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Rule
Gradus GE-405 · cite this code — it is permanent. Rule id vs-slur-sag-scaling
A slur's control points must be computed from (a) the horizontal distance between its endpoints, and (b) the highest (or lowest) intervening notehead it must clear.
Ross, The Art of Music Engraving gives explicit slur-depth-vs-span guidance; Gould, Behind Bars ch. 'Ties and slurs' shows slurs of varying depth scaled to their span in worked examples.
This rule needs the notated content and the rendered result together — the score says what should happen, the page says whether it did.
Gradus GE-405 — Slur curvature must scale with the span it covers and the height of its highest/lowest intervening note. Gradus Engraving Rulebook v1.0. https://gradusmusic.com/engraving/rule/vs-slur-sag-scaling
Rulebook v1.0 · text licensed CC-BY-4.0 · machine-readable at /api/v1/engraving/rules/vs-slur-sag-scaling