AoE
Black Mage has a streamlined and elegant AoE toolkit as the only caster with purely GCD damage.
It was improved upon in Shadowbringers with the changes to 
Freeze
Below we’ll cover these tools available to us:
Actions
Freeze
In Shadowbringers Freeze was given a new lease of life on several fronts where:
- it is now a target AoE spell without a ground AoE circle
- it now has a base GCD cast time
- it grants Umbral Ice III like
Blizzard III - at Lv. 68 the
Enhanced Freeze trait grants an Umbral Heart upon casting Freeze
When paired alongside the Lv. 72 trait 
Aspect Mastery which causes all opposing element spells under AF3 / UI3 to cost 0 mp (with the exception of 
Flare), AoE with Freeze is seamless.
Thunder IV
Thunder IV (T4) remains unchanged from Stormblood.
Use at 3+ targets, otherwise 
Sharp 
Thunder III (T3) at 2 targets.
Note: Only one type of Thunder DoT can be on a target at any time. T4’s DoT will overwrite T3’s and vice versa. This is important to keep in mind for Thundercloud procs.
Flare
Foul
General AoE Advice
Black Mage AoE is free-flowing and should be adapted to the encounter.
The same concepts of the Ice and Fire Phases apply to the AoE rotation.
The Ice Phase includes 1 filler spell, usually Foul or T4. Unlike single-target, use procs freely rather than waiting out the proc / DoT timer.
Use Sharp on T4, or on T3 single-target in preparation for adds.
If possible hold Foul or 
T4P until after Freeze to keep casting while waiting for MP.
Use 
Swift on Flare.
Use 
Triple on Flares with the Hot Flare variation even at high enemy counts.
The rotation should be adapted to the scenario and will vary on the mob count and HP. The Hot Flare and Cold Flare variations have similar dps.
In the below methods the empty 
GCDs represent filler of which the following are expected:
- T4
- T4P
- Foul
Hot Flare (3-4 Targets)
→ → 
→ →
Use at 3-4 targets or if the mobs will die just after both Flares.
Cold Flare (5+ Targets)
→ → →
Use at 5+ targets or if the mobs will die before the second Flare of the Hot Flare variation.
Examples
Triple Flare (AF3, 1 Umbral Heart)
→ → → → 
→ →