How difficulty is rated
Each score has two levels, from 1 (easiest) to 9, after Orchestrion's two ways of playing: rhythm, where you play each hand's rhythm on any keys and the score supplies the notes, and notes, where you play the notes yourself.
What is measured
Everything is computed from the score itself. Each staff is one hand, whose voices combine into the rhythm it plays. A hand acts when it presses and when it releases; a release counts when it doesn't coincide with the hand's next press: a little when a note is merely not held to the next, much more for a staccato. The measures, and the weight each currently has:
| Measure | Weight |
|---|---|
| how fast the hands act: presses and releases per second for rhythm, notes per second for notes, in the busiest passages (90th percentile of 3-second windows) [2] | 3.66 |
| independence of the hands: the share of a hand's actions the other hand doesn't share | 0.94 |
| syncopation as heard: onsets on weak beats with the stronger beat that follows left silent [7, 8] | 0.00 |
| syncopation within each hand's own rhythm [7, 8] | 0.00 |
| notes off the beat's duple and triple subdivisions (other tuplets, irregular groups) | 1.29 |
| cross-rhythm: beats where duplets and triplets meet, in one hand or between the hands | 0.13 |
| variety of the durations between a hand's onsets (entropy) [9] | 0.18 |
| notes per chord [4] | 0.50 |
| hand span: the interval within a hand's chords [4, 6] | 0.80 |
| hand shifts: how far, beyond an octave, the notes a hand plays within 0.4 s reach [3, 4] | 2.36 |
| notes held while the same hand plays others (finger independence) [4] | 0.88 |
How the levels are set
The weights are fitted to the levels of difficulty that the publisher G. Henle Verlag gives its piano editions [1], for 118 pieces from the Mutopia Project that Henle has graded. Henle grades a piece as a whole, so the fit predicts that level: a base, plus the piece's pace, plus its other rhythm and notes measures. A score's rhythm level is the base, its pace, and twice its other rhythm measures: what its level would be if its notes were as hard as its rhythm; likewise for notes. Each piece left out of the fit in turn, the fitted level is within one of Henle's for 86% of the pieces, and equal for 34%.
The levels are ours, not Henle's: a score's level here is what the model makes of it, on a scale calibrated to Henle's.
Prior work
The measures follow research on the difficulty of piano scores and on rhythmic complexity: speed and fingering [2, 3], hand span, chords and polyphony [4, 5, 6], syncopation [7, 8] and rhythmic variety [9]. Combining several aspects of performance, rather than one, follows [6]. Weighting releases, and the split into a rhythm and a notes level, are our own.
- G. Henle Verlag. Levels of difficulty (piano: after Rolf Koenen).
- E. Nakamura and K. Yoshii (2018). Statistical piano reduction controlling performance difficulty. APSIPA Transactions on Signal and Information Processing.
- E. Nakamura, N. Ono and S. Sagayama (2014). Merged-output HMM for piano fingering of both hands. ISMIR.
- V. Sébastien, H. Ralambondrainy, O. Sébastien and N. Conruyt (2012). Score Analyzer: automatically determining scores difficulty level for instrumental e-learning. ISMIR.
- P. Ramoneda et al. (2022). Score difficulty analysis for piano performance education based on fingering. ICASSP.
- P. Ramoneda et al. (2024). Combining piano performance dimensions for score difficulty classification. Expert Systems with Applications 238.
- H. C. Longuet-Higgins and C. S. Lee (1984). The rhythmic interpretation of monophonic music. Music Perception 1(4).
- F. Gómez, A. Melvin, D. Rappaport and G. T. Toussaint (2005). Mathematical measures of syncopation. Bridges.
- G. T. Toussaint (2013). The Geometry of Musical Rhythm. CRC Press.
Method rolls-1. The code and the calibration data are in
the repository
(difficulty.py, calibrate.py, difficulty-calibration.tsv).