“I'm on my own tonight.”
Your wife has gone to visit her mother and taken your children with her. You're at home alone, but you don't mind it. You're enjoying the peace and quiet. Your brother calls to say "hi", and you tell him about this. You start by saying this.
I'm on my own tonight.
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This phrase means to be alone. However, "alone" sometimes sounds sad and lonely:
It sucks being alone on Valentine's Day.
"On my own" sounds like a happy adventure:
My wife is taking the kids to her sister's place, so I'm on my own this weekend!
Being "by yourself" falls somewhere in the middle, neither happy nor sad:
A: Is Maxine with you?
B: No, I'm here by myself.