Do Chords Last Longer as Songs Get Slower?: Tempo Versus Harmonic Rhythm in Four Corpora of Popular Music Trevor de Clercq Music Informatics Interest Group Meeting Society for Music Theory November 3, 2018 San Antonio, TX Slides available at: www.midside.com/presentations/
Slides available at: www.midside.com/presentations/ Tempo Versus Harmonic Rhythm Allan Moore (2001, p. 42) the consistent appearance of a snare drum on the second and fourth beats of a bar allows this length [i.e., the bar] to be standardized. As a result, we will find that rock songs tend to change harmony every bar.
Slides available at: www.midside.com/presentations/ Tempo Versus Harmonic Rhythm Allan Moore (2001, p. 42) the consistent appearance of a snare drum on the second and fourth beats of a bar allows this length [i.e., the bar] to be standardized. As a result, we will find that rock songs tend to change harmony every bar. Average chord durations overall in the RS 200, in bars Chords Mean Trimmed Mean* Median Mode All chords 4.90 1.42 1.23 1.00 Tonic 6.19 2.03 1.59 1.00 Non-Tonic 1.14 1.03 1.00 1.00 source: de Clercq 2017, Table 11 * excludes top and bottom 10% of values (i.e., middle 80%)
Slides available at: www.midside.com/presentations/ Tempo Versus Harmonic Rhythm Allan Moore (2001, p. 42) the consistent appearance of a snare drum on the second and fourth beats of a bar allows this length [i.e., the bar] to be standardized. As a result, we will find that rock songs tend to change harmony every bar. Average chord durations overall in the RS 200, in bars Chords Mean Trimmed Mean* Median Mode All chords 4.90 1.42 1.23 1.00 Tonic 6.19 2.03 1.59 1.00 Non-Tonic 1.14 1.03 1.00 1.00 Implied Hypothesis: As the tempo of a song decreases, average chord duration increases (and vice versa)
Tempo Versus Harmonic Rhythm Implied Hypothesis: As the tempo of a song decreases, average chord duration increases (and vice versa)??????????????? Axis progression (vi IV I V) examples Taylor Swift, You re Not Sorry (2008) 67 BPM, chord durations = 0.5 bar, 1.79 seconds Justin Bieber, Love Me (2009) 125 BPM, chord durations = 1.0 bar, 1.92 seconds The Offspring, The Kids Aren t Alright (1998) 201 BPM, chord durations = 2.0 bars, 2.39 seconds
Tempo Versus Harmonic Rhythm Implied Hypothesis: As the tempo of a song decreases, average chord duration increases (and vice versa)??????????????? Axis progression (vi IV I V) examples Taylor Swift, You re Not Sorry (2008) 67 BPM, chord durations = 0.5 1.0 bar, 1.79 seconds Justin Bieber, Love Me (2009) 125 BPM, chord durations = 1.0 bar, 1.92 seconds The Offspring, The Kids Aren t Alright (1998) 201 BPM, chord durations = 2.0 1.0 bars, 2.39 seconds de Clercq (2016): Measure length considerations in pop/ rock are often best guided by a 2-second ideal bar.
Tempo Versus Harmonic Rhythm Implied Hypothesis: As the tempo of a song decreases, average chord duration increases (and vice versa)??????????????? de Clercq (2016): Measure length considerations in pop/ rock are often best guided by a 2-second ideal bar.???????????????.. A Corpus Study
Tempo Versus Harmonic Rhythm A Corpus Study A Corpora Study The 200-song Rolling Stone magazine rock corpus RS 200 (Temperley & de Clercq, 2013) The 200-song Nashville Number country corpus NN 200 (de Clercq, 2015) The 739-song McGill Billboard charts corpus MG 739 (Burgoyne, Wild, & Fujinaga, 2011) The 179-song Beatles corpus BE 179 (Harte, 2010)
Preliminary Considerations Chord lengths (secs) are log-normally distributed 2000 Histogram of chord lengths in NN 200 [0.2, 0.5] (0.8, 1.1] (1.4, 1.6] (1.9, 2.2] (2.5, 2.8] (3.0, 3.3] (3.6, 3.9] (4.2, 4.4] (4.7, 5.0] (5.3, 5.6] (5.8, 6.1] (6.4, 6.7] (7.0, 7.2] (7.5, 7.8] (8.1, 8.4] (8.6, 8.9] (9.2, 9.5] (9.8, 10.0] (10.3, 10.6] (10.9, 11.2] (11.4, 11.7] (12.0, 12.3] (12.6, 12.8] (13.1, 13.4] (13.7, 14.0] (14.2, 14.5] (14.8, 15.1] (15.4, 15.6] (15.9, 16.2] (16.5, 16.8] (17.0, 17.3] (17.6, 17.9] (18.2, 18.4] Instances 1800 1600 1400 1200 1000 800 600 400 200 0 Chord Length (in seconds)
Preliminary Considerations Chord lengths (secs) are log-normally distributed Q-Q plot of chord lengths (in seconds) in NN 200 45 40 Chord Length (in seconds) 35 30 25 20 15 10 5 0-5 -4-3 -2-1 0 1 2 3 4 5 Z-score
Preliminary Considerations Chord lengths (secs) are log-normally distributed Histogram of base-2 log transform of chord lengths in NN 200 1200 1000 Instances 800 600 400 200 0 [-2.1, -1.9] (-1.8, -1.7] (-1.6, -1.4] (-1.3, -1.2] (-1.0, -0.9] (-0.8, -0.6] (-0.5, -0.4] (-0.3, -0.1] (0.0, 0.1] (0.3, 0.4] (0.5, 0.7] (0.8, 0.9] (1.0, 1.2] (1.3, 1.4] (1.6, 1.7] (1.8, 2.0] (2.1, 2.2] (2.3, 2.5] (2.6, 2.7] (2.9, 3.0] (3.1, 3.3] (3.4, 3.5] (3.6, 3.8] (3.9, 4.0] (4.2, 4.3] (4.4, 4.6] (4.7, 4.8] (4.9, 5.1] (5.2, 5.3] Log Transformation of Chord Lengths (in seconds, base 2)
Preliminary Considerations Chord lengths (secs) are log-normally distributed Q-Q plot of log (base 2) of chord lengths (in seconds) in NN 200 Log Transform of Chord Lengths (in secs) 6 5 4 3 2 1 0-5 -4-3 -2-1 -1 0 1 2 3 4 5-2 -3 Z-score
Preliminary Considerations Chord lengths (bars) are log-normally distributed Chord Length (in bars) Q-Q plot of chord lengths (in bars) in NN 200 20 18 16 14 12 10 8 6 4 2 0-5 -3-1 1 3 5 Z-score
Preliminary Considerations Chord lengths (bars) are log-normally distributed Q-Q plot of log (base 2) of chord lengths (in bars) in NN 200 Log Transform of Chord Lengths (in bars) 5 4 3 2 1 0-5 -4-3 -2-1 -1 0 1 2 3 4 5-2 -3-4 Z-score
Preliminary Considerations Tempo is only weakly log-normally distributed Q-Q plot of tempos (in BPM) in NN 200 210 190 170 Tempo (in BPM) 150 130 110 90 70 50-3 -2-1 0 1 2 3 Z-score
Preliminary Considerations Tempo is only weakly log-normally distributed Q-Q plot of log transform (base 2) of tempos (in BPM) in NN 200 8.00 Log Transform of Tempo (in BPM) 7.50 7.00 6.50 6.00 5.50-3 -2-1 0 1 2 3 Z-score
Experiment 1: Chord Length Versus Tempo H0 : Songs in 4/4 with different median chord lengths have, on average, no difference in tempo H1 : Songs in 4/4 with shorter median chord lengths have, on average, a slower tempo
Experiment 1: Chord Length Versus Tempo H0 : Songs in 4/4 with different median chord lengths have, on average, no difference in tempo H1 : Songs in 4/4 with shorter median chord lengths have, on average, a slower tempo NN 200 results Median Chord Length gmean Tempo N 0.5 bars 97.8 28 1.0 bar 109.1 85 2.0 bars 121.8 27 Comparison t (one-tailed) p 0.5 bars to 1.0 bar t(111) = 2.03.02 1.0 bar to 2.0 bars t(110) = 1.96.03 0.5 bars to 2.0 bars t(53) = 3.37 <.01
Experiment 1: Chord Length Versus Tempo H0 : Songs in 4/4 with different median chord lengths have, on average, no difference in tempo H1 : Songs in 4/4 with shorter median chord lengths have, on average, a slower tempo RS 200 results Median Chord Length gmean Tempo N 0.5 bars 100.5 51 1.0 bar 115.6 71 2.0 bars 139.3 29 Comparison t (one-tailed) p 0.5 bars to 1.0 bar t(120) = 3.18 <.001 1.0 bar to 2.0 bars t(98) = 3.31 <.001 0.5 bars to 2.0 bars t(78) = 5.80 <.0001
Experiment 1: Chord Length Versus Tempo H0 : Songs in 4/4 with different median chord lengths have, on average, no difference in tempo H1 : Songs in 4/4 with shorter median chord lengths have, on average, a slower tempo MG 739 results Median Chord Length gmean Tempo N 0.5 bars 103.1 223 1.0 bar 117.6 305 2.0 bars 139.1 80 Comparison t (one-tailed) p 0.5 bars to 1.0 bar t(526) = 5.81 <.00001 1.0 bar to 2.0 bars t(383) = 5.22 <.00001 0.5 bars to 2.0 bars t(301) = 8.57 <.00001
Experiment 1: Chord Length Versus Tempo H0 : Songs in 4/4 with different median chord lengths have, on average, no difference in tempo H1 : Songs in 4/4 with shorter median chord lengths have, on average, a slower tempo BE 179 results Median Chord Length gmean Tempo N 0.5 bars 94.3 33 1.0 bar 122.5 76 2.0 bars 128.4 12 Comparison t (one-tailed) p 0.5 bars to 1.0 bar t(107) = 6.17 <.00001 1.0 bar to 2.0 bars t(86) = 0.76.23 0.5 bars to 2.0 bars t(43) = 3.78.0002
Experiment 2: Tempo Versus Chord Length H0 : Songs in 4/4 with different tempos have, on average, no difference in chord lengths as measured in bars. H1 : Songs in 4/4 with slower tempos have, on average, shorter chord lengths as measured in bars than songs with faster tempos.
Experiment 2: Tempo Versus Chord Length H0 : Songs in 4/4 with different tempos have, on average, no difference in chord lengths as measured in bars. H1 : Songs in 4/4 with slower tempos have, on average, shorter chord lengths as measured in bars than songs with faster tempos. NN 200 results 5 bins (N = 32 songs) gmean Tempo gmean Length (Bars) gmean Length (Secs) 74.2 0.79 2.53 93.7 0.96 2.44 108.5 1.01 2.24 124.8 1.21 2.32 153.4 1.36 2.13 High / Low 1.73 1.19
Experiment 2: Tempo Versus Chord Length H0 : Songs in 4/4 with different tempos have, on average, no difference in chord lengths as measured in bars. H1 : Songs in 4/4 with slower tempos have, on average, shorter chord lengths as measured in bars than songs with faster tempos. RS 200 results 5 bins (N = 32 songs) gmean Tempo gmean Length (Bars) gmean Length (Secs) 79.6 0.74 2.22 100.5 0.86 2.03 115.6 0.99 2.06 130.3 1.20 2.22 169.6 1.48 2.11 High / Low 2.00 1.05
Experiment 2: Tempo Versus Chord Length H0 : Songs in 4/4 with different tempos have, on average, no difference in chord lengths as measured in bars. H1 : Songs in 4/4 with slower tempos have, on average, shorter chord lengths as measured in bars than songs with faster tempos. MG 739 results 5 bins (N = 134 songs) gmean Tempo gmean Length (Bars) gmean Length (Secs) 75.9 0.71 2.22 102.5 0.93 2.15 117.2 0.90 1.84 130.7 0.90 1.65 164.3 1.19 1.75 High / Low 1.68 1.27
Experiment 2: Tempo Versus Chord Length H0 : Songs in 4/4 with different tempos have, on average, no difference in chord lengths as measured in bars. H1 : Songs in 4/4 with slower tempos have, on average, shorter chord lengths as measured in bars than songs with faster tempos. BE 179 results 5 bins (N = 28 songs) gmean Tempo gmean Length (Bars) gmean Length (Secs) 80.8 0.68 2.01 101.8 0.75 1.78 121.2 0.89 1.76 131.4 0.97 1.77 152.1 1.14 1.81 High / Low 1.69 1.11
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