower than Sun
  5. Station Retrograde
  6. Apply faster than the Sun
  7. Conjunct 
  8. Separate faster than the Sun
  9. Station direct
  10. Separate slower than the Sun
  11. Maximum elongation
  12. Apply FASTER than the Sun

You will notice that steps 3 through 11 are the same as for the outer planets, only their roles are inverted: they first apply, then separate from the Sun.

Anyway, the permutations and combinations which are possible from this model are mind-boggling. Applying musical mathematics to these proportions and establishing “intervals” and “chords” among the planets is a daunting but intriguing exercise, one which requires a computer, a programmer, and a lot of time....