All metrics
Score metrics
Pitch rangeDistance between the highest and lowest note in the movement.Chromatic ratioShare of notes outside the key signature in force in that bar (notes needing an accidental).Pitch-class entropyHow evenly the twelve pitch classes are used.Rhythm entropyHow evenly different note durations are mixed.Off-beat onset ratioShare of notes that do not start on a beat of the time signature's unit (the quarter in 3/4).Note densityNumber of note onsets per quarter-note beat, all parts combined.Mean simultaneityAverage number of notes starting together at each onset position.Top-line leap ratioShare of moves in the top line that span a minor third or more.Top-line mean intervalAverage distance in semitones between neighboring notes of the top line.Harmonic rhythmChord labels per bar, from the annotators' Roman-numeral analysis.Chord vocabularyDistinct chord labels per 100 labels.Applied-chord ratioShare of chords applied to another key's tonic (secondary dominants such as V/V).Seventh-chord ratioShare of chords containing a seventh.Modulation rateNumber of changes of the annotated local key, per 100 bars.Top-line stepwise ratioShare of top-line moves by a semitone or tone (1–2 semitones).Top-line repeated-note ratioShare of top-line moves that repeat the same pitch.Top-line rangeDistance between the highest and lowest top-line notes.Melodic direction changesHow often the top line switches between rising and falling.Mean pitchAverage pitch of all notes in the movement (MIDI number; 60 = middle C).Pitch spreadHow widely pitches spread around the mean (standard deviation).Pitch-name vocabulary (line of fifths)Number of distinct pitch names used in the movement, counting C♯ and D♭ separately.Duration vocabularyNumber of distinct note lengths used in the movement.Mean note lengthAverage length of one note (quarter note = 1).Mean chord lengthAverage length of one annotated chord (quarter note = 1).Chromatic chord ratioShare of chords whose Roman numeral carries ♯ or ♭ (♭VI, ♭II, ♯vii …), mostly chords whose root lies outside the key's natural scale.Inversion ratioShare of chords with a non-root note in the bass (first, second or third inversion).Keys visitedNumber of distinct local keys the movement passes through, per the annotation.Minor-key shareShare of chord labels whose local key is minor.Cadence densityAnnotated cadences per 100 bars.Perfect authentic cadence shareShare of cadences that are perfect authentic (PAC: V–I with the top voice ending on the tonic).Rhythmic contrast (nPVI)How much successive top-line inter-onset intervals differ — a speech-rhythm index (Grabe & Low 2002) that Patel & Daniele (2003, Cognition 87(1)) applied to musical themes.Post-leap reversalShare of top-line leaps (minor third or more) followed by a move in the opposite direction.Beat-crossing syncopationShare of notes that start off the beat and last past the next beat — the simplest definition of syncopation.Motif repetitionShare of four-interval chains (five-note motifs) in the top line that recur within the movement.Diminished-seventh ratioShare of chord labels that are diminished sevenths.Neapolitan and augmented-sixth ratioShare of the two classic chromatic pre-dominant chords: the Neapolitan (♭II) and augmented sixths (German, Italian, French).Pedal-point ratioShare of chords that sit over a sustained bass (pedal point).Phrase lengthMedian number of bars between consecutive phrase-end marks in the movement.4- and 8-bar phrase shareShare of gaps between consecutive phrase ends that are exactly 4 or 8 bars — a measure of classical phrase symmetry.
Performance metrics
Tempo minus metronome markTempo measured near the end of the track (the coda) minus Beethoven's metronome mark for that section.Performed / metronome durationTrack length divided by the theoretical length if played at Beethoven's marks without repeats.Across-performer tempo spreadHow much performers of the same piece differ in average tempo.Beat-to-beat tempo changeMedian deviation of the ratio of neighboring beat intervals from 1 — the amount of rubato.Within-performance tempo variationDispersion of beat intervals within one performance (coefficient of variation), including sectional contrasts such as slow introduction vs fast main section, not only rubato.Dynamic spreadStandard deviation of key-strike velocity (MIDI velocity, 0–127) within a performance.Tempo trend by recording yearIn Beethoven's Symphonies 1–8, how the gap between coda tempo and metronome mark differs per decade of recording year (new in 1.4).Damper pedal time shareShare of the playing time during which the damper (right) pedal is down (new in 1.4).Soft pedal useShare of performances that use the soft (left, una corda) pedal at least once (new in 1.4).
Repertoire metrics
Beethoven shareShare of a season's work performances that are Beethoven.Mozart shareShare of a season's work performances that are W. A. Mozart (new in 1.1).Bach shareShare of a season's work performances that are J. S. Bach.Repertoire concentration (HHI)How concentrated a season's work performances are among few composers — the Herfindahl–Hirschman index applied to composer shares.Composers per seasonNumber of distinct composers performed in a season.Excerpt shareShare of work performances that give only part of a work (a movement, overture, aria …) rather than the whole (new in 1.1).Living-composer shareShare of work performances by composers alive at the time (new in 1.1).Repertoire ageHow long the composers whose music is played have been dead — the median, weighted by work performances (new in 1.1).Canon turnoverHow much each decade's list of most-performed composers overlaps with the previous decade's (new in 1.1).Repertoire by conductorThe make-up of the work performances each conductor led in the NY Phil record — number of composers, concentration, most conducted composer, living-composer share (new in 1.4).New-work re-performance (10 years)Share of works first performed by the NY Phil that are played again in another season within 10 years — works whose composer was alive in the season of the first performance (new in 1.4).Women composers' shareShare of a season's work performances (individual composers) by women composers, from Wikidata sex or gender (P21) (new in 1.4).