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I was recently on @arnemancy's podcast and we talked about aspects and magic and I just wanted to take some time to expand upon and illustrate some of the ideas I talked about, specifically the elemental/quality component of aspect meaning.
Astrology recognizes five main aspects. The conjunction, the opposition, the sextile, the square, and the trine. These are the original and only aspects, used since the Hellenistic era until Renaissance astrologer Johannes Kepler introduced other, more minor aspects.
Aspects are, basically, the way planets look at and interact with one another. There are two different models for where the aspects derive their meaning. The more contemporaneously popular one has to do with the signs and their elements, and then there's the Thema model.
This might come as a shock to you and I think I just made this up but the signs each belong to one of the four elements.

You've probably heard that trines are the best aspect because occur between signs that share an element, but is that true?
The elements themselves are broken into qualities
Air is hot and wet
Fire is hot and dry
Earth is cold and dry
Water is cold and wet

The qualities between the signs plays a large part in this elemental model of aspects. Ptolemy in the 2nd century was a big proponent of it.
According to this elemental model, trines are the best aspect because they naturally occur through signs of the same element that share both qualities. The cold and wet water sign Cancer trines the other cold and wet water signs Scorpio and Pisces.
Sextiles are the second and lesser harmonious aspects. They naturally connect elements that share the active quality, so an agreement between coldness or heat.

The cold and wet sign Cancer sextiles the cold and dry signs Taurus and Virgo. Water and Earth agree in coldness.
The same is true for the fire and air signs. The hot and dry sign Leo naturally sextiles the hot and wet signs Gemini and Libra. They agree in heat.
When we get to squares we have some issues. Namely we're connecting with signs of differing elements. The cold and wet sign Cancer squares the hot and dry Fire sign Aries AND the hot and wet Air sign Libra.
For the sextile we had an agreement between the primary qualities of heat and coldness between signs, with squares we have a disagreement.

The cold sign Cancer is square two hot signs, Aries and Libra.
This creates an interesting relationship where Cancer is more disagreeable to Aries (who is hot and dry) than Libra (who is hot and wet). Both of Aries's qualities are opposite to Cancer's.
This creates an interesting pattern when you consider the Hellenistic Overcoming configuration. A planet 10 signs away from another will overcome the first. Aries is 10 signs away from Cancer, so overcomes it and the opposition in qualities is an interesting reflection of this.
This is not always the case though. Taurus (cold and dry) overcomes Leo (hot and dry) and they share a quality. The patterns appears to be that Water and Earth signs are overcome while Fire and Air are the ones dominating.
Just to illustrate. With Cancer, it was overcome by the opposite element Aries, but if we put Leo in that position it's overcome by the Earth sign Taurus and they are both dry. But Leo will overcome its opposite elemental sign Scorpio.
Air signs will also be overcome by a sign they share a quality with (Water) while overcoming Earth signs, the sign they are elementally opposite.

Just an interesting pattern with that hot signs trying to be extra.
So, squares are where the element/quality explanation starts to break down a bit, but it's really oppositions that rip it apart.

Earth and Water signs are opposed
Fire and Air signs are opposed

These are elements that agree in heat or coldness.

Whoops!
The term opposition would imply that the elements involved are...opposite, but that's not what happens and in fact we repeat the same relationship as shared by sextiles; agreement with the active quality of heat or coldness.
There is an alternative, Stoic account of the elements which assigns each element one of the four qualities; Air is Cold, Fire is Hot, Earth is Dry, and Water is wet. This might fix our problem. The Wet water signs are now opposite the Dry earth signs, Hot fire; cold air.
Except, whoops! Sextiles mess it up! The dry Earth signs are both opposed and sextile the wet Water signs, which doesn't make a lot of sense if we're arguing an elemental compatibility being the basis for aspect meanings. Sorry Ptolemy!
The best explanation of aspects doesn't involve the signs and elements, but the planets. The Thema Mundi model of aspect meaning derives the meanings of the aspects from the nature of planets.

Here's the Thema Mundi if you're unfamiliar with it.
The Thema is simply a chart with the 7 visible planets in their signs of domicile with the sign Cancer in the first house position. It's a model that depicts a lot of traditional ideas and concepts, but we're just going to focus on aspect theory within it.
The Thema aspect model takes note of the relationships formed between the sign pairs ruled by other planets and the signs of the luminaries. They repeat and we see an interesting theme emerge.
The signs of Venus aspect the signs of the luminaries via sextile. Taurus sextiles Cancer. Libra sextiles Leo. So we can think of the sextile as being the nature of Venus. It is helpful and friendly. Less in power than a trine because Venus is the lesser benefic.
The signs of Mars aspect the signs of the luminaries via square. Aries squares Cancer. Scorpio squares Leo. The square is of the nature of Mars. It's unhelpful, full of friction, and irritating. Less in power than an opposition because Mars is the lesser malefic.
Jupiter's signs aspect the signs of the luminaries via trine. Pisces trines Cancer. Sagittarius trines Leo. The trine is of the nature of Jupiter. It's uplifting and salvatory. A strong, assisting aspect because Jupiter is the greater benefic.
Saturn's signs aspect the signs of the luminaries via opposition. Capricorn opposes Cancer. Aquarius opposes Leo. So we think of the opposition as being of the nature of Saturn. It's denying and hindering. A strong, blocking aspect because Saturn is the greater malefic.
The Thema model is a lot more logically consistent and provides an example of how astrology references itself and how older forms of astrology are more planet-focused. We're able to draw from planetary symbolism and apply it to aspects, in this example.
Ptolemy's quality explanation got a bit further in the Renaissance where it was discussed a bit more frequently. Medieval texts still drew from the thema/planetary explanation as late as Bonatti (13th century).
There's always the simple, mathematical answer that oppositions (180°) are bad because the planets are visibly on opposite sides of the sky so half an opposition (squares, 90°) are half as bad. Trines are good because Greeks love triangles so half a trine (60°) is half as good!
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