Classical Music Metrics
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Performance metricsUnit: log₂ ratio

Beat-to-beat tempo change

Median deviation of the ratio of neighboring beat intervals from 1 — the amount of rubato.

Formula
per performance, median |log₂(IBIᵢ / IBIᵢ₋₁)|; the piece value is the median across performances. IBI = inter-beat interval.
How to read it
0.06 means about 4% (2^0.06 − 1) stretch or squeeze per beat. Beethoven sonatas run higher than Bach's Well-Tempered Clavier.
Caveats
Beat positions are the dataset's annotations; unannotated beats (bR) are dropped.
0.0250.0500.0750.1000.1250.150log₂ ratioBach0.0470.0470.0420.0740.0400.0290.0390.0300.0330.0320.0550.0540.0370.0430.0390.0620.0300.0470.0590.0450.0340.0810.0430.0210.0290.0380.0300.0370.0620.1040.0360.0720.0570.0510.0480.0370.0650.0600.0250.0220.0420.1010.0510.0370.0330.0700.0460.0520.0470.0350.0700.0430.0390.0390.0250.0310.0390.0390.057median 0.042Beethoven0.0680.0770.0650.0960.0850.0970.0570.1000.1300.0620.0560.0560.1050.1100.1150.0650.0490.0670.0770.0500.0670.1130.0700.0740.0590.0940.0830.0970.0870.0510.0850.1130.0970.0680.1640.1400.0940.0670.0530.1180.0820.0920.0580.0630.0600.0800.0680.1040.1440.0620.0700.0480.0510.1030.1260.095median 0.078
One dot per piece (a single-performance piece shows that performance's value). Mozart (6 pieces, 16 performances) is too small a sample for the chart and appears only in the table below.
ComposerPiecePerf.Tempo (median)Beat-to-beat tempo change
BeethovenPiano_Sonatas_29-211960.164
BeethovenPiano_Sonatas_7-322190.144
BeethovenPiano_Sonatas_29-31240.140
BeethovenPiano_Sonatas_15-131840.130
BeethovenPiano_Sonatas_9-211150.126
BeethovenPiano_Sonatas_30-18560.118
BeethovenPiano_Sonatas_17-312770.115
BeethovenPiano_Sonatas_27-21800.113
BeethovenPiano_Sonatas_21-23160.113
MozartFantasie_4751570.111
BeethovenPiano_Sonatas_17-21410.110
BeethovenPiano_Sonatas_17-1141470.105
BeethovenPiano_Sonatas_7-22180.104
BachItalian_concerto3300.104
BeethovenPiano_Sonatas_9-111470.103
BachPrelude_bwv_8661730.101
BeethovenPiano_Sonatas_14-311450.100
BeethovenPiano_Sonatas_12-13910.097
BeethovenPiano_Sonatas_26-1111800.097
BeethovenPiano_Sonatas_28-15530.097
BeethovenPiano_Sonatas_11-21300.096
BeethovenPiano_Sonatas_9-31810.095
BeethovenPiano_Sonatas_23-1171120.094
BeethovenPiano_Sonatas_29-411060.094
BeethovenPiano_Sonatas_31-272320.092
BeethovenPiano_Sonatas_26-25230.087
BeethovenPiano_Sonatas_27-171390.085
BeethovenPiano_Sonatas_11-311270.085
BeethovenPiano_Sonatas_24-191160.083
BeethovenPiano_Sonatas_31-121560.082
BachFugue_bwv_88412050.081
BeethovenPiano_Sonatas_5-132000.080
BeethovenPiano_Sonatas_18-421780.077
BeethovenPiano_Sonatas_10-11860.077
BachFugue_bwv_85611970.074
MozartPiano_Sonatas_12-141500.074
BeethovenPiano_Sonatas_22-13830.074
BachPrelude_bwv_84892670.072
BeethovenPiano_Sonatas_21-331130.070
BachPrelude_bwv_8833450.070
BachPrelude_bwv_8732450.070
BeethovenPiano_Sonatas_8-121020.070
BeethovenPiano_Sonatas_28-211390.068
BeethovenPiano_Sonatas_7-191380.068
BeethovenPiano_Sonatas_1-111120.068
BeethovenPiano_Sonatas_3-181380.067
MozartPiano_Sonatas_11-311430.067
BeethovenPiano_Sonatas_18-31810.067
MozartPiano_Sonatas_8-151330.067
BeethovenPiano_Sonatas_21-1251460.067
BeethovenPiano_Sonatas_11-171480.065
BeethovenPiano_Sonatas_18-191270.065
BachPrelude_bwv_86061860.065
BeethovenPiano_Sonatas_32-19970.063
BachFugue_bwv_87321460.062
BachFugue_bwv_89332050.062
BeethovenPiano_Sonatas_7-421180.062
BeethovenPiano_Sonatas_15-41790.062
BachPrelude_bwv_86211080.060
BeethovenPiano_Sonatas_4-191290.060
BeethovenPiano_Sonatas_22-211180.059
BachFugue_bwv_8762860.059
BeethovenPiano_Sonatas_31-3_410520.058
MozartPiano_Sonatas_12-22360.058
BachPrelude_bwv_8545670.057
BachPrelude_bwv_8933590.057
BeethovenPiano_Sonatas_13-41980.057
BeethovenPiano_Sonatas_16-21350.056
BeethovenPiano_Sonatas_16-171370.056
BachFugue_bwv_8653860.055
MozartPiano_Sonatas_12-33980.055
BachFugue_bwv_8661910.054
BeethovenPiano_Sonatas_3-21230.053
BachPrelude_bwv_87531260.052
BeethovenPiano_Sonatas_8-31970.051
BeethovenPiano_Sonatas_26-341100.051
BachPrelude_bwv_8672340.051
BachPrelude_bwv_8561780.051
BeethovenPiano_Sonatas_2-131240.050
BeethovenPiano_Sonatas_18-24940.049
BeethovenPiano_Sonatas_8-21300.048
BachPrelude_bwv_8576460.048
BachPrelude_bwv_8762970.047
BachFugue_bwv_8461450.047
BachFugue_bwv_8752530.047
BachFugue_bwv_84891040.047
BachPrelude_bwv_8742850.046
BachFugue_bwv_88031190.045
BachPrelude_bwv_88411260.043
BachFugue_bwv_8856990.043
BachFugue_bwv_8681660.043
BachPrelude_bwv_8653880.042
BachFugue_bwv_85451100.042
BachFugue_bwv_8576650.040
BachPrelude_bwv_89221030.039
BachFugue_bwv_8606630.039
BachPrelude_bwv_88711090.039
BachPrelude_bwv_8912680.039
BachFugue_bwv_87031170.039
BachPrelude_bwv_8856320.039
BachFugue_bwv_8896720.038
BachPrelude_bwv_8681720.037
BachFugue_bwv_8672620.037
BachPrelude_bwv_8582880.037
BachFugue_bwv_8922530.037
BachPrelude_bwv_8461610.036
BachPrelude_bwv_8803630.035
BachFugue_bwv_8836820.034
BachFugue_bwv_8633570.033
BachPrelude_bwv_8703540.033
BachFugue_bwv_8641670.032
BachPrelude_bwv_8896560.031
BachFugue_bwv_8621550.030
BachFugue_bwv_8911850.030
BachFugue_bwv_8743360.030
BachFugue_bwv_88811020.029
BachFugue_bwv_8582620.029
BachPrelude_bwv_8881790.025
BachPrelude_bwv_8633340.025
BachPrelude_bwv_8641910.022
BachFugue_bwv_8871490.021

Source

ASAP dataset (Foscarin et al., ISMIR 2020). Piano MIDI performances aligned beat-by-beat to scores: 169 Bach (Well-Tempered Clavier) and 271 Beethoven (sonatas); 169 and 259 of these have beat counts matching the score and only those are used. Version 1.1 adds Mozart: 6 movements (K.310/i, K.331/iii, K.332 complete, Fantasia K.475), 16 performances — one to five per piece, so they appear in tables but not in comparison charts. Performances come from MAESTRO (International Piano-e-Competition). https://github.com/fosfrancesco/asap-dataset · License: CC BY-NC-SA 4.0

asap_performance_metrics.csvasap_piece_summary.csvasap_pedal.csvasap_pedal_summary.csvasap_pedal_recordings.csv