[RPG] How many elementals can you control at once

I'm assuming here that your DM does not allow you to "cheat" by taking long rests more than once every 24 hours.

Your magic items are a Tome of the Stilled Tongue and 2 × Pearls of Power.

Every day, you have the following spell slots you can use to make or control undead:

9th level: 1 + 1 from Arcane Recovery + 1 from Tome of the Stilled Tongue = 3

8th level: 1

7th level: 2

6th level: 2

5th level: 3

4th level: 3

3rd level: 3 + 1 from Signature Spell + 2 from Pearls of Power = 6

Day 1:

• 3 × 9th level Create Undead = 6 mummies
• 1 × 8th level Create Undead = 2 wights
• 2 × 7th level Create Undead = 8 ghouls
• 2 × 6th level Create Undead = 6 ghouls
• 3 × 5th level Animate Dead = 18 skeletons
• 3 × 4th level Animate Dead = 12 skeletons
• 6 × 3rd level Animate Dead = 12 skeletons

Total: 6 mummies, 2 wights, 14 ghouls, 42 skeletons

Day 2:

• 6th, 7th, 8th and 9th level spell slots are used to reassert control over mummies, wights, and ghouls
• 6 × 3rd level spell slots and 3 × 4th level spell slots are used to reassert control over 42 skeletons
• 3 × 5th level spell slots are used to animate 24 skeletons

Total: 4 mummies, 2 wights, 14 ghouls, 66 skeletons

Day 3 and onwards:

• 6th, 7th, 8th and 9th level spell slots are used to reassert control over mummies, wights, and ghouls

• 6 × 3rd level spell slots, 3 × 4th level spell slots, and 3 × 5th level spell slots are used to reassert control over 66 skeletons

Total: 4 mummies, 2 wights, 14 ghouls, 66 skeletons

Monk: Way of the Shadow

The Way of Shadows Monk with a quarterstaff will have two rolls per melee attack, will roll a different kind of die for damage, can use flurry of blows rolls when Ki is available (die rolls for attack and damage). Deflect Missiles increases the number of rolls when ranged enemies are involved. At level 5 there's another attack. Roll again.

Presuming that you do not have a Rogue/Thief in the party, and the Monk takes a background that will offer Tools/Thieves Tools (such as Urchin) she'll have lots of chances to roll the dice by using stealth and lock picking rolls, as well as making climb checks when appropriate. As levels go up uses of Ki will offer other opportunities(though less dice intensive than the Way of Four Elements monk). By level 4, the reduced damage from a fall (Slow Fall) should entice the Monk to climb more often as it presents a lower cost for failure.

The higher Wisdom makes the monk a prime roller for Perception, if others use the Help action. (Assuming the party understands how beneficial that is). If you want to add party face to the duties of your monk (rather incongruous for a Shadow Monk IMO) consider a half elf way of shadows Monk built on a point buy(not an optimized party face but a useful one):

Str 8
Dex 15 (+1 racial)
Con 14
Int 8
Wis 15 (+1 racial)
Cha 10 (+2 racial)
Offers an initial set up of S 8 D 16 C 14 I 8 W 16 Ch 12

Make sure the Persuasion and/or Intimidation skills are chosen, to boost that modest +1 from Charisma with proficiency.

This monk need not be strong and need not be smart, but will roll the dice a lot. (Climbing checks with Acrobatics versus Athletics should keep things interesting if the adventure has plenty of climbs and chances to use acrobatics).

You could make the same Way of the Shadow Monk, almost, with a Ghostwise Halfling: Point buy: 8, 14(+2 racial dex) , 14, 8, 15(+1 racial wisdom), 12 =>
Str 8, Dex 16, Con 14, Int 8, Wis 16, Cha 12.
The added benefit of doing this, in terms of die rolls, is the Halfling's racial ability to re-roll any 1 on a 1d20. A bit more rolling on top of all of the rest of it. (Thanks to yinzanat for reminding me of this Sword Coast Adventurer's Guide racial choice for halflings).

Not a burden to the party: no serious material needs, no magic item needs (by level 6), nothing but sly contribution to the party's goals and plenty of action in combat.

Full disclosure: my Way of Shadows monk "died" because that group broke up. :( Never got that level 6 Ki Empowered Strike. I have found that both this monk, and another one (way of the open hand) in a campaign that's on hold, get plenty of action and rolls at low levels.