The bowl18
R package implements Bowling et al.’s (2018) vocal
similarity algorithms.
Within R, you can install the current version of bowl18
from Github as
follows:
if (!require(devtools)) install.packages("devtools")
devtools::install_github("bowl18")
Bowling et al. (2018) formalise two aspects of a musical chord’s ‘vocal similarity’:
1) Its similarity to the harmonic series, assessed with the
gill09_harmonicity()
function;
2) The absence of small frequency intervals, assessed with the
bowl18_min_freq_dist()
function.
gill09_harmonicity()
measures a chord’s similarity to a harmonic
series, after Gill & Purves (2009). It assumes that chord pitches are
precisely aligned with the just-tuned scale provided by Bowling et
al. (2018).
By default, gill09_harmonicity
assumes that the input is a vector of
MIDI pitch numbers. We recommend using the hrep
package to clarify
this input format, as follows:
library(bowl18)
library(hrep)
# Constructing chords with pi_chord()
pi_chord(c(60, 64, 67)) # C major chord
#> Pitch chord: 60 64 67
# Major chord
gill09_harmonicity(pi_chord(c(60, 64, 67)))
#> [1] 0.4666667
# Diminished chord
gill09_harmonicity(pi_chord(c(60, 63, 66)))
#> [1] 0.4285714
# Augmented chord
gill09_harmonicity(pi_chord(c(60, 64, 68)))
#> [1] 0.105
bowl18_min_freq_dist()
returns the minimum frequency distance between
the fundamental frequencies of a chord. It makes no assumptions about
the chord’s tuning.
By default, bowl18_min_freq_dist()
assumes that the input is a vector
of frequencies. We recommend using the hrep
package to clarify this
input format, as follows:
library(bowl18)
library(hrep)
# Constructing chords with pi_chord() and fr_chord()
x <- pi_chord(c(60, 64, 67)) # C major chord
fr_chord(x)
#> Frequency chord: 261.626 Hz, 329.628 Hz, 391.995 Hz
# Major chord
bowl18_min_freq_dist(fr_chord(pi_chord(c(60, 64, 67))))
#> [1] 62.36788
# Cluster chord
bowl18_min_freq_dist(fr_chord(pi_chord(c(60, 61, 62))))
#> [1] 15.55707
Bowling et al. (2018) argue that, in particular, frequency differences smaller than 50 Hz contribute negatively to consonance.
Bowling, D. L., Purves, D., & Gill, K. Z. (2018). Vocal similarity predicts the relative attraction of musical chords. Proceedings of the National Academy of Sciences, 115(1), 216–221. https://doi.org/10.1073/pnas.1713206115
Gill, K. Z., & Purves, D. (2009). A biological rationale for musical scales. PLoS ONE, 4(12), 1–9. https://doi.org/10.1371/journal.pone.0008144
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