mod

The root mod comes from Latin modus — a word that meant a measure: the right amount, the proper limit, the fitting way of doing something. A Roman builder used a modulus (a small measure) to keep the proportions of a column correct. A musician kept to a modus — a measured rhythm. From this single idea of "the correct measure," an entire family fans out, and almost every branch is still asking the same question: does this stay within the right limit?

Start with the plainest branch — measure as a way or pattern. A mode is a manner of doing something (the mode of operation). A model is the small measured pattern you copy a bigger thing from — a model car, a role model. A module is one measured-out unit of a larger system. To modulate is to keep adjusting something (a voice, a signal) to the right measure moment by moment.

Next, measure as the act of adjusting. To modify something is literally to make it fit a measure — the hidden -fy comes from facere, "to make." A modification is the change that results. This is the most active sense of the root: you take something and bring it back inside the right size.

Then the most human branch — measure as self-restraint. To be moderate is to keep yourself within measure: not extreme, not excessive (moderate drinking, a moderate climate). To be modest is to keep within your proper measure socially — not boastful, not showing off; a modest home is a small, unpretentious one. Immodesty is breaking that limit. A modicum is just a small measure — a modicum of respect.

Two branches surprise people. Accommodate is ad- (to) + com- (together/with) + modus — "to bring things to a common measure," i.e. to make them fit. A hotel accommodates guests by fitting them in; you accommodate someone's needs by adjusting to fit them. Commodity and commodious come from com- + modus meaning "with due measure" → "convenient, fitting": a commodity was originally something useful and fitting (now a tradable good), and a commodious room is one with comfortably ample measure — spacious.

Finally modern: from Late Latin modernus, built on modo "just now" (an offshoot of modus as "a measure of time") — literally "of the present manner." The thread holding the whole family together is the Roman builder's ruler: every mod word is checking something against the right measure — a way, a size, a limit, or the present moment.