mut

The root mut comes from Latin mūtāre, which meant both "to change" and "to exchange." These two senses are really one idea: when you swap one thing for another, the situation has changed. Every member of this family is built on that single image of one state turning into a different state.

The most literal branch is change itself. Add nothing and you get mutate (to change form) and its noun mutation. In biology these became technical terms: a gene that mūtāre — that alters its sequence — produces a mutation. A virus that mutates is, quite literally, changing into a slightly different version of itself. The same word reaches back to plain English: a plan can mutate, an argument can mutate into a fight.

The exchange branch gives us mutual. If something is mutual, it is given and received equally by both sides — each party hands the other the same thing. Mutual respect means I change my stance toward you exactly as you change yours toward me; we have swapped equal regard. The financial "mutual fund" keeps the idea: many investors pool and share in common.

The richest member is commute, from com- (completely) + mūtāre. Originally it meant to thoroughly change something into something else — and that survives in the legal sense "to commute a sentence," i.e. to change a harsh punishment into a lighter one (a death sentence commuted to life). Centuries later it picked up a second life. A railway "commutation ticket" let a traveller exchange many separate fares for one reduced season ticket — they commuted their fares. The daily holders of those tickets became commuters, and the verb commute narrowed to mean traveling regularly between home and work. So one word carries two very different modern meanings, both rooted in "change/exchange."

Transmute adds trans- (across): to change something across a boundary into a wholly new substance. This was the dream word of the alchemists, who hoped to transmute lead into gold. Today it is used for any deep transformation — transmuting grief into art.

The same root quietly powers mutable and immutable ("changeable" / "unchangeable") and permutation (a re-arrangement, where the same items are exchanged into a new order). Once you see mut = change/exchange, the whole family lines up.