Does City of Brass deal damage to you if you tap it for mana and then an effect untaps it?

City of Brass has two separate abilities: a mana ability that produces mana when you tap it, and a triggered ability that reads "Whenever City of Brass becomes tapped, it deals 1 damage to you." The trigger is tied specifically to the event of City of Brass becoming tapped (i.e., transitioning from untapped to tapped), not to the act of producing mana.

Under CR 603.2, a triggered ability checks whether its trigger event occurred. The relevant event here is City of Brass transitioning from untapped to tapped (CR 701.20). That transition happens exactly once when you tap it for mana — so the damage trigger fires exactly once at that point.

If a subsequent effect (such as Freed from the Real or Ral Zarek) untaps City of Brass after it was tapped, the card simply moves from tapped to untapped. No "becoming tapped" event occurs during untapping, so the triggered ability does not fire again. You would take another 1 damage only if City of Brass became tapped a second time.

Example: You tap City of Brass to add {G} to your mana pool. The damage trigger goes on the stack and deals 1 damage to you. An opponent then activates an effect that untaps City of Brass. City of Brass is now untapped, but no new damage trigger fires — you took only 1 damage total during this sequence.

This is confirmed by CR 603.2 (triggers check for their specific event) and CR 701.20 ("tap" means to turn a card sideways if it was previously upright). Untapping is covered under CR 701.21 and does not constitute "becoming tapped."