Metrical Structures Research Articles

Learning formulaic creativity: Chunking in verbal art and speech

Abstract The chunking problem is central to linguistics, semiotics, and poetics: How do we learn to organize a language into patterns and to use those patterns creatively? Linguistics has mainly offered two answers, one based on rule inference through innate capacities for processing and the other based on usage and on outstanding capacities for memory and retrieval. Both views are based on induction and compositionality. The Parry–Lord theory of oral composition-in-performance has argued that oral singers produce complex poems out of rehearsed improvisation through the mastery of a system of formulas, chunks that integrate phrasal, metrical, and semantic structures. The framework of formulaic creativity proposed here argues that the cognitive study of oral poetics can provide crucial insights into the chunking problem. I show the major connections between Parry–Lord and usage-based cognitive linguistics, mainly Construction Grammar and Frame Semantics. However, these approaches still remain compositional and thus struggle to model creativity and learning in oral poetry and everyday speech. The alternative is to explore a model of formulaic creativity not based on compositional patterns, but on wide learning for connecting discriminative perceptual features directly to semantic contrasts within a complex dynamic system, without the intermediation of a set of discrete units.

Theory and Practice of Long-form Non-isochronous Meters: The Case of the North Indianrūpak tāl

This paper addresses important issues in the theory of meter by means of a detailed study of a particular form of non-isochronous (NI) meter, the North Indianrūpak tāl.Rūpak tālis described as comprising 7 equalmātrās(time units), organized into three groups (3+2+2mātrās), and is therefore non-isochronous at the group rather than the beat or subdivision level. The term “long-form non-isochronous meter” is introduced to describe the phenomenon of metrical structures including a non-isochronous pulse level with IOIs >1000ms, of which this is an example. This phenomenon is explored with the aid of empirical analysis of a corpus of recordings ofrūpak tālperformances, focusing particularly on vocal performances inkhyālstyle. This empirical data is considered in light of extant literature on Indian metrical organization, on ethnomusicological theories ofaksak, on psychological theories of rhythm perception in NI-meters, and on metrical theory more broadly.The implications for a general theory of musical meter are then considered, leading to an argument that (a) while theorization is not a necessary condition of metrical perception, a recognized metrical pattern must be treated not only as a form of perception based on the entrainment of attention (London 2012), but as a form of culturally-shared knowledge contributing to top-down processing of meter; and (b) the theorization and representation of aspects of metrical structure means that metrical cycles are not limited to the extent of the psychological present.

Tempo and Metrical Analysis by Tracking Multiple Metrical Levels Using Autocorrelation

We present a method for tempo estimation from audio recordings based on signal processing and peak tracking, and not depending on training on ground-truth data. First, an accentuation curve, emphasizing the temporal location and accentuation of notes, is based on a detection of bursts of energy localized in time and frequency. This enables the detection of notes in dense polyphonic texture, while ignoring spectral fluctuation produced by vibrato and tremolo. Periodicities in the accentuation curve are detected using an improved version of autocorrelation function. Hierarchical metrical structures, composed of a large set of periodicities in pairwise harmonic relationships, are tracked over time. In this way, the metrical structure can be tracked even if the rhythmical emphasis switches from one metrical level to another. This approach, compared to all the other participants to the Music Information Retrieval Evaluation eXchange (MIREX) Audio Tempo Extraction competition from 2006 to 2018, is the third best one among those that can track tempo variations. While the two best methods are based on machine learning, our method suggests a way to track tempo founded on signal processing and heuristics-based peak tracking. Moreover, the approach offers for the first time a detailed representation of the dynamic evolution of the metrical structure. The method is integrated into MIRtoolbox, a Matlab toolbox freely available.

Interpersonal entrainment in Indian instrumental music performance: Synchronization and movement coordination relate to tempo, dynamics, metrical and cadential structure

Two complementary aspects of interpersonal entrainment – synchronization and movement coordination – are explored in North Indian classical instrumental music, in the auditory and visual domains respectively. Sensorimotor synchronization (SMS) is explored by analysing pairwise asynchronies between the event onsets of instrumental soloists and their tabla accompanists, and the variability of asynchrony by factors including tempo, dynamic level and metrical position is explored. Movement coordination is quantified using cross wavelet transform (CWT) analysis of upper body movement data, and differences in CWT Energy are investigated in relation to the metrical and cadential structures of the music. The analysis demonstrates that SMS within this corpus varies significantly with tempo, event density, peak levels and leadership. Effects of metrical position on pairwise asynchrony are small and offer little support for the hypothesis of lower variability in synchronization on strong metrical positions; a larger difference was found at cadential downbeats, which show increased melody lead. Movement coordination is greater at metrical boundaries than elsewhere, and most strikingly is greater at cadential than at other metrical downbeats. The implications of these findings for understanding performer coordination are discussed in relation to ethnographic research on the genre.

Generating Chinese Ci with Designated Metrical Structure

Ci is a lyric poetry form that follows highly restrictive metrical structures. This makes it challenging for a computer to compose Ci subject to a specified metrical requirement. In this work, we adapt the CVAE framework to automated Ci generation under metrical constraints. Specifically, we present the first neural model that explicitly encodes the designated metrical structure for Ci generation. The proposed model is shown experimentally to generate Ci with nearly perfect metrical structures.

Paying the meter: Effect of metrical similarity on word lengthening.

Language has a rhythmic structure, but little is known about the mechanisms that underlie how it is planned. Traditional models of language production assume that metrical and segmental planning occur independently and in parallel (Roelofs & Meyer Learning Memory and Cognition, 24(4), 922-939, 1998). We test this claim in two experiments. In Experiment 1, participants completed an event-description task in which a disyllabic target word shared segmental overlap with a prime that either had matching or nonmatching lexical stress. Participants lengthened words in trials with both segmental and metrical overlap, which could either be the result of metrical interference or having uttered a prime with similar segmental realizations. To adjudicate between these possibilities, Experiment 2 included segmentally distinct word pairs with either matching or nonmatching stress. Participants again showed lengthening in trials with both segmental and metrical overlap, but no lengthening from metrical overlap alone. These data suggest that the acoustic-phonetic similarity of the initial syllables of the prime and target creates competition that leads to word lengthening. These are consistent with production models in which segmental and metrical structures are tightly bound at the point of phonological encoding.

One mechanism of Russian poetic language

Traditionally, the phenomenon of the semantic aura of the verse metre was regarded exclusively as historically determined; the question of a potential synaesthesia (the imitative potential possessed by the rhythmic structure of a poetic text) was essentially disregarded. This paper aims to approach the problem of “metre and meaning” from the perspective of possible actualisation of certain language forms in the metrical structures of binary and ternary metres; in other words, to analyse how the metrical nature of verse determines its basic semantic model. We have come to the conclusion that the fundamental difference between Russian binary and ternary metres lies in the level of rhythmical prominence of metrically dual words, the majority of which are pronouns. The very structure of binary metres suggests a constant possibility for pronouns to be in proximity to an unstressed syllable and to receive more or less heavy stress. In ternary metres pronouns find themselves inside the circle of metrical stresses and, being inevitably adjacent to either the preceding or the following one, lose their accent and are swallowed during pronunciation. The latter, in turn, results in weakening of deictic and anaphoric language functions and undermines the established logic of textual development. That is where different, i. e., poetic, mechanisms of creating meaning come to the fore. Ternary metres put rhythmic stress on notional words, creating — in accordance with the law of poetic analogy and via omission of intermediary elements — linguistically unpredictable associations between them; binary metres emphasise semi-notional and functional words, stressing the logical and grammatical order of text development.

A cross-linguistic study of phonetic correlates of metrical structure in under-documented languages

Although languages with rhythmic stress have been extensively described and analyzed in the phonology literature, there has been little phonetic verification of the metrical structures suggested by these stress patterns. This paper presents results of a cross-linguistic study of the acoustic correlates of foot structure in several under-documented languages with morphologically complex words providing the necessary backdrop for the realization of rhythmic metrical structure. Various potential acoustic exponents of metrical structure are considered, including duration, F0, intensity, and formant frequencies. The targeted languages include Muskogean languages of the United States (Koasati, Muskogee, and Chickasaw), Circassian languages spoken primarily in Turkey and Russia (Kabardian and Adyghe), the Tukanoan language Kubeo of Brazil and Colombia, and the Arawak language Mojeno Trinitario of Bolivia. The languages differ in their foot templates (trochaic vs. iambic), the direction of their metrical parse (left-to-right vs. right-to-left), their degree of metrical rhythm, and whether they also possess lexical tone or not. Results suggest considerable diversity in the acoustic manifestations of metrical structure (including the possibility of lack of rhythmic feet even in long words) and in the relationship between the word-level metrical system and other prosodic features, including intonation and (in tonal languages) lexical tone.Although languages with rhythmic stress have been extensively described and analyzed in the phonology literature, there has been little phonetic verification of the metrical structures suggested by these stress patterns. This paper presents results of a cross-linguistic study of the acoustic correlates of foot structure in several under-documented languages with morphologically complex words providing the necessary backdrop for the realization of rhythmic metrical structure. Various potential acoustic exponents of metrical structure are considered, including duration, F0, intensity, and formant frequencies. The targeted languages include Muskogean languages of the United States (Koasati, Muskogee, and Chickasaw), Circassian languages spoken primarily in Turkey and Russia (Kabardian and Adyghe), the Tukanoan language Kubeo of Brazil and Colombia, and the Arawak language Mojeno Trinitario of Bolivia. The languages differ in their foot templates (trochaic vs. iambic), the direction of their metrical parse (l...

“Attractor Tempi” in Brahms’s Symphony No. 2/III

This analysis assesses tempo choice in the third movement of Brahms’s Second Symphony. It is shown that, at key moments of the movement, the average tempi used in a sample of commercial recordings align closely with those suggested by the “attractor” model of cognitively preferable (easiest) tempi (Gotham 2015). Between these stable checkpoints, the movement navigates through a variety of other metrical structures at (formally) the same tempo, each with their own attractor tempi. These necessarily align less well with the tempi used, thus providing a pattern of relative tension/relaxation, which the new model helps to elucidate.

The Temporal Prediction of Stress in Speech and Its Relation to Musical Beat Perception.

While rhythmic expectancies are thought to be at the base of beat perception in music, the extent to which stress patterns in speech are similarly represented and predicted during on-line language comprehension is debated. The temporal prediction of stress may be advantageous to speech processing, as stress patterns aid segmentation and mark new information in utterances. However, while linguistic stress patterns may be organized into hierarchical metrical structures similarly to musical meter, they do not typically present the same degree of periodicity. We review the theoretical background for the idea that stress patterns are predicted and address the following questions: First, what is the evidence that listeners can predict the temporal location of stress based on preceding rhythm? If they can, is it thanks to neural entrainment mechanisms similar to those utilized for musical beat perception? And lastly, what linguistic factors other than rhythm may account for the prediction of stress in natural speech? We conclude that while expectancies based on the periodic presentation of stresses are at play in some of the current literature, other processes are likely to affect the prediction of stress in more naturalistic, less isochronous speech. Specifically, aspects of prosody other than amplitude changes (e.g., intonation) as well as lexical, syntactic and information structural constraints on the realization of stress may all contribute to the probabilistic expectation of stress in speech.

Repetition and a Beat-Based Timing Framework: What Determines the Duration of Intervals Between Repetitions of a Tapping Pattern?

The production of speech and music are two human behaviors that involve complex hierarchical structures with implications for timing. Timing constraints may arise from a human proclivity to form ‘self-organized’ metrical structures for perceived and produced event sequences, especially those that involve repetition. To test whether the propensity to organize events in time arises even for simple motor behaviors, we developed a novel experimental tapping paradigm investigating whether participants use the beat structure of a tapped pattern to determine the interval between repetitions. Participants listened to target patterns of 3, 4, or 5 events, occurring at one of four periodic rates, and tapped out the pattern 11 times, creating 10 inter-pattern intervals (IPIs), which participants chose freely. The ratio between mean IPI and mean inter-tap interval (ITI) was used to measure the beat-relatedness of the overall timing pattern; the closer this ratio is to an integer, the more likely the participant was timing the IPI to match a multiple of the target pattern beat. Results show that a beat-based strategy contributes prominently, although not universally, to IPI duration. Moreover, participants preferred interval cycles with even numbers of beats, especially cycles with four beats. Finally, the IPI/ITI ratio was affected by rate, with more beats of silence for the IPI at faster rates. These findings support the idea that people can generate a larger global timing structure when engaging in the repetition of simple periodic motor patterns, and use that structure to govern the timing of those motor events.

Neural processing of musical meter in musicians and non-musicians

Musical sounds, along with speech, are the most prominent sounds in our daily lives. They are highly dynamic, yet well structured in the temporal domain in a hierarchical manner. The temporal structures enhance the predictability of musical sounds. Western music provides an excellent example: while time intervals between musical notes are highly variable, underlying beats can be realized. The beat-level temporal structure provides a sense of regular pulses. Beats can be further organized into units, giving the percept of alternating strong and weak beats (i.e. metrical structure or meter). Examining neural processing at the meter level offers a unique opportunity to understand how the human brain extracts temporal patterns, predicts future stimuli and optimizes neural resources for processing. The present study addresses two important questions regarding meter processing, using the mismatch negativity (MMN) obtained with electroencephalography (EEG): 1) how tempo (fast vs. slow) and type of metrical structure (duple: two beats per unit vs. triple: three beats per unit) affect the neural processing of metrical structure in non-musically trained individuals, and 2) how early music training modulates the neural processing of metrical structure. Metrical structures were established by patterns of consecutive strong and weak tones (Standard) with occasional violations that disrupted and reset the structure (Deviant). Twenty non-musicians listened passively to these tones while their neural activities were recorded. MMN indexed the neural sensitivity to the meter violations. Results suggested that MMNs were larger for fast tempo and for triple meter conditions. Further, 20 musically trained individuals were tested using the same methods and the results were compared to the non-musicians. While tempo and meter type similarly influenced MMNs in both groups, musicians overall exhibited significantly reduced MMNs, compared to their non-musician counterparts. Further analyses indicated that the reduction was driven by responses to sounds that defined the structure (Standard), not by responses to Deviants. We argue that musicians maintain a more accurate and efficient mental model for metrical structures, which incorporates occasional disruptions using significantly fewer neural resources.

No More Conflicting Directionality:Metrical Conditions on Tianjin Chinese Trisyllabic Tone Sandhi

Abstract Tianjin Chinese (hereafter Tianjin) exhibits complex interactions among its disyllabic tone sandhi rules, leading to both left-to-right and right-to-left rule applications in trisyllabic sequences (e.g. Chen 1986, X. Wang 2003, Lin 2008). Which directionality to adopt for each particular sequence is arbitrary and cannot be accounted for by any known principles. In addition, some disyllabic tone sandhi rules do not always apply in trisyllabic sequences. Based on the results of a multi-speaker acoustic study, we propose that both issues can be attributed to interactions of metrical structures, sandhi rules, and tonal complexity. We claim that Tianjin tone sandhi applies when both metrical and tonal complexity conditions are satisfied, thereby removing the need for conflicting directionality.

The Fieldwork Encounter and the Colonized Voice of Indigeneity

This essay follows the indexical (context-indicating) clues of linguistic form in spoken Kiksht (Wasco-Wishram Chinookan) and reconstructs the emerging poetic or metrical structures of a long-ago Kiksht-mediated encounter during anthropological linguistic fieldwork, memorialized in a published text. In this way we can hear something of the voice of a Native American speaker coming to grips with the impact of social and cultural change in the American settler state of the turn of the twentieth century.

Articulatory correlates of metrical structure: Studying jaw displacement patterns

AbstractPrevious phonetic studies of metrical prominence have primarily focused on its acoustic manifestations, including pitch, intensity, duration, spectral tilt, etc. In this paper we outline our new research program in which we explore jaw displacement patterns as another articulatory reflex of metrical prominence. We present our studies of English and Japanese in some detail, which show that jaw movement patterns are neither flat nor random, but instead the degrees of jaw displacement correlate well with metrical prominence. Based on these results, we argue that there are at least two articulators to express metrical prominence: the larynx and the jaw. Our aim is not so much to object to looking at the acoustic manifestations of metrical structures or other articulation-based approaches; we instead would like to encourage other researchers to investigate metrical structure in terms of jaw movement as well.

Hierarchy and position usage in ‘mixed’ metrical structures

Musical metre is commonly formalised in hierarchical terms, and defined or represented on the basis of regular, interacting pulse streams. These hierarchies are often merely asserted a priori, though systematic studies by Palmer and Krumhansl and Prince and Schmuckler suggest that such hierarchies are also strongly manifest in the relative usage of metrical positions: a strong metrical position is also a frequently used one. If position usage provides an insight into metrical structure, then this may provide a way of engaging with a wider range of metrical structures, including ‘mixed’ metres (5/8, 7/8 ) which are excluded by many systems of well-formedness invoked in the canonical studies of ‘simple’ metres (2/4, 3/4 ). This article assesses whether position usage in mixed metres is similarly indicative of the metrical structures asserted for them by music theory. The complete set of Bartók’s solo piano works in 7/8 (223) provides the primary case study repertoire. This is complemented by a look at the more ambiguous 8/8 (323), as part of considering how position usage might relate to distinctions between syncopation and mixed metre. An introductory discussion of sample size also provides new data and observations for larger corpora of common practice music by Bach. Brief analytical comments keep the study grounded in ‘the music’ throughout.

Evidencia fonológica para los pies métricos trisilábicos

En este trabajo se estudian las principales propiedades lingüísticas del pie métrico, unidad fonológica entre la sílaba y la palabra prosódica, indispensable para dar cuenta de la posición del acento y de otros fenómenos fonológicos en las lenguas naturales. Aunque suele considerarse que los pies métricos son máximamente bisílabos, en este artículo se propone que en determinadas lenguas los pies pueden ser máximamente trisilábicos, siempre y cuando surjan de la adjunción de una sílaba átona a otro pie. Para sustentar nuestra propuesta teórica, se presentan diversos argumentos y datos lingüísticos a favor de la inclusión de los pies trisilábicos en el repertorio de posibles estructuras lingüísticas, entre los que destacan: (i) varios casos de alargamiento vocálico en dos lenguas aborígenes australianas, (ii) la distribución de consonantes oclusivas sordas aspiradas y sin aspirar en inglés y (iii) la asignación de acento en la lengua esquimal chugach alutiiq yupik. Se demuestra que, más allá de permitir explicar patrones de acentuación ternaria poco frecuentes, estas estructuras métricas resultan óptimas para dar cuenta de sutiles diferencias entre tipos de sílabas fuertes y sílabas débiles, documentadas en algunas lenguas del mundo.

Implicit learning of between-group intervals in auditory temporal structures.

Implicit learning of temporal structure has primarily been reported when events within a sequence (e.g., visual-spatial locations, tones) are systematically ordered and correlated with the temporal structure. An auditory serial reaction time task was used to investigate implicit learning of temporal intervals between pseudorandomly ordered syllables. Over exposure, participants identified syllables presented in sequences with weakly metrical temporal structures. In a test block, the temporal structure differed from exposure only in the duration of the interonset intervals (IOIs) between groups. It was hypothesized that reaction time (RT) to syllables following between-group IOIs would decrease with exposure and increase at test. In Experiments 1 and 2, the sequences presented over exposure and test were counterbalanced across participants (Pattern 1 and Pattern 2 conditions). An RT increase at test to syllables following between-group IOIs was only evident in the condition that presented an exposure structure with a slightly stronger meter (Pattern 1 condition). The Pattern 1 condition also elicited a global expectancy effect: Test block RT slowed to earlier-than-expected syllables (i.e., syllables shifted to an earlier beat) but not to later-than-expected syllables. Learning of between-group IOIs and the global expectancy effect extended to the Pattern 2 condition when meter was strengthened with an external pulse (Experiment 2). Experiment 3 further demonstrated implicit learning of a new weakly metrical structure with only earlier-than-expected violations at test. Overall findings demonstrate learning of weakly metrical rhythms without correlated event structures (i.e., sequential syllable orders). They further suggest the presence of a global expectancy effect mediated by metrical strength.

Fixed points of mappings defined on spaces with distance

In the present article we study distinct metrical structures guaranteeing the existence of fixed points for a given mapping (Propositions 3.4 and 5.9, Theorems 4.1 and 7.3, Corollaries 2.1, 3.3, 4.4, 4.7, 5.10, 6.12, 6.13). Some examples are proposed (Examples 1.4, 4.9, 6.12).

An Attentional Effect of Musical Metrical Structure.

Theories of metrical structure postulate the existence of several degrees of beat strength. While previous work has clearly established that humans are sensitive to the distinction between strong beats and weak ones, there is little evidence for a more fine grained distinction between intermediate levels. Here, we present experimental data showing that attention can be allocated to an intermediate level of beat strength. Comparing the effects of short exposures to 6/8 and 3/4 metrical structures on a tone detection task, we observe that subjects respond differently to beats of intermediate strength than to weak beats.