Explanation:

- Perjury is the act of lying or making false statements under oath in a legal context.

- Option 1: Melancholy refers to a feeling of deep sadness or gloom. It's unrelated to truth-telling or lying.

- Option 2: Frankness denotes honesty and openness in communication. It's essentially the opposite of lying.

- Option 3: Penury means extreme poverty or destitution. It has no relation to truth or deception.

- Option 4: Falsehood refers to the act of lying or stating something untrue. It is synonymous with the concept of perjury.

Therefore, the most appropriate synonym for perjury is:

Option 4: Falsehood