Elemental dignity is an old idea with a simple core: a card's strength depends on its neighbours. A Wand between two other Wands burns hot. A Wand between two Cups gutters.
The Relationships
Same element — intensified. Two Cups together amplify each other. Whatever the feeling is, it is more so.
Friendly — strengthened. Fire and Air (Wands and Swords). Water and Earth (Cups and Pentacles). Air feeds fire; earth holds water. These pairs support one another.
Hostile — weakened. Fire and Water (Wands and Cups). Air and Earth (Swords and Pentacles). Drive against feeling; abstraction against material fact. Both cards are undercut.
Neutral. Fire and Earth, Air and Water. They coexist without much interaction.
What This Buys You
Dignities do not change what a card means. They change how loudly it speaks.
The Knight of Wands flanked by the Ace of Swords and the Eight of Wands is a plan moving at speed and it will probably happen. The same Knight flanked by the Four of Cups and the Nine of Cups is enthusiasm that will not survive contact with how the querent actually feels — the energy is there, and it will not carry.
Same card. Same position. Different weight, because the neighbours are different.
Majors and Courts
The Major Arcana carry elemental attributions too — The Emperor is Fire, The Moon is Water, and so on — but they outrank the Minors in practice. A Major beside a Minor tends to dominate rather than negotiate with it.
Court cards take the element of their suit, with the rank adding a second: Knights are fiery, Queens watery, Kings airy, Pages earthy. The King of Cups is therefore Air of Water — feeling handled with detachment, which is exactly the therapist-shaped person that card so often describes.
The Warning
It is possible to turn dignities into arithmetic — tallying strengths, declaring cards cancelled, producing a numerical answer. Do not.
Dignities are a way of hearing which cards are loud and which are muted. The moment the system starts producing conclusions you would not have reached by looking at the spread, you have stopped reading and started calculating.