* A misheard or mistyped phrase: Could you be thinking of "harmonization of interests" or "shared interests"? These are common phrases in law, politics, and economics.
* A specific term used in a particular field: It's possible that "harmony interest" has a specific meaning in a particular field or sub-discipline. If you can provide more context about where you encountered this phrase, I might be able to help.
* A metaphorical expression: Perhaps "harmony interest" is used metaphorically to describe a situation where multiple parties have a shared interest in achieving a peaceful or cooperative outcome.
To better understand what you mean, please provide some context:
* Where did you encounter this phrase? Was it in a legal document, a political discussion, a news article, or somewhere else?
* What was the topic being discussed? Knowing the broader context can help me understand what the phrase might mean.
Once I have more information, I can give you a more accurate and helpful answer.