History has a way of wiping away institutions thought to be invulnerable. However, one order has remained throughout time: The Harmonium. This mysterious order only appears in times of dire circumstance, shifting the flow of events subtly for the singular goal of preventing the destruction of humanity. Are they even from this world? Any world?  Nobody quite knows where they come from, and very few can even claim to have ever met a Harmonium. That may be for the best, for their appearance typically marks times of great turmoil to come.

The process of joining the Harmonium as an acolyte is just as illusive as the group itself. Some even surmise that one only joins as part of a blueprint by the Harmonium itself. Nevertheless, the martial prowess of these monks is not their focus, but rather a tool in the toolbox. No, the Harmonium's focus is Calculation: a form of meditation that someone grants the user the ability to mathematically predict events on both large and small scale.

Level 3: Derivation

At 3rd level, you gain the ability to predict and alter the flow of events in battle. 

When you spend a focus point to use Patient Defense, you may choose a creature you can see within 30 feet to Analyze. If you do, you may do the following until beginning of your next turn:

Derive Weakness: When the creature is damaged, you may use your reaction to increase the damage received by a roll of your Martial Arts die plus your Wisdom modifier.

Derive Movement: When the creature moves, you may use your reaction to move up to your movement speed. The DM will show you where the creature will move, but your movement occurs first.

Derive Intention: At the beginning of any creature's turn, you may use your reaction to read the creature's intended movement direction and action. The DM will also tell you if this intention is Hesitant, Confident, or Certain.

• Hesitant: The creature is likely waiting to see what happens next before deciding its intention
• Confident: The creature will execute this intention if a tactically better option does not appear.
• Certain: The creature will execute this intention unless doing so obviously becomes gravely harmful.

Additionally, you can the ability to subtly communicate this information to your allies as a free action, though a creature may be able to tell you did so if their Passive Insight meets your Focus Point DC (8 plus your Wisdom modifier plus your proficiency bonus) 

Level 3: Predication

You understand the flow of battle before it even begins. You gain the following benefits: 

• You cannot be surprised
• If you are unconscious when initiative is rolled, you are no longer unconscious. 
• You may spend 1 Focus Point to alter the initiative roll of a creature you can see by a roll of your Martial Arts dice

Level 6: Multivariate Derivation

At 6th level, you increase your mental capacity for more complex equations. When you perform Derivation, you may spend an additional Focus Point to target 2 additional creatures.

Branching Predication

You now predicate creature's actions further in the future. When alter a creature's initiative using Predication, that creature begins the battle Analyzed. 

Level 11: Calculation

Your induction into the Harmonium has truly begun. As an action, you can spend one hour in a meditative state. During this time you lose all access to your senses. You gain a near-certain understanding of all events to occur in the next 24 hours, with the following restrictions

• You must specify a scope. This can include anything from the events of what occurs in a small tavern or room, all the way to the large scale interactions between nations. The DM will then provide the sequence of events at that scope. If you choose a city level scope, for example, you will calculate events such as large gatherings, notable crimes, or important decisions by city officials, but not  movement of singular persons or conversations at a dinner table.
• Any action by PCs are outside the bounds of Calculation. You are unable to predict what any PC will do, and therefore cannot predict how the flow of events will change as the result of player action.
• When you complete a Calculation, you gain 2 levels of exhaustion. 

Level 17: Mulithreaded Mind

You now delegate an entire section of your mind to mathematical analysis, and no longer have to focus to do so. You can now activate Derivation when you spend a Focus Point to use Step of the Wind or Flurry of Blows.

Level 17: Alter History

At 17th level, you finally learn the most important function of the Harmonium: to alter the flow of history as needed. Your Calculation improves as follows

• You may Calculate a 24 hour time span any day in the future as you wish. The level of exhaustion you gain depends on how far in the future you Calculate.

Time in Future	Levels of Exhaustion
24 Hours or Less	2
0 - 1 Years	3
1 - 5 Years	4
5 - 10 Years	5
10+ Years	6 for each decade, rounded up

If more than one creature with this feature performs the same Calculation, these levels of exhaustion can be divided evenly amoung those creatures.

• As opposed to Calculating out the flow of events in 24 hours timespans, you may now attempt to discern the actual results of some action or event (including those caused by the PCs). Generally, the further out you calculate, the more vague the results. For example, you may be able to predict the exactly who will become king, but Calculations years from now may only derive the King's general ideology or alignment. This is at the DM's discretion. The DM may also give you the option to see how an event will effect further and further times in the future. The exhaustion suffered is based on the latest time predicted.

Finally, you may fully assert your position as a Harmonium and attempt alter history. When you Calculate, you may target a creature attached to an event that is to occur. Using the secret pathways of the Harmonium, you may teleport to that creature's location, given that they are on the same plane of existence to you. That creature must succeed on a Wisdom saving throw with a DC equal to that of your Focus Point abilities.

On a failure, that creature must do all in their power to prevent that event from occurring for the next year. You may choose to not make your influence known to the creature. In this case, the creature will self-rationalize their actions. Once that year is passed, they may or may not continue acting in a way that prevents that event depending on their individual circumstance following this. Generally, a creature who has set themselves on a life path for a year are unlikely to alter that path without interference.