Whir of Invention

Improvise doesn't change a spell's mana cost or mana value.

When using improvise to cast a spell with X generic mana in its mana cost, first choose the value for X. That choice, plus any cost increases or decreases, will determine the spell's total cost. Then you can tap artifacts you control to help pay that cost. For example, if you cast Whir of Invention (a spell with improvise and mana cost X generic mana blue mana blue mana blue mana ) and choose X to be 3, the total cost is 3 generic mana blue mana blue mana blue mana . If you tap two artifacts, you'll have to pay 1 generic mana blue mana blue mana blue mana .

Equipment attached to a creature doesn't become tapped when that creature becomes tapped, and tapping that Equipment doesn't cause the creature to become tapped.