The phrase "ringed the curtain" can be replaced by a variety of other phrases, depending on the context of the situation. For example, in a theater, you might say "pulled back the drapes" or "raised the valance" instead of "ringed the curtain". Similarly, in a home or event space, "unveiled the backdrop" or "revealed the scenery" might be appropriate. Other options could include "parted the drape", "opened the curtain", "peeled back the veil", or "lifted the blind". Ultimately, the synonym chosen will depend on the nature of the environment and the desired level of formality or informality in the language used.