A measurement of piano playing

Arch depth

How much the tempo swells and recedes across a phrase — the long rise and fall, not beat-to-beat unevenness.

What it sounds like

The same passage — Rachmaninoff Prelude, bars 10–12 — from the recordings that sit lowest and highest on this measurement. Every clip is a note list replayed on one sampled grand at one gain, so the only difference you are hearing is the playing.

Least

Barry Douglas, 1993 — bars 10–12, arch depth 91 ±%27 s

Giovanni Alvino, 2021 — bars 10–12, arch depth 94 ±%21 s

Most

Santiago Rodríguez, 1994 — bars 10–12, arch depth 133 ±%36 s

Olga Kern, 2006 — bars 10–12, arch depth 129 ±%32 s

How it is calculated

The beat period is put on a log scale and smoothed over one bar to leave the phrase-scale trend; arch depth is 2 to the power of that trend's standard deviation, minus 1, as a percentage.

How much pianists differ on it

Every piece in the library, with the range across its recordings. The units mean the same thing in every row, except for basic tempo, which is in each piece’s own beat.

Piece	Recordings	Lowest	Median	Highest
Bach Prelude in C	27	4	7	17
Mozart K. 545	37	4	8	16
Chopin Étude 10/1	31	7	10	17
Gymnopédie 1	23	7	11	18
Pathétique II	47	6	11	18
Schubert Op. 90/3	43	10	14	28
Nocturne Op. 9/2	32	10	16	21
Chopin Étude 10/12	19	13	18	23
Ravel Pavane	33	14	19	27
Träumerei	31	11	19	28
Ravel Ondine	61	18	25	33
Brahms Op. 118/2	28	19	27	38
Schubert Op. 142/3	9	25	29	38
Nocturne Op. 48/1	27	18	30	44
Clair de lune	27	22	30	52
Chopin Ballade 4	12	30	35	48
Fantaisie-Impromptu	20	37	46	55
Rachmaninoff Prelude	29	91	109	133

How reliably it can be measured

A Disklavier capture — the pianist’s own key sensors, no microphone — was rendered to audio, transcribed as if it were a recording, and re-measured. The error the transcription step introduces, as a multiple of how far pianists actually differ on this dial, is 0.06. solid This dial survives transcription intact: where one recording sits on it can be argued from.

All measurements