Rhythmic Structure Research Articles

The Influence of Dissonance on Listeners’ Perceived Emotions in Rhythmically Complex Musical Excerpts

ABSTRACT This study investigates the influence of dissonance on listeners’ ratings of five emotional dimensions (mood, energy, movement, dissonance, and tension) using excerpts from twentieth-century keyboard music that feature complex rhythmic structures. Dissonance was operationalized as randomized pitches from four scale types: pentatonic major, diatonic major, whole-tone, and chromatic. Register presentation of two contrasting rhythmic groups within each excerpt was counterbalanced, while rhythmic structure was held constant, resulting in 64 distinct stimuli (8 excerpts × 4 scales × 2 register conditions), from which rhythm and pitch measures were extracted. There was a main effect of scale type, but not register. Pentatonic excerpts were rated as more positive and less dissonant than diatonic, whole-tone, and chromatic excerpts. Whole-tone and chromatic were also perceived as more negative and dissonant than diatonic, as well as more tense and less entraining than both pentatonic and diatonic. There was no effect of scale on energy. Sonority dissonance was a reliable predictor of perceived dissonance and tension, as well as mood and movement. Furthermore, several rhythmic features were predictive of participants’ perceived emotions, providing support for the use of pitch-randomized naturalistic stimuli to assess the influence of musical structure on perceived emotions.

Korvais in Karnatak Music - Improvisation through Training

Korvai is a Tamil word meaning joining or beading. When rhythmic syllables are joined or beaded together in a logical development and culminate in a structural format of definable Purvanga and Uttaranga then they can be termed as Korvai. Korvais form an essential part of every Karnatak concert. They are being extensively used by Vocalists, Instrumentalists and various types of percussion artistes also. Since, Korvai is an integral and important aspect of a concert, there is a necessity to analyze the process of making them and also quantify them for easier approaches to its various types. There are two parts in a Korvai, that are generally being used to identify them distinctively. They are Purvanga (the first part or the introductory part) and Uttaranga (the ending part or the subsequent part). The purvanga and uttaranga are constant factors irrespective of the rhythmic structure or Tala structure. Same Purvanga can be used with different Uttarangas for same tala or extended to other talas as well. Such being the case, the purvangas and uttarangas are clearly quantifiable in terms of numbers and rhythmic phrases or combination of phrases. When a number is being used, there can be logical build up and hence this article explores such logical build-up using numbers in a structured way converted as cognizable rhythmic varieties. Talas are cyclical in nature having specified fixed number of beats per cycle. For a tala which is having 9 beats per cycle, the total number for 3 or 4 cycles can be calculated by simple multiplication. For example, for 4 cycles the total would be 36 beats. Whenever calculations are made mostly they are done on either as number of beats or on pulses. Both methods can be employed for quick results. In the above case, there were 36 beats which can give us 144 pulses (36 X 4).The purvanga can be anything like 108 and the uttaranga can be 36. The general ratio of purvanga and uttaranga could be 60:40 or 70:30 for. Longer Purvangas of 90:10 or shorter purvangas of 20:80 are generally not preferred. This article also covers various examples where different combinations are improvised. Different types of korvais can also be made using such improvisations.

Outburst flood events since the Last Glacial Maximum in the Hutiao Gorge of Jinsha River: Geomorphological evidence from eddy gravel bars

Breaching of natural dams in the Hutiao Gorge of the Jinsha River across the Yulong-Haba Mountains is one of the major geomorphological events in the largest river of Asia. Catastrophic flood events have an important influence on the geomorphological evolution of the First Bend of the Yangtze River since the Last Glacial Maximum (LGM). However, detailed geomorphological evidence, ages, and depositional phases of outburst flooding remain unclear. In this paper, large-scale gravel bars overlying the river terraces and dammed lakes are analyzed within the Daju Basin. The macroscopic geomorphological characteristics of megaflood landforms with large thickness and uniform gravel bars are similar to those of Missoula and Altai megafloods. Morphological analysis shows that eddy gravel bars (EGBs) with rhythmic structure are characterized by a dome-shaped protrusion in the cross section and a gravel mound in the longitudinal section. Each bar with oblique, parallel and massive bedding was analyzed from the horizontal and vertical directions. Three dome-shaped bars clearly show at least three palaeoflood phases. Quartz grain surface macrotextures are mainly V-shaped pits and conchoidal fractures, which exhibits a high-energy environment during the flood. The stratigraphic sequence model of EGBs is dominated by coarse sand and fine gravel rhythmic bedding in high-energy eddy environments and suspended sand deposits in low-energy backwater environments. Such phenomenon reveals megaflood fluctuates, which is also confirmed by geochemical difference. The episode of natural dam break floods triggered by tectonic activity and glacier fluctuation was dated to 20–17 ka during the LGM. Sedimentary pattern of EGBs offers fresh insights into understanding the megaflood geomorphological characteristics of the upper Yangtze River and better identification similar high-energy palaeoflood landforms in the southeast Tibetan Plateau.

Open-Set Recognition of Pansori Rhythm Patterns Based on Audio Segmentation

Pansori, a traditional Korean form of musical storytelling, is characterized by performances involving a vocalist and a drummer. It is well-known for the singer’s expressive narrative (aniri) and delicate gesture with fan in hand. The classical Pansori repertoires mostly tell love, satire, and humor, as well as some social lessons. These performances, which can extend from three to five hours, necessitate that the vocalist adheres to precise rhythmic structures. The distinctive rhythms of Pansori are crucial for conveying both the narrative and musical expression effectively. This paper explores the challenge of open-set recognition, aiming to efficiently identify unknown Pansori rhythm patterns while applying the methodology to diverse acoustic datasets, such as sound events and genres. We propose a lightweight deep learning-based encoder–decoder segmentation model, which employs a 2-D log-Mel spectrogram as input for the encoder and produces a frame-based 1-D decision along the temporal axis. This segmentation approach, processing 2-D inputs to classify frame-wise rhythm patterns, proves effective in detecting unknown patterns within time-varying sound streams encountered in daily life. Throughout the training phase, both center and supervised contrastive losses, along with cross-entropy loss, are minimized. This strategy aimed to create a compact cluster structure within the feature space for known classes, thereby facilitating the recognition of unknown rhythm patterns by allocating ample space for their placement within the embedded feature space. Comprehensive experiments utilizing various datasets—including Pansori rhythm patterns (91.8%), synthetic datasets of instrument sounds (95.1%), music genres (76.9%), and sound datasets from DCASE challenges (73.0%)—demonstrate the efficacy of our proposed method to detect unknown events, as evidenced by the AUROC metrics.

The Early Work of Paul Fraisse: The Timing of ‘Spontaneous’ Rhythms

Abstract The article discusses Paul Fraisse’s early study of the timing of what he called ‘spontaneous’ rhythms, where people were required to perform a specified sequence of spaced taps on a response key without the times between the responses being controlled. Results come from his doctoral thesis, carried out under the supervision of Albert Michotte in Louvain/Leuven in Belgium between 1935 and 1937. In spite of the lack of timing instructions, responses were divided into ‘short times’ (around 200 ms), ‘long times’ (usually around 450 ms), and ‘pauses’ (the times between execution of consecutive rhythmic sequences). This division held over changes in the tap sequence, when different patterns of three, four, and five responses were produced. A later experiment varied total sequence duration, including the pauses, and the ratio of long to short times was approximately preserved even with marked changes in sequence duration, except at the slowest speed. Fraisse regarded the pause as having a different function from the short and long times. It changed only slightly when the pattern changed, but marked changes in the duration of the pause did not affect the pattern. Fraisse suggested it was a kind of separator, needed to maintain the rhythmic structure of the patterns, and used the idea of a temporal ‘Gestalt’ where the pause represented the ‘ground’ or ‘framework’ and the rhythmic sequence the ‘Figure ’.

Relationships between the expectations based on the regularity of preceding sound sequences and the medial olivocochlear reflex.

Rhythms are the most natural cue for temporal anticipation because many sounds in our living environment have rhythmic structures. Humans have cortical mechanisms that can predict the arrival of the next sound based on rhythm and periodicity. Herein, we showed that temporal anticipation, based on the regularity of sound sequences, modulates peripheral auditory responses via efferent innervation. The medial olivocochlear reflex (MOCR), a sound-activated efferent feedback mechanism that controls outer hair cell motility, was inferred noninvasively by measuring the suppression of otoacoustic emissions (OAE). First, OAE suppression was compared between conditions in which sound sequences preceding the MOCR elicitor were presented at regular (predictable condition) or irregular (unpredictable condition) intervals. We found that OAE suppression in the predictable condition was stronger than that in the unpredictable condition. This implies that the MOCR is strengthened by the regularity of preceding sound sequences. In addition, to examine how many regularly presented preceding sounds are required to enhance the MOCR, we compared OAE suppression within stimulus sequences with 0-3 preceding tones. The OAE suppression was strengthened only when there were at least three regular preceding tones. This suggests that the MOCR was not automatically enhanced by a single stimulus presented immediately before the MOCR elicitor, but rather that it was enhanced by the regularity of the preceding sound sequences.

Leveraging Hybrid Adaptive Sine Cosine Algorithm with Deep Learning for Arabic Poem Meter Detection

Poetry is a significant aspect of any language. Many cultures and the history of nations are recognized in poems. Compared to prose, each poem has a rhythmic structure that is quite different. The language has its set of lyrical structures for poems, known as meters. Detecting the meters of Arabic poems is a complicated and lengthy procedure. The text must be encrypted using the Arudi method to classify the poem's meter, which requires complex rule-based transformation before another set of rules classifies the meters. Applying deep learning (DL) to meter classification in Arabic poems includes constructing a neural network to discern rhythmic patterns inherent in various meters. The model can extract essential features, like word lengths or syllable patterns, by tokenizing and preprocessing text datasets. Architectures such as Long Short-Term Memory Networks (LSTM) or Recurrent Neural Networks (RNNs) are fitting solutions to capture temporal relations in poetic verses. This research introduces a Hybrid Meta-heuristics with Deep Learning for the Arabic Poem Meter Detection and Classification (HMDL-APMDC) model. The main intention of the HMDL-APMDC system is to recognize various kinds of meters in Arabic poems. The HMDL-APMDC technique primarily preprocesses the input dataset to make it compatible with the classification process. Besides, the HMDL-APMDC technique applies Convolution and Attention with a Bi-directional Gated Recurrent Unit (CAT-BiGRU) for the automated recognition of meter classes. Furthermore, the adaptive sine-s-cosine particle swarm optimization (ASCA-PSO) algorithm is applied to optimize the hyperparameter tuning of the CAT-BiGRU model, enhancing the meter detection results. A detailed simulation analysis is made to highlight the improved performance of the HMDL-APMDC technique. The empirical outcomes stated that the HMDL-APMDC technique had a superior outcome of 98.53% over recent models under the MetRec dataset.

Speech's syllabic rhythm and articulatory features produced under different auditory feedback conditions identify Parkinsonism

Diagnostic tests for Parkinsonism based on speech samples have shown promising results. Although abnormal auditory feedback integration during speech production and impaired rhythmic organization of speech are known in Parkinsonism, these aspects have not been incorporated into diagnostic tests. This study aimed to identify Parkinsonism using a novel speech behavioral test that involved rhythmically repeating syllables under different auditory feedback conditions. The study included 30 individuals with Parkinson's disease (PD) and 30 healthy subjects. Participants were asked to rhythmically repeat the PA-TA-KA syllable sequence, both whispering and speaking aloud under various listening conditions. The results showed that individuals with PD had difficulties in whispering and articulating under altered auditory feedback conditions, exhibited delayed speech onset, and demonstrated inconsistent rhythmic structure across trials compared to controls. These parameters were then fed into a supervised machine-learning algorithm to differentiate between the two groups. The algorithm achieved an accuracy of 85.4%, a sensitivity of 86.5%, and a specificity of 84.3%. This pilot study highlights the potential of the proposed behavioral paradigm as an objective and accessible (both in cost and time) test for identifying individuals with Parkinson's disease.

The impact of song-based english lessons in the motivation of efl students

Despite decades of research on the motivational impact of songs in English as a Foreign Language (EFL) classrooms, many educators remain unaware of their potential. This study investigates how EFL learners perceive their learning journey when incorporating song-based lessons. Songs are valuable tools for achieving personal and group language learning goals. They offer a multifaceted approach, encompassing cultural immersion, vocabulary acquisition, enhanced listening comprehension, facilitated grammar application, and the sharpening of various language skills – all presented within a rhythmic structure. Recognizing the impact of music on mood and motivation is crucial. Research in this area is essential to understand how specific songs influence motivation levels. By investigating these effects, educators can choose music that optimizes learning environments and supports students in reaching their academic objectives. Songs are powerful tools in EFL classrooms, providing an engaging approach to language learning on multiple levels. Understanding their impact on mood and motivation allows educators to leverage these benefits and enhance the overall learning experience for students.

Trajectories and revolutions in popular melody based on U.S. charts from 1950 to 2023

In the past century, the history of popular music has been analyzed from many different perspectives, with sociologists, musicologists and philosophers all offering distinct narratives characterizing the evolution of popular music. However, quantitative studies on this subject began only in the last decade and focused on features extracted from raw audio, which limits the scope to low-level components of music. The present study investigates the evolution of a more abstract dimension of popular music, specifically melody, using a new dataset of popular melodies spanning from 1950 to 2023. To identify "melodic revolutions", changepoint detection was applied to a multivariate time series comprising features related to the pitch and rhythmic structure of the melodies. Two major revolutions in 1975 and 2000 and one smaller revolution in 1996, characterized by significant decreases in complexity, were located. The revolutions divided the time series into three eras, which were modeled separately with autoregression, linear regression and vector autoregression. Linear regression of autoregression residuals underscored inter-feature relationships, which become stronger in post-2000 melodies. The overriding pattern emerging from these analyses shows decreasing complexity and increasing note density in popular melodies over time, especially since 2000.

Exploration of the Rhythmic Structure Patterns in Chinese

Exploration of the Rhythmic Structure Patterns in Chinese

Enhancing rhythmic temporal expectations: The dominance of auditory modality under spatial uncertainty.

To effectively process the most relevant information, the brain anticipates the optimal timing for allocating attentional resources. Behavior can be optimized by automatically aligning attention with external rhythmic structures, whether visual or auditory. Although the auditory modality is known for its efficacy in representing temporal information, the current body of research has not conclusively determined whether visual or auditory rhythmic presentations have a definitive advantage in entraining temporal attention. The present study directly examined the effects of auditory and visual rhythmic cues on the discrimination of visual targets in Experiment 1 and on auditory targets in Experiment 2. Additionally, the role of endogenous spatial attention was also considered. When and where the target was the most likely to occur were cued by unimodal (visual or auditory) and bimodal (audiovisual) signals. A sequence of salient events was employed to elicit rhythm-based temporal expectations and a symbolic predictive cue served to orient spatial attention. The results suggest a superiority of auditory over visual rhythms, irrespective of spatial attention, whether the spatial cue and rhythm converge or not (unimodal or bimodal), and regardless of the target modality (visual or auditory). These findings are discussed in terms of a modality-specific rhythmic orienting, while considering a single, supramodal system operating in a top-down manner for endogenous spatial attention.

Automated Determination of Music Genre and Linguistic Categorization

The main objective of the project is to build a system that allows users to predict genre as well as language out of some music . The Automated determination of musical genre and linguistic categorization is a machine learning based prediction model which is used to predict the genres and languages of an audio . Musical genres are categorical labels created by humans to characterize piece of music. A musical genre is characterized by common characteristics typically related to the instrumentation, rhythmic structure and harmonic content of the music. The performance and relative importance of the proposed features are investigated by training the statistical pattern recognition classifiers using real world audio collections and using machine learning algorithm.In this project, we built systems called music genre and language classification and the effects of different feature extraction methods and their various combinations were also investigated. This task is of great interest in music information retrieval and recommendation systems. In recent years, several machine learning algorithms have been developed to tackle this task, using features such spectral, temporal, and tonal characteristics of audio signals. Music genre prediction and language classification is a task that involves automatically predicting a piece of music into a specific genre category as well as language based on its audio features. Keywords-machine-learning,music,music genre and language classification

The Role of an Art Object in the Formation of Characteristic Features of Interior Space

The aim of the article is to study the role of different types of art objects in the formation of characteristic features of interior space. Research methods included bibliographic, typological and comparative analysis, field survey, compositional method, systematization and generalization. The scientific novelty lies in the research, analysis and systematization of the functional and aesthetic role of art objects in the formation of characteristic features of interior space. Conclusions. As a result of the study, the main features of the interior space, which can be achieved by placing an art object in it, were determined: intensification, assimilation, hyperbolization and transformation. Thus, the intensification of the interior is achieved through the dominant position of the art object, its compositional coherence with other elements, the subordination of rhythmic structures to it, and the creation of space for the effects of dynamism and expressiveness. Assimilation is achieved by subtly combining the geometric shapes of the interior space and the art object, creating a sense of balance, homogeneity, and compositional completeness. Hyperbolization relies on a pronounced semantic and stylistic contrast between the art object and the interior elements, resulting in the effect of compositional dissonance, revitalization, and at times, irony, sarcasm, and satire. Transformation involves visually altering the geometric form, size, or shape of both the interior space and the art object. This is achieved through methods such as dismemberment, emphasis, and the reconfiguration of spatial elements, leading to the effect of compositional asymmetry, dissymmetry, and dynamism. The study tested specific results in the design work of design students. The prospect for further research is to analyze the role of art objects in the qualitative transformation of modern interiors, to identify and systematize modern trends in the relationship between fine art and the object and spatial environment.

DNA of Music: Identifying Relationships among Different Versions of the Composition Sadhukarn from Thailand, Laos, and Cambodia Using Multivariate Statistics

Sadhukarn, a sacred music composition performed ritually to salute and invite divine powers to open a ceremony or feast, is played in Thailand, Cambodia, and Laos. Different countries have unique versions, arranged based on musicians’ skills and en vogue styles. This study presents the results of multivariate statistical analyses of 26 different versions of Sadhukarn main melodies using non-metric multidimensional scaling (NMDS) and cluster analysis. The objective was to identify the optimal number of parameters for identifying the origin and relationships among Sadhukarn versions, including rhyme structures, pillar tone, rhythmic and melodic patterns, intervals, pitches, and combinations of these parameters. The data were analyzed using both full and normalized datasets (32 phrases) to avoid biases due to differences in phrases among versions. Overall, the combination of six parameters is the best approach for data analysis in both full and normalized datasets. The analysis of the ‘full version’ shows the separation of Sadhukarn versions from different countries of origin, while the analysis of the ‘normalized version’ reveals the rhyme structure, rhythmic structure, and pitch as crucial parameters for identifying Sadhukarn versions. We conclude that multivariate statistics are powerful tools for identifying relationships among different versions of Sadhukarn compositions from Thailand, Laos, and Cambodia and within the same countries of origin.

Features of the development of speed skills in football players

This article examines the issues of speed training, training speed in football players aimed at increasing running speed and "transferring" this speed to running with the ball. This process of "transferring" speed abilities is more effective when an athlete in normal running emphasizes the frequency of movements, but not the length of running steps, that is, he overcomes training segments with slightly shortened steps, which in their rhythmic structure are similar to steps in running with m' cell. Speed training falls, in fact, on the pubertal phase of the body development of young athletes, when puberty is accompanied by a rapid increase in muscle mass, glycogen reserves, and an increase in the level of secretion of adrenaline and gonadal hormones. At this time, optimal biological prerequisites are created for the development of anaerobic capabilities, maximal strength, power endurance, and speed-power qualities. The volume of loads should increase at the fastest pace in the development of strength endurance, which reaches its maximum values by the end of the stage. Gradually, exercises with maximum efforts, performed in overcoming, yielding and isokinetic modes, are included in the training.
 Speed abilities are very difficult to develop. The possibility of speed increase in locomotor cyclic acts is very limited. In the process of sports training, an increase in the speed of movements is achieved both by influencing the actual speed abilities, and in another way - through the development of strength and speed-strength abilities, speed endurance, improvement of the technique of movements, etc., i.e. improvement of those factors that significantly depend on the manifestation of certain qualities of speed. Numerous studies have shown that the aforementioned types of speed abilities are specific. Direct positive transfer of speed takes place only in movements that have similar semantic and programming aspects, as well as motor composition. The specific features of speed abilities are noted, so they require the use of appropriate training tools and methods for each of their varieties.

Isochrony in barks of Cape fur seal (Arctocephalus pusillus pusillus) pups and adults.

Animal vocal communication often relies on call sequences. The temporal patterns of such sequences can be adjusted to other callers, follow complex rhythmic structures or exhibit a metronome-like pattern (i.e., isochronous). How regular are the temporal patterns in animal signals, and what influences their precision? If present, are rhythms already there early in ontogeny? Here, we describe an exploratory study of Cape fur seal (Arctocephalus pusillus pusillus) barks-a vocalisation type produced across many pinniped species in rhythmic, percussive bouts. This study is the first quantitative description of barking in Cape fur seal pups. We analysed the rhythmic structures of spontaneous barking bouts of pups and adult females from the breeding colony in Cape Cross, Namibia. Barks of adult females exhibited isochrony, that is they were produced at fairly regular points in time. Instead, intervals between pup barks were more variable, that is skipping a bark in the isochronous series occasionally. In both age classes, beat precision, that is how well the barks followed a perfect template, was worse when barking at higher rates. Differences could be explained by physiological factors, such as respiration or arousal. Whether, and how, isochrony develops in this species remains an open question. This study provides evidence towards a rhythmic production of barks in Cape fur seal pups and lays the groundwork for future studies to investigate the development of rhythm using multidimensional metrics.

Classical Turkish Music Composition with LSTM Self-Attention

Synthetic symbolic music generation, the process of creating new musical pieces using symbolic representations, has gained significant traction in the field of music informatics and computational creativity. It holds immense potential for various applications, ranging from music education and composition assistance to music therapy and personalized music recommendation systems. Classical Turkish music (CTM) exhibit distinct characteristics regarding Western Tonal Classical Music (WCM) such as melodic organization, formation of rhythmic structure or melodic expressions. This study tackles the challenge of symbolic music composition, focusing on CTM. Unlike WCM, CTM incorporates microtonal intervals. These intervals are smaller than the semitones in Western music, allowing for a more nuanced expression of pitch. This leads to a more diverse set of pitch ranges. The proposed method employs a combination of self-attention and long-short term memory (LSTM) networks to capture long-term relational information and generate realistic CTM compositions. LSTMs effectively model sequential dependencies and improve local relations within musical structures and self-attention improves the context vector, allowing the model to attend to different aspects of the musical context simultaneously. This combination enables the proposed method to generate compositions that are both musically coherent and stylistically consistent with distinct features of CTM. The proposed method was evaluated on two datasets, the CTM dataset and Classical Music Piano (CPM) dataset. The assessment of musical contents is evaluated through melodic similarity and stylistic consistency metrics. The results demonstrate that the proposed method is able to generate musical content that is coherent and produce music that is pleasing-to-hear. Overall, the article presents a novel and effective approach to symbolic music composition, focusing on CTM.

Auditory-motor synchronization and perception suggest partially distinct time scales in speech and music

Speech and music might involve specific cognitive rhythmic timing mechanisms related to differences in the dominant rhythmic structure. We investigate the influence of different motor effectors on rate-specific processing in both domains. A perception and a synchronization task involving syllable and piano tone sequences and motor effectors typically associated with speech (whispering) and music (finger-tapping) were tested at slow (~2 Hz) and fast rates (~4.5 Hz). Although synchronization performance was generally better at slow rates, the motor effectors exhibited specific rate preferences. Finger-tapping was advantaged compared to whispering at slow but not at faster rates, with synchronization being effector-dependent at slow, but highly correlated at faster rates. Perception of speech and music was better at different rates and predicted by a fast general and a slow finger-tapping synchronization component. Our data suggests partially independent rhythmic timing mechanisms for speech and music, possibly related to a differential recruitment of cortical motor circuitry.

SPOTİFY “TÜRKİYE İLK 50” LİSTESİNDE YER ALAN ŞARKI VE ŞARKICILARIN ÇEŞİTLİ AÇILARDAN İNCELENMESİ

Listening to music has been a need throughout human history and the need to listen to music has become more easily met as the ages progressed. Starting from the invention of the phonograph to today’s music listening technologies, many music listening platforms have emerged through the internet. Spotify is among the most preferred of these platforms, enabling the masses to access music faster. Since the music that societies listen to reflects certain traces of those societies, it is important to analyze the most listened songs at certain intervals. In this study, Spotify 2023 November “Turkey Top 50” Analyses of the songs on the list are included. The songs on the list throughout November were analyzed in terms of the duration of their inclusion on a daily basis, their appearance in terms of genre, tonality/modality/mode and rhythmic structure, the gender of the singers who performed the songs, the local/foreign status of the songs, the themes contained in the lyrics and the duration of the songs. The data obtained were tabulated and exhibited under the relevant headings.