Corpus-based learning of tonal expectations with expectation networks

Verosky, Niels

doi:10.1080/09298215.2018.1542447

Cited by 5 publications

(17 citation statements)

References 32 publications

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“…Previous work suggests that generalized scale degree associations learned in this fashion better predict (asymmetrical) ratings of pitch similarity between pairs of scale degrees than transition probabilities between scale degrees (Verosky, 2019). The current work adds to that finding by showing that such learned associations between pairs of scale degrees can also be combined to predict melodic continuations.…”

Section: Discussionmentioning

confidence: 97%

“…The current study did not explore cognitive mechanisms that might allow recently heard notes’ scale degree associations to supersede n ‐grams in listeners’ predictions of melodic continuations, but interference is one process that might plausibly contribute to such an effect. Verosky (2019) points out that decay as modeled in expectation networks can more precisely be thought of as representing interference than temporal decay per se (Berman, Jonides, & Lewis, 2009; Lewandowsky, Oberauer, & Brown, 2009; Oberauer & Lewandowsky, 2008; Spyra, Stodolak, & Woolhouse, 2019). Given that inserting additional musical material between pairs of pitches separated by a fixed duration interferes with recall (Pechmann & Mohr, 1992), an influence of recent notes’ scale degree associations on melodic expectations irrespective of broader n ‐gram or intervallic context could be understood in light of interference.…”

Section: Discussionmentioning

confidence: 99%

“…Because more recently encountered scale degrees have higher activations, the relative connection strength from one scale degree to another represents the tendency of the latter scale degree to occur following the former closely in time. Verosky (2019) discusses the expectation network learning algorithm in depth and notes that although expectation networks can be expressed as weighted sums of n-grams, the learning algorithm has linear time complexity and requires maintaining only a 12×12 expectation matrix and a length-12 activation vector. Expectation networks infer the expectation of encountering any scale degree followed in close succession by any other scale degree, and these learned expectations were shown in Verosky (2019) to be a good fit with listener ratings of pitch similarity (where the similarity between two pitches is not symmetrical in time).…”

Section: Melodic Prediction With Expectation Networkmentioning

confidence: 99%

“…However, these generalized scale degree expectations can also be combined to predict continuations of some melodic context. Given a 12×12 matrix E of learned expectations between chromatic scale degrees, a decay constant λ (set to 1.618 here, as in Verosky, 2019), and a melodic sequence M, let the activation A of scale degree sd at time step t in the melody be the following:…”

Section: Melodic Prediction With Expectation Networkmentioning

confidence: 99%

“…Thus, pitch classes (represented as chromatic scale degrees) are associated according to their tendency to appear in close temporal succession, in a direct analogy to neural learning that can be summarized colloquially by saying that "pitches that fire together wire together." Verosky (2019) shows that scale degree associations learned from a corpus of Schubert vocal melodies better predict empirical ratings of pitch similarity (Krumhansl, 1979;Krumhansl 1990) than either bigram probabilities from the same corpus or the positions of the individual pitches in the Krumhansl-Kessler tonal hierarchy (Krumhansl & Kessler, 1982). Expectation networks represent a type of statistical learning underpinned by activation-based associations formed between events proximate in time.…”

Section: Introductionmentioning

confidence: 99%

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Pitches that Wire Together Fire Together: Scale Degree Associations Across Time Predict Melodic Expectations

Verosky¹,

Morgan

2021

Cognitive Science

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The ongoing generation of expectations is fundamental to listeners' experience of music, but research into types of statistical information that listeners extract from musical melodies has tended to emphasize transition probabilities and n-grams, with limited consideration given to other types of statistical learning that may be relevant. Temporal associations between scale degrees represent a different type of information present in musical melodies that can be learned from musical corpora using expectation networks, a computationally simple method based on activation and decay.Expectation networks infer the expectation of encountering one scale degree followed in the near (but not necessarily immediate) future by another given scale degree, with previous work suggesting that scale degree associations learned by expectation networks better predict listener ratings of pitch similarity than transition probabilities. The current work outlines how these learned scale degree associations can be combined to predict melodic continuations and tests the resulting predictions on a dataset of listener responses to a musical cloze task previously used to compare two other models of melodic expectation, a variable-order Markov model (IDyOM) and Temperley's music-theoretically motivated model. Under multinomial logistic regression, all three models explain significant unique variance in human melodic expectations, with coefficient estimates highest for expectation networks.These results suggest that generalized scale degree associations informed by both adjacent and nonadjacent relationships between melodic notes influence listeners' melodic predictions above and beyond n-gram context, highlighting the need to consider a broader range of statistical learning processes that may underlie listeners' expectations for upcoming musical events.

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Section: Discussionmentioning

confidence: 97%

Section: Discussionmentioning

confidence: 99%

Section: Melodic Prediction With Expectation Networkmentioning

confidence: 99%

Section: Melodic Prediction With Expectation Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pitches that Wire Together Fire Together: Scale Degree Associations Across Time Predict Melodic Expectations

Verosky¹,

Morgan

2021

Cognitive Science

Self Cite

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Predictive processing of music and language in autism: Evidence from Mandarin and English speakers

Zhao,

Ong,

Veic

et al. 2024

Autism Research

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Atypical predictive processing has been associated with autism across multiple domains, based mainly on artificial antecedents and consequents. As structured sequences where expectations derive from implicit learning of combinatorial principles, language and music provide naturalistic stimuli for investigating predictive processing. In this study, we matched melodic and sentence stimuli in cloze probabilities and examined musical and linguistic prediction in Mandarin‐ (Experiment 1) and English‐speaking (Experiment 2) autistic and non‐autistic individuals using both production and perception tasks. In the production tasks, participants listened to unfinished melodies/sentences and then produced the final notes/words to complete these items. In the perception tasks, participants provided expectedness ratings of the completed melodies/sentences based on the most frequent notes/words in the norms. While Experiment 1 showed intact musical prediction but atypical linguistic prediction in autism in the Mandarin sample that demonstrated imbalanced musical training experience and receptive vocabulary skills between groups, the group difference disappeared in a more closely matched sample of English speakers in Experiment 2. These findings suggest the importance of taking an individual differences approach when investigating predictive processing in music and language in autism, as the difficulty in prediction in autism may not be due to generalized problems with prediction in any type of complex sequence processing.

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Interval patterns are dependent on metrical position in jazz solos

Cross

Goldman

2021

Musicae Scientiae

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During jazz improvisation, performers employ short recurrent musical motifs called licks. Past research has focused on the pitch, intervallic, and rhythmic characteristics of licks, but less attention has been paid to whether they tend to start in the same place within the measure ( metrical dependence). Licks might be metrically dependent, and where a given lick starts in a measure ( metrical position) may thus be part of the performer’s mental representation of that lick. Here we report the use of a corpus study to investigate whether licks are metrically dependent. We analyzed a subset of solos, all those in 4/4 time ( n = 435), from the Weimar Jazz Database (WJD; Pfleiderer et al., 2017). Using a sliding window technique, we identified melodic sequences ( interval n-grams) between 3 and 10 intervals in length. We counted the number of times each interval n-gram occurred, and noted the metrical position of the initial note of each occurrence, using different levels of quantization (8th and 16th note). We compared the entropy of the distribution of metrical positions for each n-gram—with lower values indicating a stronger metrical dependence—against simulated counterparts that assumed no relationship between an n-gram and its metrical position (no metrical dependence). Overall, we found that shorter n-grams were metrically dependent, with varying results for longer n-grams. We suggest two possible explanations: either mental representations of licks may encode their metrical features or the metrical position may make certain licks more accessible to the performer. On the basis of our findings we discuss future studies that could employ our methods.

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Corpus-based learning of tonal expectations with expectation networks

Cited by 5 publications

References 32 publications

Pitches that Wire Together Fire Together: Scale Degree Associations Across Time Predict Melodic Expectations

Pitches that Wire Together Fire Together: Scale Degree Associations Across Time Predict Melodic Expectations

Predictive processing of music and language in autism: Evidence from Mandarin and English speakers

Interval patterns are dependent on metrical position in jazz solos

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