1 Release Notes

Created: 1/2/2021.

These files contains the computational models for “Automatic Responses to Acoustically Rough Intervals,” particularly the models of roughness and harmonicity. See also the behavioural data and the analyses at a separate repository. The data is also available at OSF: https://osf.io/zmjpd/.

The paper is:

Armitage, J., Lahdelma, I., & Eerola, T. (2021). Automatic responses to musical intervals: Contrasts in acoustic roughness predict affective priming in Western listeners. Journal of Acoustical Society of America, 150(551). https://doi.org/10.1121/10.0005623

2 Harmonicity

Harmonicity for three common models: Harrison and Pearce (2018), Parncutt (1988) and Milne (2013), including the ranks of the model means and the model correlations.

# Harmonicity 3 models: Harrison & Pearce 2018, Parncutt 1988, Milne 2013 
source('model_harmonicity_data.R')
Model output (normalised to 1-10)
Interval Parn88 Milne13 Har18 HarmonicityMean HarmonicityRank
m2 1.00 1.00 1.00 1.00 1
M2 5.27 3.35 5.42 4.68 6
m3 1.00 1.51 2.79 1.76 4
M3 7.03 3.45 4.72 5.07 8
P4 10.00 10.00 10.00 10.00 10
TT 1.00 1.28 1.02 1.10 3
P6 10.00 10.00 10.00 10.00 11
m6 7.03 3.45 4.72 5.07 9
M6 1.00 1.51 2.79 1.76 5
m7 5.27 3.35 5.42 4.68 7
M7 1.00 1.00 1.00 1.00 2
Correlations
Parn88 Milne13 Har18
Parn88 1.00 0.90 0.94
Milne13 0.90 1.00 0.96
Har18 0.94 0.96 1.00

3 Roughness

Roughness values for three common models: Hutchinson and Knopoff (1978), Vassilakis (2001), and Wang et al. (2013), including the ranks of the model means and the model correlations.

# Roughness 3 models: Hutchinson 1978, Vassilakis 2001, Wang et al 2013
source('model_roughness_data.R')
Model output (normalised to 1-10)
Interval Hutc78 Vass01 Wang13 RoughnessMean RoughnessRank
m2 10.00 10.00 10.00 10.00 11
M2 5.51 7.63 4.79 5.98 10
m3 2.74 1.94 3.66 2.78 4
M3 1.92 3.52 4.66 3.37 5
P4 1.43 1.00 3.64 2.02 2
TT 2.44 2.64 2.70 2.60 3
P5 1.00 3.50 1.00 1.83 1
m6 2.37 4.93 4.75 4.01 7
M6 1.66 4.51 5.98 4.05 8
m7 2.54 5.03 5.70 4.42 9
M7 4.94 2.90 2.58 3.47 6
Correlations
Hutc78 Vass01 Wang13
Hutc78 1.00 0.79 0.69
Vass01 0.79 1.00 0.77
Wang13 0.69 0.77 1.00
Model output for additional mistuned intervals
Interval Wang13 Wang13_interpolated
d2 (Detuned piano m2) 1.36 14.44
s2 (Detuned Shepard m2) 1.07 10.11
s5 (Shepard P5) 0.06 -5.56

4 Empirical dissonance ratings

Empirical ratings from classic studies by Huron (1994) and Bowling, Purves, and Gill (2018).

# Empirical data from Huron 1994 and Bowling et al 2018
source('empirical_data.R')
Empirical ratings (normalised to 1-10)
Interval Malm18 Hutch79 Kame69 Bowl18 EmpiricalMean EmpiricalRank
m2 10.00 10.00 10.00 10.00 10.00 11
M2 8.58 5.76 8.71 7.80 7.71 10
m3 5.88 2.71 6.14 4.19 4.73 6
M3 3.51 1.64 5.50 2.16 3.20 4
P4 3.37 1.44 4.86 3.10 3.19 3
TT 6.35 2.37 7.43 7.31 5.87 8
P5 1.00 1.00 1.00 1.00 1.00 1
m6 4.17 2.20 6.79 5.10 4.56 5
M6 2.42 1.49 2.93 4.10 2.74 2
m7 6.87 2.50 5.50 8.16 5.76 7
M7 8.58 5.03 6.14 8.16 6.98 9
Correlations
Malm18 Hutch79 Kame69
Malm18 1.00 0.86 0.86
Hutch79 0.86 1.00 0.78
Kame69 0.86 0.78 1.00

5 Create variable deltas for the interval pairs

source('deltas.R')
IntervalPairs Harmonicity_Delta Roughness_Delta Empirical_Delta
m2P5 9.00 8.17 9.00
m2tt 0.10 7.40 4.13
m3M3 3.30 0.59 1.53
m6M6 3.30 0.04 1.83
M7P5 9.00 1.64 5.98
ttP5 8.90 0.76 4.87
m2M3 4.07 6.63 6.80
m2P5 5.32 4.15 6.71
IntervalPairs Harmonicity_Delta Roughness_Delta Empirical_Delta Harm_D_Class Rough_D_Class Emp_D_Class
m2P5 9.00 8.17 9.00 High High High
m2tt 0.10 7.40 4.13 Low High Low
m3M3 3.30 0.59 1.53 Low Low Low
m6M6 3.30 0.04 1.83 Low Low Low
M7P5 9.00 1.64 5.98 High Low High
ttP5 8.90 0.76 4.87 High Low Low
m2M3 4.07 6.63 6.80 Low High High
m2P5 5.32 4.15 6.71 High High High

[1] “Mistuned pairs”

Mistuned intervals
IntervalPairs Roughness_Delta
d2P5 12.61
s2S5 15.67

6 Create graphs for selected stimuli

Take four intervals that together span low to high delta in roughness and plot the amplitude and spectra for each.

7 References

Bowling, Daniel L., Dale Purves, and Kamraan Z. Gill. 2018. “Vocal Similarity Predicts the Relative Attraction of Musical Chords.” Proceedings of the National Academy of Sciences 115 (1): 216–21.
Harrison, Peter, and Marcus Pearce. 2018. “An energy-based generative sequence model for testing sensory theories of Western harmony.” In Proceedings of the 19th International Society for Music Information Retrieval Conference, 160–67. Paris, France.
Huron, David. 1994. “Interval-Class Content in Equally Tempered Pitch-Class Sets: Common Scales Exhibit Optimum Tonal Consonance.” Music Perception: An Interdisciplinary Journal 11 (3): 289–305.
Hutchinson, William, and Leon Knopoff. 1978. “The acoustic component of Western consonance.” Interface 7 (1): 1–29.
Milne, Andrew J. 2013. “A Computational Model of the Cognition of Tonality.” PhD thesis, The Open University.
Parncutt, Richard. 1988. “Revision of Terhardt’s psychoacoustical model of the root(s) of a musical chord.” Music Perception 6 (1): 65–93.
Vassilakis, Panteleimon Nestor. 2001. “Perceptual and Physical Properties of Amplitude Fluctuation and Their Musical Significance.” PhD thesis, University of California, Los Angeles.
Wang, YS, GQ Shen, H Guo, XL Tang, and T Hamade. 2013. “Roughness Modelling Based on Human Auditory Perception for Sound Quality Evaluation of Vehicle Interior Noise.” Journal of Sound and Vibration 332 (16): 3893–3904.