The flute songs provide an AoE buff (or debuff) which differs between each tune played...
Here are the ones I know: (NOTE: Names might be totally wrong)
Irratius - Causes any Allies / Enemies in effect to become confused
Angere - Allies within effect have "ATK +100% / DEF -50%" Valere - Allies within effect have "ATK -50% / DEF +100%"
Prudentiae - Allies / Enemies within effect suffer from Silence. Prevents magic spells from striking within area of effect, removes non-conditional debuffs and/or delay-damage magic (Astroluminous, Hydrain). DOES NOT block special attacks!
Song of Prayer (name?) - Allies within effect have "All Parameters +100%" (However, Capell must spend 100 MP per second to maintain the effect)
Placare (used in town) - Earns small amounts of Fol at irregular times whilst playing.
Hypnoticus - Enemies in range may suffer from Sleep condition.
Alucinati (non-continuous) - Creates a clone-image of Capell which explodes after a short time. Enemies which detect the clone-image will act predictably, attacking it and setting off the explosion.
Obduratus - Targeted enemy may suffer from Charmed condition Obstreporus - No effect whatsoever. As an aside, it can be used to get an enemy's attention (if they don't suffer from Unhearing condition) but it provides no benefits.
NOTE: Capell must continuously play the song to apply the effect. (Except for Alucinati) If Capell is struck by an attack his song is interrupted (avoid this with the enchantment "No Stun / DEF -50%" or "Damage Zero / No Attacking")