Published 14 July 2026 · Deterministic analysis
The question is smaller than it first appears
“How difficult is this song?” is not precise enough to answer. Different arrangements of the same song can demand completely different technique. Encoded tempo may be wrong. A passage may be slow but require a blind multi-octave landing. A repetitive stream can be physically extreme while remaining structurally simple.
Elevation therefore answers a narrower question: what demands does this exact encoded arrangement place on a canonical reference pianist? It does not predict how hard the music will feel to a particular player, and it is not a graded-exam equivalence.
A scale with a frontier, not a ceiling
Elevation is nonnegative and unbounded. A score of 100 represents the practical frontier of human piano performance for the reference profile. Values above 100 remain meaningful: they describe arrangements whose encoded demands exceed that range instead of compressing them into a maximum score.
An integer is useful for sorting. Ten-point bands are the more defensible unit for calibration and comparison.
Nine factors, kept visible
The analyzer produces an overall Elevation, confidence and playability status, a hardest passage, and a factor vector:
| Factor | Demand represented |
|---|---|
| Speed | Physical rate implied by notes and encoded tempo |
| Density | Concurrent and near-concurrent note load |
| Reach | Vertical hand span and chord geometry |
| Travel | Velocity of hand movement across the keyboard |
| Rhythm | Temporal subdivision and rhythmic complexity |
| Coordination | Independent and simultaneous bilateral demands |
| Endurance | Sustained exposure to demanding material |
| Pattern | Pitch entropy and chunked pitch-set complexity |
| Landing | Worst absolute relocation, independent of tempo |
Pattern is deliberately important. It prevents structurally varied music from being treated as a small correction to local execution peaks. A separate execution-weighted path can still keep repetitive but physically impossible streams above the human frontier.
Calibration requires repertoire and provenance
The human frontier is anchored with exact MIDI or MusicXML artifacts. Each usable anchor records a digest, provenance, authority references, the technique it exercises, and an acceptable Elevation range. The practice corpus then samples every ten-point band across multiple genres and technical mechanisms.
Calibration material is not automatically redistributable because the underlying composition is old. Modern engravings, editorial fingerings, performance timing, and dataset annotations can carry separate rights. Helicon keeps public, research-only, and local material visibly separate.
What changed when physical fingering entered the model
Elevation 1.2 tested several measurements derived from a physically constrained fingering path. Most were rejected. Path ambiguity, crossings, movement velocity, and repeated-note changes did not add a stable monotonic signal.
Only the 90th-percentile vertical/chord cost added consistent information. On a five-fold held-out CIPI ablation, it reduced grade RMSE from 1.169 to 1.120 and improved cross-grade pair ordering from 83.79% to 84.68%.
| Validation set | Result |
|---|---|
| CIPI, 660 works | Spearman rank correlation rose from 0.774 to 0.790 |
| Mikrokosmos, 146 works | Henle-label ordering rose from 92.01% to 92.19% |
| Mixed local library | 4,363 of 4,405 files analyzed; 13.4 ms median |
| Human-frontier anchors | Five available artifacts remained within their reviewed ranges |
Elevation 1.3 then aligned hand assignment with the resolver used by fingering generation and practice rendering. Stored analyses retain their analyzer version so recalibration cannot silently change their meaning.
What the number does not know
- It does not know a specific player's anatomy, background, or learned repertoire.
- It cannot repair misleading tempo metadata without outside evidence.
- It describes the encoded arrangement, not the abstract composition.
- It does not convert cleanly to a conservatory grade or pedagogical sequence.
- It is a white-box rubric under active calibration, not ground truth.
The useful result is not merely 73. It is 73, analyzer 1.3, with this factor vector, this confidence, and this hardest passage.