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I got the tension as tight as I possibly could without being too tight.
This suggests you do not have a geared drivetrain.
It would really help if you'd tell us whether you are fixed or freewheel.
"...as tight as I possibly could without being too tight..." sounds like a bit of an oxymoron.
If you are not sufficiently experienced to set a chain at correct tension and to identify the slack that will be felt in a correctly tensioned chain while trackstanding* etc then I suggest you befriend someone who is and ask them to teach you.
*This kind of presumes you are riding fixed.
If you are riding freewheel then excess tension in the chain may cause freewheel pawls to not engage correctly, befriend mechanically minded person as above.
I got the tension as tight as I possibly could without being too tight.