Since I'm horrible in describing spells and their effects, I've temporarilly borrowed a gamefaqs extract to list Jade's artes.
strike artes
Artes that could be performed through physical attacks (or well using the spear in Jade's case)
Sonic Spear (Shunjinsou)
Jade thrusts forward with his spear.
Crushing Spear (Ganzairetsujinsou) (Earth FOF)
A crystal appears where the target is. Jade then thrusts through the crystal,
exploding it as well as impaling the target.
Thunder Lance (Tenraisou)
Jade slices upwards, and a bolt of lightning strikes.
Lightning Tempest (Raijinsenpuusou) (Wind FOF)
A tornado of lighting strikes and shears at all within its reach.
arcane artes
Developments from the simple strike artes.
Impaling Heaven (Tenshoutsuigasou)
Jade thrusts forward, lifts the enemy, then impales it whilst in the air.
Goring Hell (Tsuigabakuensou) (Fire FOF)
Jade thrusts forward, lifts the enemy, then the tip of his spear
explodes with fiery goodness.
Sovereign Gale (Fuujinkousenshou)
Jade thrusts his spear into the ground, creating a whirlwind.
Mighty Deluge (Suijinkaryuusou) (Water FOF)
Jade thrusts his spear into the ground, and powerful waves of water
crash onto the enemy.
fonic artes
Artes consisting in spells of different genres (elemental based)
Energy Blast
Energy is concentrated onto the enemy, then exploded.
Photon (Wind FOF)
Light energy is concentrated onto the target, then exploded.
Stalagmite (Rock Break)
Spikes of rock burst from the ground, perforating the unfortunate.
Eruption
An opening to the fiery mantle is created, and blooms of lava sear the enemy.
Splash
Powerful waterfalls pour their load onto the enemy.
Icicle Rain (Water FOF)
A cloud appears and it showers down icicles that skiver multiple targets.
Drain Magic
Drains a small amount og TP from target, and restores TP to caster.
Absorption
Drains Target's TP, and Restores TP to all.
Turbulence
A burst of wind tears at all caught up in it.
Flare Tornado (Fire FOF)
A cyclone of flame burns all caught in it.
Flame Burst
Streams of fire close in on a target, then flare up in an inferno.
Explosion (Explode) (Wind FOF)
A falling spike slams into the ground and explodes.
Ground Dasher (Grand Dasher)
A fissure opens up in the target area, sending wave after wave of spikes that puncture enemies.
Frigid Coffin (Water FOF)
A area of ice envelops targets, then a large lance of ice crashes onto the target.
Blessed Drops (Saint Bubble)
An innocent-looking bubble appears, slowly drifting to the ground. When it hits, a swarm of painful bubbles pop and crack, destroying all within.
Divine Saber (Wind FOF)
Supercharged bolts of lightning crash around the enemy, and a final coup de grace strike finishes off the spell.
Thunder Blade
A sword of lightning smashes into the ground, and then explodes, releasing its charged material.
Gravity Well (Gravity) (Earth FOF)
An enclosed dome traps all inside, whilst extreme pressure crushes.
Infernal Prison (Ignite Prison)
A glyph appears and fiery jets blare up all around, scorching those within.
Raging Mist
Both a cloud of ice and a scorching pool of fire appear. They mix and create hot-spring mayhem.
Absolute
The target is snapped frozen then blown up.
Prism Sword
Many sharp shards of crystal land to form a binding glass-like prison, until the coup de grace comes crashing on the construct.
Meteor Storm (Meteor Swarm)
The sky rains with huge balls of rock, annihilating enemies across the entire battlefield.
mystic artes
The most powerful artes performed by a character, in its two forms (and only usable when the overlimits is activated and a high spell is casted):
mystic cage
Jade binds the entire battlefield in a sphere of energy, then at his command it explodes in a flash of light.
indignation
Jade literally calls upon the thunder of heaven to channel its power
(a gigantic bolt of lightning) onto unsuspecting enemy heads.