Empirically testing<i>Tonnetz</i>, voice-leading, and spectral models of perceived triadic distance

Milne, Andrew J.; Holland, Simon

doi:10.1080/17459737.2016.1152517

Cited by 29 publications

(31 citation statements)

References 41 publications

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“…Similar to previous literature (e.g. Hutchinson & Knopoff, 1978;Milne & Holland, 2016;Parncutt & Strasburger, 1994), we default to modelling each complex tone with 11 partials, and give the th partial an amplitude of 1/ , with the amplitudes being provided in arbitrary units. These defaults are somewhat arbitrary, and the researcher is encouraged to adjust the number of harmonics and their amplitudes to reflect the particular sound being modelled.…”

Section: Sparse Frequency Spectrummentioning

confidence: 99%

Representing Harmony in Computational Music Cognition

Harrison¹,

Pearce²

2020

Preprint

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Cognitive theories of harmony require unambiguous formal models of how listeners internally represent chords and chord progressions. Various model representations have been used in previous research, but it is not always clear what cognitive assumptions are implied by these different representations, and how these representations might be converted to one another. The present research systematically addresses these issues. First, we compile a network of 13 low-level harmonic representations relevant for music cognition, organised into three categories: symbolic, acoustic, and sensory. Second, we define integer encodings for four of these representations, which provide bijective mappings between set-based chord representations (e.g. '(0, {0, 3, 6})') and integer-based representations (e.g. '289'). Third, we introduce a new open-source R package, hrep (http://hrep.pmcharrison.com), which implements these different representations in an easy-to-use object-oriented framework. We also discuss computational methods for deriving higher-level representations from these low-level representations. This work should provide a useful platform for future research into harmony cognition.

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Section: Sparse Frequency Spectrummentioning

confidence: 99%

Representing Harmony in Computational Music Cognition

Harrison¹,

Pearce²

2020

Preprint

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“…These algorithms have three free parameters: the number of harmonics modeled in each complex tone, the harmonic roll-off rate (ρ), and the standard deviation of the Gaussian smoothing distribution (σ). We set the number of harmonics to 11 (including the fundamental frequency), and set the other two parameters to the optimized values in Milne and Holland (2016): a roll-off of ρ = 0.75, and a standard deviation of σ = 6.83 cents. (2006), whose description includes a parametric approximation for the relationship between interval size and pure-dyad dissonance (see also Bigand et al, 1996).…”

Section: Modelsmentioning

confidence: 99%

Simultaneous consonance in music perception and composition

Pmc¹,

Mt²

2019

Preprint

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Simultaneous consonance is a salient perceptual phenomenon corresponding to the perceived pleasantness of simultaneously sounding musical tones. Various competing theories of consonance have been proposed over the centuries, but recently a consensus has developed that simultaneous consonance is primarily driven by harmonicity perception. Here we question this view, substantiating our argument by critically reviewing historic consonance research from a broad variety of disciplines, re-analyzing consonance perception data from four previous behavioral studies representing more than 500 participants, and modeling three Western musical corpora representing more than 100,000 compositions. We conclude that simultaneous consonance is a composite phenomenon that derives in large part from three phenomena: interference, periodicity/harmonicity, and cultural familiarity. We formalize this conclusion with a computational model that predicts a musical chord’s simultaneous consonance from these three features, and release this model in an open-source R package, incon, alongside 15 other computational models also evaluated in this paper. We hope that this package will facilitate further psychological and musicological research into simultaneous consonance.

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“…It avoids much of the complexity of Leman's (2000) model: it has no explicit modeling of the peripheral auditory system and does not model the time-course of echoic memory. Nonetheless, the model has demonstrated best-in-class results in modeling certain important results from the psychological literature (Milne & Holland, 2016;Milne, Laney, & Sharp, 2015). Milne et al's (2011) model estimates the perceptual dissimilarity of pairs of pitch or pitch-class sets.…”

Section: Milne Et Al's (2011) Spectral Distance Modelmentioning

confidence: 99%

“…It combines each harmonic series implied by every pitch(-class), smooths the resulting spectra to account for perceptual imprecision, and then computes the cosine distance between these spectra. This cosine distance has been shown to predict perceptual 1 http://www.ipem.ugent.be/Toolbox judgements of triadic similarity rather effectively (Milne & Holland, 2016). We applied this model to harmonic expectation by using it to model the perceptual dissimilarity of a chord and its context.…”

Section: Milne Et Al's (2011) Spectral Distance Modelmentioning

confidence: 99%

“…Additionally, there is freedom to choose either a pitch representation or a pitch-class representation. This study followed the model configuration as psychologically optimized in Milne and Holland (2016): 12 harmonics, roll-off parameter of 0.75, spectral smoothing parameter of 6.83, and a pitch-class representation. The model was given a new Common Lisp implementation, with a selection of results verified against the original author's MATLAB implementation.…”

Section: Milne Et Al's (2011) Spectral Distance Modelmentioning

confidence: 99%

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Dissociating sensory and cognitive theories of harmony perception through computational modeling

Harrison¹,

Mt²

2018

Preprint

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Two approaches exist for explaining harmonic expectation. The sensory approach claims that harmonic expectation is a low-level process driven by sensory responses to acoustic properties of musical sounds. Conversely, the cognitive approach describes harmonic expectation as a high-level cognitive process driven by the recognition of syntactic structure learned through experience. Many previous studies have sought to distinguish these two hypotheses, largely yielding support for the cognitive hypothesis. However, subsequent re-analysis has shown that most of these results can parsimoniously be explained by a computational model from the sensory tradition, namely Leman’s (2000) model of auditory short- term memory (Bigand, Delbé, Poulin-Charronnat, Leman, & Tillmann, 2014). In this research we re-examine the explanatory power of auditory short-term memory models, and compare them to a new model in the Information Dynamics Of Music (IDyOM) tradition, which simulates a cognitive theory of harmony perception based on statistical learning and probabilistic prediction. We test the ability of these models to predict the surprisingness of chords within chord sequences (N = 300), as reported by a sample group of university undergraduates (N = 50). In contrast to previous studies, which typically use artificial stimuli composed in a classical idiom, we use naturalistic chord sequences sampled from a large dataset of popular music. Our results show that the auditory short-term memory models have remarkably low explanatory power in this context. In contrast, the new statistical learning model predicts surprisingness ratings relatively effectively. We conclude that auditory short-term memory is insufficient to explain harmonic expectation, and that cognitive processes of statistical learning and probabilistic prediction provide a viable alternative.

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Empirically testingTonnetz, voice-leading, and spectral models of perceived triadic distance

Cited by 29 publications

References 41 publications

Representing Harmony in Computational Music Cognition

Representing Harmony in Computational Music Cognition

Simultaneous consonance in music perception and composition

Dissociating sensory and cognitive theories of harmony perception through computational modeling

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