Research note 02 · Ergonomic sequence search

Generating playable fingerings.

Why a useful system preserves human evidence, searches complete paths, reports confidence, and sometimes declines to answer.

Published 14 July 2026 · Current production decision

A valid number is not necessarily a useful fingering

Piano fingering is contextual. Several paths can be playable. Editorial choices depend on articulation, phrasing, hand shape, learned technique, and what comes before and after the visible passage. A system that fills every note can appear complete while hiding uncertainty.

Helicon treats fingering as a sequence problem with provenance. The current decision is to ship the physically constrained generator and its confidence-gated practice interface, while keeping the difficult-arpeggio specialist experimental.

The product contract comes first

Practice Setup exposes four source policies:

  1. No finger numbers—the default.
  2. Human-authored only—MusicXML and manual edits.
  3. Human-authored, then fill gaps—recorded values become anchors.
  4. Machine-generated only—an independent generated layer.

A 20–99% confidence threshold previews shown human labels, generated labels, ambiguous notes removed by the threshold, and notes that cannot be safely analyzed. Human and generated values use different visual treatment. The generator never overwrites recorded evidence.

Core decision

Abstention is a feature. A conservative generator must not be rewarded merely for avoiding every hard note, but the product must not force low-confidence advice into practice.

The generator uses dynamic programming with hard physical constraints, ergonomic costs, and complete-path alternatives. Candidate finger assignments are evaluated as transitions through time rather than independent classifications.

This lets the solver represent reach, vertical chord geometry, crossings, repeated notes, hand travel, and the cost of one decision on the next. Confidence comes from competing complete paths rather than a decorative probability added afterward.

Data volume is not evidence quality

The research harness assembled 94,015 mechanically clean labels from 1,247 pieces before cross-corpus deduplication. The sources ranged from public-domain symbolic scores to community MusicXML and research-only material. Those categories remain separate because a clean label is not necessarily authoritative or redistributable.

Evaluation requirementWhy it matters
Whole-work splitsPrevent related exercises from leaking across training and test folds
Coverage with precisionPrevent abstention from masquerading as accuracy
Physical violationsKeep impossible paths visible even when note accuracy looks good
Pattern and hand breakdownsExpose localized weaknesses hidden by one aggregate score
Rights and provenance tiersSeparate useful research inputs from publishable material

What the current generator can claim

On a manually checked 22-score public corpus with 612 labelled notes, the available comparison was:

GeneratorCoveragePrecisionViolations
Keyfire, reporting threshold 0%78.9%60.0%0
PianoPlayer 3.0.2100.0%45.3%0

The coverage difference matters. This result supports selective output; it does not establish that Helicon has solved full-coverage fingering. On 94 arpeggio-like positions, Keyfire covered 42.6% at 70.0% precision, while PianoPlayer covered all positions at 43.6% precision.

The negative results changed the product

An all-corpus fitted model improved the held-out result by only 11 net labels, with p = 0.704. That is not evidence of improvement, so the model was not promoted.

An earlier positive result disappeared after Hanon exercises were grouped by complete work. The split had leaked closely related material. The benchmark caught the error and preserved the stronger existing hand-built baseline.

The difficult-arpeggio specialist also remains experimental. Its raw result was worse than the general generator, and confidence-gated routing returned essentially to baseline. A hand-position planner produced inspectable movement hypotheses, but the alternatives were too ambiguous to affect production ranking.

A research harness earns its keep when it prevents a plausible model from shipping.

What comes next

More undifferentiated labels are unlikely to be the best next investment. Future collection should target independently annotated difficult arpeggios, multiple acceptable paths, and specific failure cells. The current generator remains useful precisely because its product boundary is narrower than the unsolved research problem.