If you cast {Syncopate} with a {Goblin Electromancer} on the field can you cast the {Syncopate} for just its {B} and have it still count at 1.
I assume you mean {U}. The process is slightly more in depth, but yes, this would work.
Just to explain the depth:
When you cast a spell, you declare its cost. Any X or additional/optional costs are declared, an the cost is calculated. Additions and deductions are then calculated, and then you have time to tap the mana or whatever you need to generate mana (if you hadn't generated it yet. {Ommnath, locus of mana} or some mana combos have you produce mana before you cast spells and keep it till end of the phase. Or forever, in the case of locus.).
So, with {syncopate} you would declare you are casting it, declare X is 1 (or 1 + the amount of mana you want to pay) + {U}, then the reduction is applied and you pay only {U} + X -1
TL; DR
When you declare cost of the spell, you need to declare X=1