Feel: your way through the Labyrinth outside Alcazar (pictured above).
Feel: how much your calves will sting as you scale the tower of the Cathedral. It hurts, but it's worth it. Bonus: no stairs, the climb is a ramp (below).
Hear: the soulful plucking of guitar, hand claps, and wavery singing of flamenco. Often performed by dark, handsome soulful Spaniards that put Antonio Banderas to shame. Bonus sensory experience: watching the dance. I tried to get a picture (below) of one of the dancers but it came out blurry because he moved that fast.
Smell: the overpowering scent of the orange trees that appear to outnumber Spaniards in Seville. The oranges on these trees are bitter, not to be eaten. They are there for decoration, and apparently, to make you hungry because of how good they look and how tempting they smell.