Harmonious aspects are those formed in a chart between planets of similar energetic placements. These aspects tend to provide natural abilities and strengths. Particularly in synastry where they indicate harmonious relationships.
'Perfect' alignment only lasts briefly for fast-moving planets, so each aspect has some 'breathing room' which is called the 'orb'. Major aspects have an orb of about 8<sup>o</sup> for which it is considered that the aspect is 'active'.
When two planets are in conjunction they will be seen in approximately the same Zodiac sign and astrological house, hence emphasising these qualities more strongly (through each planet).
Conjunctions are actually not inherently harmonious and are the only neutral aspect, with the harmony or tension of a conjunction depending on the compatibility of the planetary energies involved.
When two planets form a trine, they essentially form one side of an equilateral triangle surrounding the Earth in the centre. Of course, this is only from the perspective of the Earth and the true distances aren't as harmonic, but the harmony of the 120o angle means that the planets tend to sit in signs of the same Element and hence emphasise the qualities of this element more strongly.
When two planets form a sextile, they are separate by 60o as viewed from Earth, forming one side of a hexagon with the Earth as the centre. Since a hexagon has 6 corners and the Zodiac has 12 signs, perfect sextiles form between signs and their next-nearest neighbors in the Zodiac. Since the Zodiac alternates between Yang and Yin Polarity a sextile skips the alternate and pairs up signs with the same polarity, but different Element and Connectivity.