General Antonyms:
* Loose
* Slack
* Relaxed
* Floppy
* Sagging
* Flaccid
* Unstrained
* Easy
Antonyms related to specific contexts:
* (for a rope) : Slack **
* (for muscles) : Relaxed
* (for a situation) : Calm , Easy
* (for nerves) : Calm , Relaxed
The best antonym will depend on the specific context in which you are using the word "taut."