Exegesis Issue #25

Exegesis Digest Tue, 25 Jun 1996 Volume 1 Issue 25


Date: Sun, 23 Jun 1996 21:43:05 +0200
From: Denis Daost <m-24443@mailbox.swipnet.se>
Subject: Re: Harmonic Aspects Method

Hello Exegesians!

I would like to comment upon an article posted in Exegesis #23 by Michael Freedman.=20

Hi Michael!

Thanks for sharing your interesting theories and experiences regarding aspects. However, there are some things that aren't very easy to understand, at least not for me. This is why I want you to clarify some things. If I sometimes sound a bit skeptical or critical, you shouldn't take it personally. It's probably just my exact Mercury-Saturn sextile that WANTS to be skeptical and critical when checking a theory out.

Here we go...


[lots of text deleted]

PROPOSITION 1: Every planet is in aspect to every other planet.What this means is that every Angular Separation between two planets potentially has significance for the person or event for whom the horoscope has been cast.

For example, let Venus be separated from Mars by 137 degrees 30 minutes 28 seconds. Only a few astrologers in the late 20th century would be comfortable treating this as a Sesquisquare (135 degrees), as it is beyond the 1 or 2 degrees orb most would allow. Therefore, most astrologers would ignore it, while even harmonic astrologers would be lucky to pick it up unless they happened to cast a 21st or 34th Harmonic Chart; or a 1597th Harmonic Chart, in which it would it is within 0.18 seconds of partile, that is, exact.

The Harmonic Aspect Method restricts itself, for good reasons discussed elsewhere to the first 36 Harmonic Aspect Series. It would regard the following as a full definition of this aspect:

I have added some own figures to the table below. The figure after "orb:" tells how much the actual distance between the planets (137d 30m 28s) differ from the ideal orb of the harmonic. Here is an example:=20

The 13/34 aspect indicates planets separated by 360*13/34=3D 137d 38m 49.4s. The difference between 137d 38m 49.4s and 137d 30m 28s is 0d 8m 21.4s. 0d 8m 21.4s can also be expressed as 0.13928 degrees (the value below).

Planets: Venus/Mars Angular Separation: 137d 30m 28s Primary Aspect: 13/34 37% strength orb: 0.13928 deg Secondary Aspect: 8/21 13% strength: 0.04 orb: 0.36492 deg

I don't understand this! Please explain it further. How do you calculate the values 37% and 13%? (But first see the following two paragraphs!)

What this description shows is that 137d 30m 28s is within orb of a 13/34 aspect, close enough to exact to have 37% of its potential strength.

After reading your whole letter I think I understand what you mean. Using a 12 degree orb for the conjunction, the maximum orb allowed for an aspect based on the 34th harmonic would be 12/34 = 0.35293 degrees (0d 21m 11s). 0.35293 - 0.13928 = 0.21366 0.21366 / 0.35293 = 0.60539 0.60539**2 = 0.36650 which gives 37% when rounded off.

Is this how you mean?

Maybe you ought to include some more examples, or?

It is also within orb of an 8/21 aspect, but at only 13% of the potential strength it would have if exact.

13/34 is called the primary aspect, because it is the strongest aspect between Venus and Mars; 8/21 is the secondary aspect, because it is the weaker.

So there are actually two aspects between Mars and Venus? And the 13/34 aspect has 37% of its "potential strength", while the 8/21 aspect has 13% of its "potential strength". The makes me wonder about several things:

* Should we mix the interpretations for the 13/34 and the 8/21 apects (whatever they may mean) when interpreting the chart? * Would it be "wrong" to simply treat the whole thing as a wide/weak seskisquare?

Please understand that I do not intend to critize in any way. I find your theories very interesting, which also is the reason I spend time analyzing them. Maybe I also should point out that I have an exact sextile between Mercury and Saturn which should explain my sometimes flaw-finding nature.

Since some terms are very unfamiliar to me, I include the Swedish terms within "[...]". Sorry for that!

PROPOSITION 2: A harmonic aspect is any division of the 360-degree circle which can be defined by a fraction in which both the numerator and the denominator are integers.

This proposition sounds more complex than it actually is. It merely states that you can redefine the angular separation between two planets, which is usually expressed in terms of degrees, minutes and seconds, in terms of a simple fraction, such as 1/2, 1/4, 5/12, 4/9 or 13/34. It has long been an implicit principle of astrology that the denominator (the lower figure) of such fractions reveals the nature and effects of the aspect on the two planets linked by it.

Isn't the denominator the HIGHER of the two figures? Isn't "34" the denominator in 13/34? If so, I think I follow you.

PROPOSITION 3: Aspects become stronger as they approach partile; and their strength varies inversely as the square of the distance from partile.

I'm sorry, but "partile" can't be found in any of my dictionaries. If you could explain "partile" with other words it would be great. An example illustrating how this works would also be great.

Then I understand, and even agree with, your next paragraphs (which I've deleted). But...

Conjunction 1H 12/1 = 12 degrees Opposition 2H 12/2 = 6 degrees Trine 3H 12/3 = 4 degrees Square 4H 12/4 = 3 degrees and so on.

I don't agree with this! For instance, I can't possibly accept the idea of allowing an orb for the conjunction which is four times larger than the orb for the square. It definately goes against my own experiences. The same goes for most of the other aspects, for instance the idea of the quintile (1/5) being almost as "important" as the square (1/4).

[text deleted]
Example: If an Opposition has an orb of 6 degrees and an Angular Separation is 175 degrees, then it is 5 degrees from exact. [6-5] divided by 6 = 1/6]= 0.1667.

This is exactly how I've been working myself during the last 6-7 years! It's very practical!! Of course it has its limits, but if we're only aware of them, then there shouldn't be any problems. We are able to sort aspects by "importance", to include the strength of the aspect in our Tables of aspects, chart drawings, etc.

Personally, I also multiply this number with another number which is unique for every pair of planets. Sun-Moon aspecs are multiplied by 1.00, while e.g. Jupiter-Pluto aspects may be multiplied by .60.

Square of 0.1667 = .0278 which is 0.03 to two decimal places. Expressed as a percentage, this aspect has 3% of its potential strength

This is something I don't do. I have thought about doing like this, but I think using the square with be a bit too dramatic. Best would probably be to do something like x =3D x**1.2 , but then there are some practical problems= I have to consider. My astrology program is already too large to be run on a PC (I have to delete a lots of functions) and I rather not add any more memory demanding calculations.

The following Table sets out an indication of how to assess the comparative strength of any aspect from its Strength No. 100% Partile [exact] aspects are dominant factors in a chart 90% to 99% Powerful aspects; pay close attention to them. 70% to 89% Very strong aspects. 50% to 69% Strong aspects. 30% to 49% Fairly strong aspects. 10% to 29% Not strong; only occasionally have much effect 01% to 09% Weak; rarely have much effect, unless they are part of a larger structure.

I have an option to chose on which level I want to operate on. I can choose if I only want to see aspects > e.g. 30%. Also very practical...

I'm not telling this in order to boast or something. You are sharing your ideas, and I'm just sharing mine. Hopefully I'll be able to include some of your ideas into my way of applying astrology, and hopefully some of my ideas might be useful to you.

By the way...

If anyone is alarmed by the enormity of a 12 degree orb for a conjunction, consider that in this system the strength of an aspect is a vital consideration. If you are not taking much notice of any aspect below 10% strength, then the Orb of a conjunction is effectively 8 degrees.

Hmm... The square of 0.10 is 0.3162277.
0 0.3162277 * 12 = 3.79473
12 - 3.794733 = 8.205267 degrees = 8d 12m 19s

This is how you mean, isn't it?

PROPOSITION 4: There are fundamental differences between the effects of the Major & Minor Aspects and those of all other Aspects.

An infinite number of Aspect Series can be formed by dividing the circle by a whole number of whatever magnitude, e.g. 5, 7, 9, 10, 11, 13, 37, 144, 180, 380, 1597 or any other number. Before the 20th century, aspects other than Majors and Minors were virtually ignored entirely,


OK. They cannot easily be divided into "good" and "bad" aspects (using old-fashioned and simplistic terms). They are more subtle.

I also think, which you too mentioned, that most astrologers have problems "finding" the aspects that aren't based on miltiples of 30 degrees. They are extremely hard to handle without a computer. However, as more and more astrologers are using computers, I think more and more astrologers will start using aspects based on the multiples of 1/5, 1/7, 1/9 and so forth.

PROPOSITION 5: There are four levels of aspects, to one or more of which every angular separation belongs: [lots of text deleted]

Very interesting, but also very hard to comment upon. At least at this point.

I also agree on almost everything you say in the part beginning with "In practice, I rarely analyse a chart beyond the 12th harmonic" and the parapraphs following.

Therefore, I jump straight to the more practical paragraph:


The major task for every astrologer is how to handle the vast amount of information generated by an astrological chart. Even using only the Sun, Moon and Planets, North Node, Ascendant & Midheaven, normally do, a full Harmonic Aspect analysis of any chart will yield 78 primary aspects, plus some secondaries. If Chiron and the four asteroids were added, there would be 153 primary aspects to interpret.

If you also use Midpoints and i find them very useful, especially when considering events rather than traits, the amount of information poured at the hapless astrologer is beyond handling.

Definitely!! Especially when using midpoints by groups of 3 or more planets, which one sometimes wants to do when a transiting planet is aspecing several natal planets.

The way I handle this problem is: 1. I do not use any but the solar system planets and points, except in unusual circumstances, when the particular light thrown by Chiron or the asteroids is warranted. This would only happen if I knew enough about the individual already for me to consider it warranted.

Personally I use Sun, Moon, the 8 planets, Asc, IC, Vertex, Moons Node and Chiron in my everyday working. However, I always check the positions for the four asteroids for learning purposes. Regarding Vertex, Moons Node and Chiron, I actually don't know much about how to e.g. write delinations for aspects to them.

Anyway, I agree that it's wise to limit the amount of objects/points used.

2. I use only the first 12 harmonics, i.e., the Overt and Potential aspects, unless the native is also undergoing depth analysis of some kind.

This sounds wise. Personally, I don't use aspects based on 1/7, 1/9 or 1/11, but this is because I don't know much about how to interpret them.

3. I pay regard only to those midpoints where all three of the aspects involved are on the same harmonic, using all 36 harmonic aspect series. This means that the midpoint has to be very close to exact for it to be considered.

All THREE? The aspects involved? Sorry, but I seem unable to follow you on this. Please explain further.


Further papers are written or in preparation on Behaviour Chains; and on the suggested interpretation of all Harmonic Aspect Series to the 37th Harmonic.

You present a whole lot of interesting ideas, but one major problem exists. How do we interpret all those aspects??? I really hope you'll succeed in suggesting interpretations, because without the knowledge of how to interpret all those "odd" aspects, there are not much point using them. (Well, except for learning purposes.)

Hope you (or anyone else) don't mind, but I have a suggestion regarding your writing. Sometimes I have problems following you, and I suspect that other astrologers might have the same problem. I think it would be much easier if you could include some more examples. This is one of the strong points of Robert Hand (he surely has many strong points). His books are very easy to read, he gives plenty of examples and the examples are very easy to follow.

Maybe you also should change the sequence of some paragraphs? I spend almost an hour trying to understand some terms (e.g. "major","minor") and examples that were explained later on in the text. Once I had read the whole article, though, I began to understand what you meant.


Good luck with your work on "odd" aspects! You're also welcome to email me in case you need/want to.

Regards, Denis

PS: Should I dare press the [Send] button...? We'll se...


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