The concrete decision rule for switching clef mid-stream versus tolerating ledger lines

Combine the three preceding rules into one decision procedure: (1) compute the ledger-sum for the CURRENT clef over the excursion; (2) compute the ledger-sum for the best alternative clef over the same excursion (clef-choice-general-criterion); (3) if the alternative's sum is not meaningfully lower, stay on the current clef and tolerate the ledger lines (up to the absolute ceiling in ledger-line-sustained-threshold); (4) if the alternative is meaningfully better AND the excursion's duration exceeds the octave-sign span limit (octave-sign-preferred-over-ledger-threshold), prefer a clef change; (5) if the alternative is meaningfully better but the excursion is brief, prefer an octave sign over a clef change (clef-change-frequency-cost's thrashing concern favors this); (6) never introduce a clef change for an excursion of only 1-2 notes under any circumstance — ledger lines or, at most, an accidental awkward moment, are always preferable to a same-passage clef round-trip that short.

Any passage where the individual rules above (ledger-line-sustained-threshold, clef-choice-general-criterion, octave-sign-preferred-over-ledger-threshold, clef-change-frequency-cost) disagree about the right fix because they were evaluated independently rather than through this combined procedure — e.g. a tool that recommends BOTH a clef change (from the general criterion) AND tolerating ledger lines (from the sustained-threshold rule) for the same passage, which is a contradictory pair of findings a user should never see.

This decision procedure is Gradus's own synthesis of the individual rules Gould (Behind Bars), Ross (The Art of Music Engraving), and Read (Music Notation) each state qualitatively but never combine into one explicit algorithm — the brief specifically asks 'when a piece should change clef mid-stream vs tolerate ledger lines,' which none of the four authorities answers as a single formula. This chapter's contribution is making that judgment call mechanizable.

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