Wednesday, December 11, 2013

Nelson Mandela: a grand trine put to good use!!

An exercise in rectification using musical harmonics.

There are many ways to rectify the chart of a famous person, and this is what I came up with using the musical harmonics for Venus and Mercury when trying to rectify the chart of the great leader, statesman, and voice for change, Mr Nelson Mandela.

While a glance at the musical harmonics here revels nothing terribly exciting, there is more here than meets the eye.

Firstly, the axial harmonics (the left column) have EVERY planetary relationship with the Sun exactly resonant on some axial harmonic level (this is quite unusual, Mozart is the only other chart I have managed this feature with).

Now, those axial harmonics show us some interesting facts about the expanded aspects of Venus and Mercury (the ones we get by multiplying the difference between Sun and Venus by 4 and the distance between Sun and Mercury by 8, with proper reduction of their orbs).

We will notice that Venus has a “natural” harmonic value of 2/11, while its natural musical harmonic value is 6, meaning it is close to 1/6 = 2/12. When we multiply 2/12 by 4 we get 2/3 which is axial harmonic shorthand for the trine aspect. Now, when we multiplied this aspect to get the trine, we had to reduce the orb, so that the expanded musical harmonic for Venus reads “Major 6th, None” meaning there would not be a trinary relationship there if we were to consider this aspect in isolation. However, let’s take a closer look at what else is in a trinary relationship with that Sun. We will notice that both the Moon of this chart and it’s ascendant have a trinary relationship with this Sun, and that the Ascendant and Moon also share a trinary relationship, so the Sun is involved in a grand trine....this boosts the orb of our aspect by a factor of 3, and allows Venus to exert a virtual trine from its “natural” 1/6 position.

By the way, when I say “natural” with respect to Venus and Mercury, I am talking about the relationship which exists in the regular way we calculate harmonics. The expanded or “virtual” values for these planets are derived by treating their maximum possible longitude from the Sun as if it were an “opposition” and working from there. I give Venus a Maximum of 45 degrees, because the highest it gets is a bit over 46, and the lowest it gets is 45; and I give Mercury a max of 22.5 degrees because its actual maximum elongations (Highest is 27, lowest is 18) are symmetrical to this point, and it is a perfect division by 8 of the 180 degree half circle.

Back to this chart, and this time we’ll look at Mercury. Again, on the expanded aspect we see the words “Octave, None” which would say that Mercury, in isolation, has no resonant aspect with the Sun. The word “octave” tells us that it is very near to Mercury’s expanded  opposition point, but not close enough for the relationship to be considered resonant. Remember that in musical astrology, we consider conjunction and opposition to be equivalent aspects, and together they share the number 1. Mercury is tightly conjoined to Saturn, effectively doubling it’s orb for first harmonic involvement. This is plenty wide enough to bring Mercury’s “virtual opposition” into play.

To say that Mr Mandela is a great orator is an understatement, a strong relationship between Mercury and the Sun would therefore be implied in his chart. This strong Mercury/Sun relationship also brings Saturn’s pacement into higher profile with his Sun.

Regardless of what else we may think of Mr Mandela, his oratory style is always measured and disciplined (Saturnine traits), and his life was marked by much forbearance and suffering, such forbearance being rewarded in the long term so that he became a great statesman for his people. (Again Saturnine traits). When we think of revolutionaries, we look for charts with strong Uranus positions and square aspects, rarely do we see trines, but then rarely is a revolutionary leader actually able to broker such a lasting peace as Mandela did, and rarely, if ever, has a peace been brokered in the spirit of reconciliation after the manner which Mr Mandela has accomplished.

To me Mr Mandela represents the very best use of the trine energy. The trine is about harmony rather than about inertia, it is about harmonious action rather than being about ease. There was nothing easy about Mr Mandela’s lot, and so the Sun/Moon trine drove him to sue for harmony, and his Saturnine nature understood that harmony was not going to come easily.

In terms of difficult aspects, Mr Mandela has few, and those are largely based on this rectification (which may or may not be accurate, though the Mercury/Venus expansions in this chart are telling, and the only way to get enough oomph for the “virtual trine” from  Sun to Venus is to have this ascendant). 

The tension between Jupiter and Saturn tells us he is well aware of the difficult balance between progress and tradition. The square between Ascendant and MC shows a recognition of the tension between spiritual and material ideals. Mandela was not oblivious to the difficulty of the path he was trying to forge, but  he managed to find creative solutions for those tensions rather than allow the tension to dominate.

In more general terms, this chart is lacking the appeal to “cookbook astrology” that some other rectifications have, but a Pisces rising (quite close to 0 Aries), Sag MC, with the NN very close to that MC, has enough of the “potential world changer” about it to allow for a more nuanced interpretation of his other house placements. For instance, a 5th house Cancer Sun with both Jupiter and Pluto sharing the sign lends great gravity to his personality, and a certain amount of fun or good humor about his lot in life. 

Uranus in 12 suggests that his genius lay in a realm not easily accessible to him materially, and therefore requires either a spiritual approach or a global approach for him to access it. Uranus in Aquarius suggests his genius lies in interpreting “group mind”, and the musical association between Saturn, Mercury, and the Sun suggest that he has the ability to make use of such genius once he has found access to it.

Part of Fortune joining with his 9th house Moon, and part of Spirit with his 5th house Sun suggest that he was both lucky (Fortuna, Moon, Nine) and willful (Spirit, Sun, Five) which are a good combination in a man who would be a world leader. The grand trine which makes that possible (Asc, Sun, Moon) suggests that Mr Mandela is about harmony and reconciliation above and beyond any other motivating factor, and in the bitterly polarized world in which he lived, such an example was and is priceless.

Venus joining the South Node and the IC in 4, suggests he would always be charming, and that his purpose in this incarnation was to make a difference in the world, which he did in a very big way. Venus’ musical “trine” with his Sun adds a layer to that charm, bringing the gravity of Jupiter/Pluto and the charm of Venus together with his Sun, along with the stability of Mercury/Saturn to make him a far more irresistible force for change than might otherwise be perceived.

I short, the gravity of this man’s chart is not easily seen on the surface, but with a little work, this chart fits the remarkable life of the man who lived it.

Tuesday, October 08, 2013

Discount Offer

I have not raised my prices in many years, and my costs have gone though the roof,  so I have decided to rise my prices, but to make the transition a bit easier, I have decided to offer a significant discount that actually brings my fee down until the end of the month. So beat the price hike, do yourself a favor, and book a reading BEFORE October 31!!

Saturday, October 05, 2013

Harmonic Impasse

I figure its high time I looked at this impasse, which has shut down the US government, in astrological terms.

The chart I am using is the 1789 ingress chart , March 19, 1789, 11:23pm NY, NY

At first glance there is “nothing new here”, however the harmonics tell a different story.

The trine from Transit Saturn to the Pisces stellium looks nice enough, and should bode well, on its own, for stability. It is wide of trine for natal Saturn, but the stellium there drags natal Saturn into the hurley-burley of Venus/Mercury/Mars in Pisces.
So a Saturn trine, time to prepare, revamp get energized and get ready for the coming Saturn Square...right? well not quite.....

Our dear friends, Pluto and Uranus have been duking it out in Square formation for a while.....this is a real heavy hitter, and is the “dark aspect” which has overseen an escalation of tension and violence.....every piece of nastiness in the last year or so has been blamed on these two, it is a real shame we don’t get to look at these “big hitters” as agents of change rather than some foreboding threat...... however, be that as it may, the heavy hitters with a bad rep have elbowed their way into the otherwise peaceful Saturn trine pattern...(actually, Saturn has waked in on their brawl, so his otherwise gentle scheduled reminder to get things in order finds him presiding over a prize fight)...they are still square with each other, square being the kind of tension and difficulty which makes humans great.....its a pity we allow ourselves to be manipulated by media and political forces into fighting each other rather than overcoming obstacles together....but again I digress.

Saturn, on its way to making a useful trine aspect, has encountered the “big hitters” by making a 6th “Overtone Harmonic” relationship (an overtone harmonic is a harmonic division of the circle described by axes rather than by points) which is known to the rest of astrology as the 12th harmonic. Saturn makes a sextile (3rd OH) with Pluto and an “inconjunct” aspect (6th OH) with Uranus.

Pluto makes a sextile aspect with the Pisces stellium (again, a fairly peaceful relationship) while Uranus makes a semi-sextile with that same stellium (less peaceful, particularly when a brawl is happening).
In short, the square between Pluto and Uranus successfully divides the trine aspect (3rd OH) into a sextile and a semi-sextile, invoking the 6th OH (12 harmonic) and causes a disruption of the peace.

It is the nature of the 6th OH (12th harmonic) to supply a lot of energy, but to sue for a sensible, harmonious resolution.

As things stand in the US government at the moment, both sides of the impasse are riding the wave of tension to fuel further violence, rather than doing the best thing by the country (whom they all claim to serve) and come to a reasonable solution. The energy of the configuration is right for a solution, but when the energy of the 12th (6OH) is used to fuel violence, greater impasse is the result.

The tension is not going anywhere any time soon, resolution or no, because Saturn is the fastest moving of these planets, and Saturn is never in a hurry to do anything.

The intransigence on both sides of this debacle is fueling an angry violence in the community, I hope, for all of our sakes, that these parties come to terms sooner rather than later, and put this energy to creative use rather than let it tear our country apart.

October 18 is the date at which the voice of reason should have sway, (coincidentally, it is the time the debt-ceiling crisis becomes critical) and November 12 before we get a real handle on this.......the fight is not going anywhere, but calmer heads will prevail in the longer term.

I do not want to join the doomsayers who are predicting revolution out of this, however I do believe that this impasse is indicative of more violence down the is on its way, but I don’t think America’s next revolution is beginning with this impasse, this is just an indicator for where America’s real trouble lies.

Sunday, June 16, 2013

Musical Approach to Aspect. Part 3: Trine and Sextile

Harmonic Level 3: The Perfect 4th, Trine and Sextile

The prefect 4th is the other relationship (apart from the perfect 5th) without which we would not have a musical system. The “circle of 5ths” employs the perfect 5th in one direction and the interval we call the perfect 4th in the other direction (it is a 5th in the reverse direction, but a 4th when it appears in our primary of the many reasons that Music theory gives people headaches until they can grasp how that works.)

Anyway, sufficient to say that our music system could not exist without this interval.

It is our habit, in astrology, to think of the trine as an easy aspect, but any of us who have looked at aspect for a while will attest to the observation that trine tends towards idleness like no other aspect. Folks with grand-trines (3 planets each in trine aspect to the other around the chart) tend to feel the need to be poked and prodded in order to achieve anything.

So what does the “perfect 4th” say about the trine?

The perfect 4th will depart from the tonic in a way that will beg for resolution (via the perfect 5th or some other means). This is a far cry from the easy idleness we experience with the trine. However, it does tell us what that “lull” is for. It is a chance for us to regroup, to make plans while things are going easily, plan our next adventure carefully, to make use of positive ease while we have it, rather than to lay about and wait for others to do the work.

The difficulty for those who have a grand trine in the natal chart (or any trine really), is to get over the idleness which is brought about by ease, use the energy to plan your adventures and to provide support while you meet the challenges of square aspects (either in transit or in the natal). Trine and sextile represent the easy energy of positive relationship, and need to be used to their fullest extent.

In the axial pattern of aspect, the Perfect 4th actually belongs to the Sextile, and the Major 6th gets the Trine, which all adds up to saying these aspects are not to be used to produce idleness, instead we are to use the harmony created by such aspects to further our adventures as humans on this planet.

The sextile is seen as “more active” than the trine, and so it should be, but it is all too often used by the native as an excuse to goof off “nothing challenging here, lets take it easy”. We have just established that this idle attitude represents a terrible waste of resources. As Astrologers, it is our duty to suggest our clients renew themselves to get ready for the coming storm when trine and sextile aspects are coming their way. This attitude makes sense of the overtone which the sextile and trine aspects represent.

The disposition towards “needs to be poked and prodded” speaks to both the 4th’s need for closure, and the idle attitude of the trine and sextile aspects. Use the trine and sextile aspects to explore closure while things are relatively easy. Poke and prod yourself, the rewards will be well worth it.

Musical Approach tooAspect Part 2: Square

Harmonic level 2: The Perfect 5th, Square

I know there will be a lot of astrologers who look at this and say that a square aspect is not a perfect anything unless you like a lot of suffering.

Let me ask you this: How many stories have you read where the protagonist goes along smoothly in life, meeting few obstacles, overcomes them all easily, and essentially lives an uneventful life? I have not read any, because I have just outlined the plot of the world’s most boring story.

We are human, and humans have always celebrated our ability to overcome obstacles. The great stories of our mythology are stories of meeting adversity head-on and overcoming in spite of the odds. Epic tales of mountain climbers are not filled with easy climbs and leisurely strolls, they are filled with hardship and adversity, and the ability to prevail in the face of impossible odds. There are plenty of news reports about climbers who didn’t make it, but the joy of such stories is that these people died doing what they love. 

Why did they do it if they knew it was dangerous?

Because to be truly alive, to be truly human, is to meet adversity head-on and, win or lose, give it your best shot.

The reason, then, that the square aspect gets the perfect 5th interval, (without which we would never have a musical pitch system) is that without the adversity present in the square aspect, we have no room to express the most important facet of being human!!

When we have a square aspect in our chart, we have the natural tension of adversity in our chart and it is ours to rise to that challenge and prevail against the odds. We should celebrate our squares as much, if not more than, our trines. It is our squares which make us truly human, and will make us more likely to achieve. It is our failures to cope which drive us forward to do better next time.

When we have an outer planet square transit, it is our first instinct to panic, however we should look at the challenges (which are BOUND to come our way) as opportunities  to excel at being our most human, our most frail, and our most triumphant. There are times when we will feel the need to duck our heads and ride out the storm, however, greater joy awaits when we meet the storm headlong. The choice is truly ours.

Musical Approach to Aspect Part 1: Conjunction and Opposition

The application of musical theory to equate  overtone with the aspect half-circle presents us with a whole new set of tools with which to interpret aspects. 

Harmonic Level 1: the Octave: Conjunction and Opposition

It will seem strange to the observer at first to consider conjunction and opposition in the same harmonic level, however if we intend to use musical overtones to describe our aspects and consider astrology to be part of the vibrating whole we call our universe, then it is vitally important that we find a way to reconcile these two.

Let’s embark on a side-note for a second, and consider what we have always been taught about these two phenomena.

We consider two planets in close proximity on the ecliptic to be conjoined, or to be occupying the same space. We consider the number of that relationship to be 1 because there is little room for argument or discourse in this relationship. We are often taught that such planetary energies are “fused” and become a homogenized unit. This is  a teaching I have always questioned. Where do we see such a homogenous joining in real life?

I will venture to say that when we have two people or planets occupying the same space there needs to be room for discourse or there will be trouble, particularly if the two do not naturally get along.

Remember we are taking about 2 occupying 1 space. Our expression needs to be a 1 with a 2 attached to it somehow. We use the word “conjoined” to imply the one-ness of an intimate partnership, whether the two people or planets like being intimate or not is another question, but in the description of this relationship we have 2 expressed as a 1. The old biblical line “the two become one flesh” comes to mind, however I have yet to meet a couple where sexual union makes the couple into some homogenous entity where neither can be seen as an individual. In some circumstances the couple may produce a third individual, but then 2 becomes 3 and that involves a time component, whereas our chart describes an instant and is seen in terms of immediately before and immediately after, so our 2-into-1 is still lacking some vital component of meaning. We could use the word “communion” which implies two people sharing space in harmony, and its very nice and good, but it still lacks an expression for the scenario where the two don’t get on very well. We could go with co-habitation then, which is more accurately descriptive, but lacking expression for the type of dialogue two people (or planets) need if they are going to co-habit successfully.

Enter the Octave. An octave is a musical phenomenon whereby doubling a frequency, or halving it, produces the same pitch with a different audible expression. By this I mean one will be high, the other low, but when played together they make a sound that is virtually indistinguishable. Each member of the “co-habitation” has room for its unique expression, and when they join forces, they become indistinguishable. In this relationship we could say they are “equal yet opposite”, “the same, yet different”. This is a fairly accurate description of how a native might describe conjoined energies in a natal chart.

OK so how can we express this “octave” in the natal chart? How can we tie 1 with 2 and still make sense? We shall see shortly, but first let us consider opposition.

Opposition should not be discussed without discussing polarity in the chart. Polarity is where we examine the nature of signs on opposite sides of the ecliptic.

We know that Aries is martial and a bit naive, Libra is just and a bit pretentious, they are both about doing things, they just disagree on how they should be done.

We know that Taurus is self-indulgent, and loves to hoard resources, Scorpio indulges in pleasure and loves to manipulate resources. They are both interested in resources, they just disagree on what they should do with them.

We know that Gemini loves to talk and amass information, and Sagittarius loves to think and share information. They are both interested in information, they just disagree about what to do with it.

We know that Cancer is about family and nurture, and that Capricorn is about business and control. Both are clearly concerned with how life is lived, they just disagree about what is important.

We know that Leo is self-interested and likes center stage, and that Aquarius is group-centered, yet likes to stand out from the crowd. Both are clearly interested in personal dynamics, they just disagree about how one should conduct themselves.
We know that Virgo knows about details and organization, and that Pisces prefers to live life unfettered by details or organization, believing those things will sort themselves out. They both feel strongly about details, they just disagree about how those details should be employed.

I will freely admit to have stacked these descriptions to suit my purposes here, but given the polar descriptions I have given above, it is fairly plain that each polar opposite could learn a lot from the other.

Our astrology texts, as a rule, teach us that opposition is a difficult aspect because of the radical differences between the two perspectives. People fear opposition because it can result in conflict, however a closer examination of the conflict will reveal that each set of opposing signs has a unifying principle, something they can agree is important if they can just learn to appreciate the perspective of the other. 

Unlike the people (or planets) in co-habitation, there is no need to make the space for interaction, there’s plenty of space here, but again the resolution of this dispute is found in recognizing the equal yet opposite nature of the polarity.

I believe this is the most fundamental energy of aspect in the astrology chart. If we consider the Conjunction and Opposition together to represent the Octave, Conjunction is fundamental note, the Opposition is the  Octave either higher or lower (higher in our example), the line between them unifying their energy as together “C” (or “A”, or any other note you can come up with), then we have brought “equal and opposite” together in our chart, and allowed each planet room to express itself fully no matter how closely they interact.

Example: Two Cancers in a relationship, one will feel the need to be “more Capricorn” than the other, someone will need to deal with business, order, and discipline. I will wager that the one with its moon more strongly aligned to Capricorn will fill that role most often, and the other will fill that role in the areas where the first one lacks it. The two Cancer suns need to find a way to co-habit in a way which lets them each express themselves rather than becoming an overly-sensitive homogenized couple.

By giving the first principle of aspect to the “Octave” we have defined an aspect as a relationship between planets, and have plotted a path for resolution of differences incurred by each planet in that relationship.
In using the Octave in this way, we have described the purpose of aspect as finding resolution between differring expressions of planetary energy.

The value of this principle is validated by the axial principle (joining conjunction and opposition on an axis) of aspect being consistent with the “overtones” of musical string theory. Thus the planets can be said to be “resonant” with each other when they are in aspect. The point of such resonance, is finding the unifying principle between the planets.

A note about “bad aspects.” Bad aspects occur when we let life happen to us and are unwilling to take command of our personal energies and find the best expression for planetary configurations. Sometimes, transits will be tough. There is no getting past that, but we need to look for opportunities to expand ourselves while we are going through the mill.

Musical Approach to Astrology

This is a project I have been working on for some time, and it is time it saw the light of day, ready for review and comment

 I particularly want to know if there is enough interest in this idea to publish a book.

Take Care


Mercury Retrograde in the sign of its own exultation, aka, Mercury retrograde in Virgo.

Hmmm this post was shelved back in 2010, and I can't see why I didn't publish it while Mercury WAS retrograde in Virgo.....anyway, it's not a bad look at retrograde Mercury (which comes up 3 times a year, so I'l post it now anyway, with the ceveat that the

Mercury is happiest of all in the sign of Virgo. Yep, pragmatic, anal-retentive, hyper-detail oriented, Virgo. I can just about hear the Gemini’s I know saying, “hang on, communication, music, knowledge, these are all mercurial celebrations....... what’s this about stick-in-the-mud details?”

Well, lets see...... at his heart, Mercury is the great translator.... yes, you heard me, translator. He takes what has meaning to one, and gives it a similar (though not identical) meaning to another through various languages, such as the many languages of speech and writing, the language of mathematics, the language of music, (which is applied mathematics) the language of physics (which is also applied mathematics), the language of astrology (yep, applied mathematics again), and the language of medicine (for which we have still to find the best application of mathematics, because the abuse of statistics is killing us.)

Now, its the similarity of this knowledge that makes all sorts of extraordinary achievements possible, but its the unique meaning, that is uniquely true for each and every person, that extends the realm of what is possible far and beyond the collective understanding.

Lets take Beethoven as an example. I expect it is possible to hear beethoven’s 9th and remain unmoved, but I have never found it possible. However, the things that stir my emotions will vary, slightly, from those that stir yours, and you and I together in our similar and united appreciation, could completely miss the point that Mr Beethoven was making, yet still come away improved for the experience..... and this is the miraculous nature of Mercury, that it is even possible for this to occur.

The gift of translation, so that each person takes away from a common experience, those things the person needs to be improved, is Mercury at its finest.

The problem with translation is that it is never perfect. If each hearer takes away a slightly different message, and builds certain assumptions on that message, what happens when those assumptions meet? Often, nothing very much, because the assumptions were similar enough to begin with that they interweave seamlessly when they come back together.

On occasion, however, it is necessary to deconstruct our assumptions in order to homogenize our understanding, this mostly occurs under retrograde Mercury. For this reason, retrograde Mercury is associated with misunderstandings, things blown out of all proportion, arguments that end in impasse, long-term friendships dissolving over trifles and so forth.

For what its worth, retrograde mercury has a lot less to do with blowing up equipment, but the assumptions you made about that faulty equipment are worth examining.

So, what happens when Mercury, in the height of is glory in Virgo, goes retrograde? Well, I guess this period truly defines what all retrograde Mercury’s should look like, after all, Mercury is strongest here, and is more Mercurial than in any other sign.

My expectation is for more disputes to be solved more rationally, and fewer to be left to blow up in an uncontrolled fashion. This doesn’t mean it will always happen that way, Mercury is also a trickster who seems far too fond of folks falling foul of their assumptions, however the assumptions are more likely to come to light in Virgo than in any other sign, and this is where I see more likelihood for resolution of disputes.

We can expect the word ASSUME to make an ASS out of U and ME while Mercury is retrograde in Virgo, and if we are prepared to listen to its lessons, we can learn a lot about each other.

So, while we learn to cut each other a little more slack in our interpretation of details, we can gain the advantage of multiple perspectives.... or we can continue to fight and brawl as usual, its really up to us after all.

Take Care


PS.......again Mercury will be retrograde in Cancer this time, not Virgo, but the rest of the information was too much fun to leave unpublished.

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....