A dot is forbidden on a note whose onset is off the beat, and forbidden wherever its added length would cross a barline

A dotted note is legible only when it starts exactly on a primary beat — dots on off-beat onsets must become a tied pair instead. Separately and unconditionally, no notehead (dotted or not) may ever span a barline; that is always a tie, never a dot, regardless of beat alignment. Within a bar, once a dotted note's onset is confirmed on-beat, its length may legitimately cover several further beats with no additional restriction — the extremely common dotted-half-note spanning beats 1-3 of 4/4 hides two interior beat onsets and is nonetheless universal, unremarkable notation precisely because it starts on the downbeat.

(1) A dotted quarter note starting on the 'and' of beat 1 in 4/4 (onset 0.5, duration 1.5, ending at 2.0) obscures beat 2 with no marker — Gould requires a tied pair instead. (2) A dotted half note starting on beat 3 of a 4/4 bar (onset 2, duration 3) extends 1 beat into the next bar with no tie — forbidden unconditionally, independent of onset alignment.

Gould, Behind Bars, ch. 'Time signatures'/'Notes and note relationships', dot-vs-tie guidance (dots permitted only when they do not obscure the beat) and the universal never-cross-a-barline rule shared by Read and Ross with no documented exception. NOTE ON A CORRECTION: an earlier draft of this rule additionally capped a legal on-beat dotted note's span at 2 primary beats and downgraded longer spans to a suggestion.

This rule can be decided from pitches, durations and voices — no layout required. A validator can check it before anything is drawn.