The trine measures 120°, exactly one third of the circle, so it is the aspect of the 3rd harmonic: three trines close a perfect triangle. Harmonic astrologers from John Addey onwards associated the number three with enjoyment, creativity and things fitting together, in contrast to the striving of the 4th harmonic, the square. That fits the traditional reading of the trine as the most harmonious aspect, though it is a symbolic correspondence rather than a demonstrated mechanism.
By whole sign, a trine joins two signs of the same element and so of the same polarity: Fire and Air signs are yang, Earth and Water signs yin. The modalities always differ. In the Earth triangle, Capricorn is cardinal, Taurus fixed and Virgo mutable, so a trine between them pairs one way of acting (starting, keeping or adapting) with another, inside a shared temperament. That is why trines feel like agreement rather than repetition.
Degrees and signs do not always line up. A planet at 28° Aries and one at 2° Virgo are 124° apart, a trine by degree with a 4° orb, yet Aries (Fire) and Virgo (Earth) are five signs apart, the relationship of a quincunx. Astrologers call this an out-of-sign or “dissociate” trine. Most still count it, but the ease is mixed with the awkwardness of two signs that share neither element nor modality, and Hellenistic astrologers, judging by whole sign, would have treated those signs as not seeing each other at all.
Worked orb example. The wheel at the top of this page shows the Moon at 20° Virgo and Saturn at 16° Capricorn. The arithmetic runs like this:
Applying or separating? The Moon is by far the faster planet, covering roughly 12° to 15° a day, while Saturn moves only a few arcminutes. The Moon sits behind Saturn in zodiac order and is moving toward it, so the gap is shrinking: from 116° toward 115°, 114° and below. Since the exact trine needs 120°, the angle is moving away from exactness, and the trine is separating. It was exact several hours earlier, when the Moon stood at about 16° Virgo. Within about two days the Moon would reach 16° Libra and form a square to Saturn instead. Many astrologers read a separating trine as support that is already established, something the person can draw on rather than still assemble.
Pairs that cannot form a natal trine. In a geocentric chart, Mercury stays within about 28° of the Sun, and Venus within about 47°. Neither can reach 120° from the Sun, and since Mercury and Venus can be at most about 76° apart, they cannot form a natal trine either. If a description promises you a Sun–Venus trine in your birth chart, it is mistaken. These pairs can still trine across charts: transiting Venus can trine your natal Sun, and your Mercury can trine a partner’s Venus.