Musical Parameters Research Articles

Towards a mathematical foundation for music theory and composition: a theory of structure

This paper proposes mathematical foundations for music theory and composition. While mathematical methods have proven effective in music theory, a deficiency in rigorous mathematical foundations often leads to ad-hoc constructions and a reliance on intuitive notions with inexplicit definitions. The proposal introduces a comprehensive environment for encoding musical phenomena, as well as a theory of musical parameter. Drawing from the methodologies of (Mazzola, Guerino. 2002. The Topos of Music: Geometric Logic of Concepts, Theory, and Performance. Basel: Birkhäuser Verlag), the proposed framework aims to extend his theory of forms to accommodate a wider class of musical structures. Additionally, I advocate for a framework characterized by “comprehensive comprehension” (accommodating a broad class of musical objects), “explicit encoding” (capturing essential features of objects), and “limited ontological commitments” (minimizing posited ontological primitives). These three aspects aim to ensure the framework's generality, explicit representation of structure, and economic efficiency in theoretical constructions. Minimizing ontological commitments also has the benefit of facilitating easier comparisons between entities. This approach is motivated by the desire for a highly versatile framework that enables systematic and standardized construction methods without constraining the intended domain of discourse. To achieve these goals, the paper introduces a mathematical theory of structure grounded in topos theory. By offering a unified and systematic approach, this work contributes to establishing a more rigorous and standardized basis for mathematical music theory. This, in turn, fosters a deeper understanding of musical phenomena and enables more robust theoretical constructions and compositional applications.

Heathering Winds von Dan Dediu, oder die Ausbreitung der Melodie

As a musical parameter, melody – conventionally understood as a (consecutive) succession of sounds – is an essential coordinate of Romanian music, which claims stylistically and historically from the parlando-rubato aesthetics of tradition folk music. In Dan Dediu’s piano piece Heathering Winds we discover a new perspective on the composition of melody (an essential parameter in the composition of music), which can also be regarded as a new view, as a different aesthetics, both for first, and the second half of the 20th century, therefore characteristic to our time. The analytical approach presents an overview of the piano piece inspired by Emily Brontë’s novel Wuthering Heights, in which key points from the British writer’s novel are presented, followed by an overview of the formal dramaturgy and presentation of the piano piece’s main musical ideas. Finally, our melodic analysis uses the theorising of the composer himself (Dan Dediu, Melodia, 2006) to capture the complexity of melodic structuring, which – breaking the traditional pattern of a melodic line, in which the ratio of durations and pitches is optimal to be perceived as such – expands, tending towards what Dediu calls infra- and supermelody, i.e. a melody that pushes its boundaries, creating, from a single “melodic thread”, the illusion of an innovative musical syntax.

The pedagogical–artistic strategies of community music facilitators as an inspiration for formal music education: A single case study

In this article, we elaborate on the pedagogical–artistic strategies of a community music project and how they may inspire formal music educational practices. To do so, we draw on findings from a study on the pedagogical–artistic strategies of the musicians–coaches of The Ostend Street Orchestra (TOSO), a community music project that started as an artistic response towards the commotion around a group of homeless people in the coastal town of Ostend, Belgium. The pedagogical–artistic strategies adopted by the TOSO coaches foster the emergence of an educational approach that may have the potential to enrich music educational practices by creating a learning environment that is more democratic and inclusive. Data collection included in-depth semi-structured interviews with the TOSO coaches in 2017 and 2021, as well as video-stimulated recall. The interview data were analysed using thematic analysis. Seven themes emerged from our analysis: embodied interaction, co-coaching, re-thinking musical parameters, personal musical skills, collaboration, collective experiential learning and inclusion. We present the framework and rationale of the study, describe the pedagogical–artistic strategies of the coaches, and discuss the results. In conclusion, we briefly consider possibilities for further research and music teacher education.

The Neural Correlates of Food Preference among Music Kinds.

The calorie and taste choices of food have been shown to be related to the external environment, including music. Previous studies have mostly focused on manipulating basic auditory parameters, with few scholars exploring the impact of complex musical parameters on food selection. This study explored the effects of different kinds of music (classical, rock, jazz, and hip-hop) on food liking based on the calories (high and low) and taste (sweet and salty) using event-related potentials (ERPs). Twenty-four participants (8 males, 16 females) were recruited from Southwest University, China to participate in the food liking task using a Likert seven-point rating and simultaneously recording EEG signals (N2, P2, N3, and LPC). This study used repeated-measures analyses of covariances and found that the score of the high-calorie foods was greater than that of the low-calorie foods. Additionally, results revealed that the score in classical music was greatest for sweet foods, while there was no difference among music kinds in the salty foods. The ERP results showed that P2 amplitudes were greater for sweet foods than those for the salty foods. N2 amplitudes for the salty foods were greater than those for the sweet foods during rock music; in addition, N2 amplitudes during hip-hop music were greatest for sweet foods. However, N2 amplitudes during rock music were the greatest for salty foods. The results also revealed that N2 amplitudes during hip-hop music were greater than those during jazz music. This study provides unique operational insights for businesses.

Teaching free improvisation: European higher music education teachers’ conceptual tools

In higher music education (HME) contexts, free improvisation is currently a rapidly evolving field across musical genres. Previous research indicates that teaching and learning improvisation can be challenging, depending on students’ experience and how improvised music-making is facilitated, but few studies address free improvisation in HME. Our study has explored this field by utilising qualitative interviews with teachers of free improvisation in European HME institutions. Results provided insight into teachers’ motivation and the educational aims which informed their approaches to teaching improvisation. Some teachers referred to a canon of free improvised or experimental music and well-known improvisers, interpreted as a need amongst the teachers to position and legitimise a potentially marginalised subject within institutions. Teachers in our study used different types of frameworks to develop students’ ability to interact and listen. Focusing on musical parameters, limitations of choices or language metaphors were often used as tools for acquiring such aims. Results further indicate that free improvisation should be a safe space, enhance democratic values and disrupt hierarchies of knowledge. In sum, our study contributes to mapping and understanding contradictions and complexities of this developing area of pedagogy.

Accessory respiratory muscles performance among people with spinal cord injury while singing songs with different musical parameters.

People with spinal cord injury (SCI) experience respiratory dysfunctions which include hypersecretions, bronchospasm, and respiratory muscles weakness. Singing therapy has been implemented as part of respiratory muscle training (RMT) to improve their muscle strength. Singing different types and genres of songs may elicit specific recruitment of respiratory muscles, attributed to the variation of the songs' characteristics including tempo, pitch, and rhythmic complexity. This study aims to determine the effect of singing songs with different characteristics on the accessory respiratory muscle performance among people with SCI. Thirteen male SCI participants of ASIA A and B (C4 -T11) were recruited. Respiratory muscle signals were retrieved by placing two mechanomyography (MMG) sensors on the sternocleidomastoid (SCM) and rectus abdominis (RA) muscles. Eight music experts categorized several songs into four categories based on their pitch, tempo, and rhythmic complexity. Each participant sang one song from each category. Findings showed statistically significant difference in RA and SCM responses among all categories (P < 0.01). The SCM muscle is most active while singing high pitch songs. While the RA is most active during slow tempo and easy rhythmic complexity. This shows that different accessory respiratory muscle is activated by people with SCI while singing songs with different characteristics. Clinicians could benefit from this knowledge while prescribing singing therapy or exercise among people with SCI in the future.

THERAPEUTIC FEATURES OF THE UKRAINIAN TRADITIONAL SINGING

The purpose of the article is the study of the therapeutic features of the Ukrainian traditional singing (UTS). Research methods are as follows. The characteristic features of Ukrainian folklore performance (such as timbre, varia- bility, etc.) are described in terms of their influence on the psychophysiological state of singers. Features of singing in different timbres, as well as solo and ensemble are compared. The complex influence of different UTS indicators (per- forming, musical-therapeutic, psychophysiological, etc.) is analysed. Data on powerful therapeutic musical resources contained in UTS are identified. Conclusions. The study reveals 1) the UTS ability to reduce the level of stress, to pro- mote relaxation and rest; 2) the opening voicing capability to enhance the antistress effect of UTS; 3) the influence of singing variability on creativity level increasing, a sense of freedom and positive emotions enhancing; 4) the ensemble UTS ability to strengthen self-reliance, motivation, to bring joy, to promote the emotional unity of singers. 5) The unique therapeutic capacity of the UTS is formed due to the complex action of its musical parameters. The relevance of the study is seemed to be explained by the understanding of the therapeutic properties of UTS as an effective means of stress reducing and overcoming the post traumatic stress disorder consequences.

Depressed adults’ experiences of listening to their own clinical improvisations at home: A process evaluation of the music therapy homework

ABSTRACT Introduction Depression has a negative impact on millions of people worldwide, necessitating research into appropriate therapeutic methods. The aim of this qualitative study is to investigate how music therapy clients experience listening to their own clinical improvisations at home, as a part of treatment for depression. Method Adults with major depressive disorder were offered 12 individual sessions of bi-weekly integrative improvisational music therapy, as part of a randomised controlled trial. Participants were asked to complete an online diary after listening to their clinical improvisations. Reflexive thematic analysis was performed on diary entries, and content analysis was applied to music therapists’ reports. Results Fourteen of 32 participants submitted a total of 58 diary entries. Participants' experiences were represented by five themes: music (playing, listening, music perception, music parameters), therapy (therapeutic processing, illness, music therapy trial), emotions (positive emotions, negative emotions, other emotions), embodiment (body parts, sensations, actions) and narrative (chronology, symbolic references). Music therapists’ reports indicated that low compliance and negative experiences during the task could be affected by severity of depression, and ease of use of the technological interface. Discussion Participants’ experiences varied from extremely negative to positive in every theme, finding music they produced beautiful or hideous, feeling proud or ashamed of making it, being energised, or exhausted by it, feeling supported or pressured by the music therapist, and recalling happy or terrifying memories. The findings suggest that a homework task can affect the therapeutic process in both positive and negative ways and should be further researched before implementation.

The Sound of Swarm. Auditory Description of Swarm Robotic Movements

Movements of robots in a swarm can be mapped to sounds, highlighting the group behavior through the coordinated and simultaneous variations of musical parameters across time. The vice versa is also possible: Sound parameters can be mapped to robotic motion parameters, giving instructions through sound. In this article, we first develop a theoretical framework to relate musical parameters such as pitch, timbre, loudness, and articulation (for each time) with robotic parameters such as position, identity, motor status, and sensor status. We propose a definition of musical spaces as Hilbert spaces and musical paths between parameters as elements of bigroupoids, generalizing existing conceptions of musical spaces. The use of Hilbert spaces allows us to build up quantum representations of musical states, inheriting quantum computing resources, already used for robotic swarms. We present the theoretical framework and then some case studies as toy examples. In particular, we discuss a 2D video and matrix simulation with two robo-caterpillars; a 2D simulation of 10 robo-ants with Webots; a 3D simulation of three robo-fish in an underwater search-and-rescue mission.

The Music of Perfume

Reported studies about crossmodal correspondences between music and smell basically focus on individual musical parameters. An experiment was carried out to explore such correspondences emerging from musical improvisation elicited by 20 olfactory stimuli, which allows the study of multiple musical parameters at the same time. A group of 14 pianists was asked to smell each stimulus and to play a short free improvisation inspired by it. From each improvisation, 14 musical parameters were extracted. The same odorants were also described by a panel of 15 volunteers. The main outcomes were the following: 1) The mean sensory ratings on a scale of fresh vs. warm appeared correlated with the average pitch of the improvisation. 2) The four odorants perceived as somewhat camphoraceous like lavender and mint yielded more non legato/staccato articulation or rests. 3) The feminine odor character was negatively correlated with the ambitus of the improvisation, defined as the difference between the highest and lowest note, and was positively correlated with pitch-class entropy. 4) Pleasantness yielded a negative correlation with pitch-class entropy and dissonance, being positively correlated with the lowest note. The first outcome is consistent with earlier studies, but outcomes 2–4 were novel findings.

The influence of musical parameters and subjective musical ratings on perceptions of culture

Recent research suggests that music can affect evaluations of other groups and cultures. However, little is known about the objective and subjective musical parameters that influence these evaluations. We aimed to fill this gap through two studies. Study 1 collected responses from 52 American participants who listened to 30 folk-song melodies from different parts of the world. Linear mixed-effects models tested the influence of objective and subjective musical parameters of these melodies on evaluations of the cultures from which they originated. Musical parameters consistently predicted cultural evaluations. The most prominent musical parameter was musical velocity, a measure of number of pitch onsets, predicting more cultural warmth, competence and evolvedness and less cultural threat. Next, with a sample of 212 American participants, Study 2 used a within-subjects experiment to alter the tempo and dissonance for a subset of six melody excerpts from Study 1, testing for causal effects. Linear mixed-effects models revealed that both dissonance and slow tempo predicted more negative cultural evaluations. Together, both studies demonstrate how musical parameters can influence cultural perceptions. Avenues for future research are discussed.

The influence of tonality, tempo, and musical sophistication on the listener's time-duration estimates.

Music listening affects time perception, with previous studies suggesting that a variety of factors may influence this: musical, individual, and environmental. Two experiments investigated the effect of musical factors (tonality and musical tempo) and individual factors (a listener's level of musical sophistication) on subjective estimates of duration. Participants estimated the duration of different versions of newly composed instrumental music stimuli under retrospective and prospective conditions. Stimuli varied in tempo (90-120 bpm) and tonality (tonal-atonal), in a 2 × 2 factorial design, while other musical parameters remained constant. Estimates were made using written estimates of minutes and seconds in Experiment 1, and the reproduction method in Experiment 2. Two-way analyses of variance (ANOVAs) showed no main effect of tonality on estimates and no significant interactions between tempo and tonality, under any condition. Musical tempo significantly affected estimates, with the faster tempo leading to longer estimates, but only in the prospective condition, and with the use of the reproduction method. Correlation matrices using the Pearson correlation coefficient found no correlation between musical sophistication scores (measured using the Goldsmiths Musical Sophistication Index [Gold-MSI]) and verbal or reproduction estimates. In conclusion, together with the existing literature, findings suggest that (1) changes in tonality, without further changes in rhythm, metre, or melodic contour, do not significantly affect estimates; (2) small changes in musical tempo influence only prospective reproduction estimates, with larger tempo differences or longer stimuli being needed to cause changes in retrospective estimates; (3) participants' level of musical sophistication does not impact estimates of musical duration; and (4) empirical research on music listening and subjective time must consider potential method-dependent results.

Order and Continuity in Igor Stravinsky’s Music:

The works of Igor Stravinsky (1882-1971) have been criticised for the tendency of their compositional technique towards ‘repetition,’ ‘stasis,’ ‘non-progression,’ ‘block juxtaposition,’ and even ‘discontinuity’ by musicologists and analysts including Taruskin (1996), Whittall (1997), Cross (1998), and Boulez (1968). However, more and more contemporary theorists argue that his music is not only characterised by repetition or consistency, but also that many structural phenomena and musical parameters have distinct development within the internal structure. Moreover, they point out that characteristics of both discontinuity and continuity are found at different structural levels within his compositions (Cone; Horlacher 2018; Wang 2004; Kramer 1986, 1988).&#x0D; &#x0D; Taking the above scholarship into consideration, this essay analyses several musical elements to explore features of order, regularity, continuity, and consistency in the first movement of Stravinsky’s L’Histoire du Soldat, “Marche du Solda”. Closer analysis reveals that this movement exhibits many tendencies of order and consistency within individual parameters, but this order is broken when considering all parameters together, as each has its own pace and structural pattern. The analytical results presented in this essay align with the emphasis by contemporary musicologists and scholars on Stravinsky’s tendency towards consistency and order in his compositions, affirming that his music does indeed possess these features, but they require a different perspective to observe.

HYPERBOLIC SPACE AND VIOLETA DINESCU'S MUSICAL REPRESENTATION OF THE ‘WOMAN'S SOUL’

AbstractThis paper proposes an approach to the representation of mental musical space, understood here as a mental ‘hologram’ of a musical structure created while composing or listening to a piece of music. Composers claim to ‘hear’ music in their mind and ‘see’ it in their spatial imagination; normally we see music graphically represented on two-dimensional staves, but we could mentally decode it in a three- or multi-dimensional space, and I argue that Violeta Dinescu's musical vision occupies a non-Euclidean imaginary musical space rather than the Western classical-music template. Dinescu's graphical design suggests a hyperbolic space, distorting the musical parameters accordingly. Two of her works are discussed: Gehen wir zu Grúschenka, for cello with voice ad libitum, and Herzriss – Aus deinem Herzen kannst du die Liebe nicht ausreißen, an opera for solo voice(s), percussion and cello. The first views the behaviour of musical parameters as if in an imaginary hyperbolic space; the latter exemplifies intertextuality in a cultural hyperbolic space. Both are metaphors of the woman's soul.

How does background music affect drivers’ behaviours, emotions and mood behind the wheel?

The purpose of this study was to better understand how music listening impacts driving behaviours, two common activities. Driving behaviours were categorized into three levels of cognitive control (operational, tactical, and strategical) while the selection of the musical background experienced during simulated driving was left to participants. The following characteristics were considered as candidates to investigate driving behaviours changes: individual characteristics in terms of driving experience and music listener (i.e., individual sensitivity to music reward and frequency of music listening), music parameters (i.e., tempo, mode), and mood and emotional changes induced by music. Ninety-two drivers’ behaviours were analysed in a variety of simulated driving situations. The findings support the rationale that musical background has the potential to impact driving behaviours. Driving behaviours requiring an “operational” level of cognitive control were found to be the most influenced by the musical stimuli. Music listening was also found to generate mood and emotion changes, which can in turn influence driving behaviours, especially when the induced emotional valence is negative. However, background music's influence on driving behaviours, either direct or mediated by emotional or mood changes, seemed rather limited in terms of effect size.

Steve Reich’s Style and Componistic Concepts Reflected in Tehillim Score

"The present article traces the way compositional conceptions and writing style are highlighted in the creation of Tehillim belonging to one of the most prolific contemporary composers – Steve Reich. The research starts from the composer’s ideas about what the compositional journey means, continues with a musical analysis that emphasizes the ways of development of the musical data, and ends with the observation of how the principles of composing are objectified in realities and musical choices. I chose this score because it differs from the previous ones with original elements, with musical parameters that Reich did not use in his career, so it is very interesting to find the composer’s specific compositional archetypes in this specific work. Keywords: componistic concepts, style, Steve Reich, vocal music, 21st century music, Tehillim. "

BETWEEN AUDIATION AND EKPHRASIS: PASCAL DUSAPIN'S ‘FALSE TRAILS’

AbstractThis article investigates the prolific deployment of images in Pascal Dusapin's scores of the mid to late 1990s. Using Edwin Gordon's concept of ‘audiation’ and Siglind Bruhn's concept of ‘musical ekphrasis’, as well as Neal Curtis’ ideas on the agency and liveness of images, interdisciplinary interpretations of three Dusapin works are offered, using the score image as the main analytical starting point. Beginning with his Piano Études and Loop, these analyses will demonstrate how the score images, derived from the study of ‘catastrophe theory’, prefigure the control of various musical parameters relating to the relationship of variables in this mathematical concept and its forms. An analysis of String Quartet No. 4, notable for its use of both a score image (of a machine) and textual quotation (from Samuel Beckett's Murphy), will then demonstrate how the visual can interact with the verbal to construct a plurality of musical metaphors. The article concludes by positing that Dusapin's elusiveness on the role and function of the images within his work could amount to what W. T. J. Mitchell describes as ‘ekphrastic fear’: an anxiety that the composer's success amalgamating image and music might have broken down the ontological boundary between them.

Projection, Call‐Response and the Improvisational Moment

Projection, Call‐Response and the Improvisational Moment

Inpatient stroke survivors with low gait functioning benefit from music interventions during cardiorespiratory exercise: A randomized cross-over trial

ABSTRACT Introduction Stroke survivors struggle to meet clinical recommendations for physical exercise duration and intensity. During the past two decades, emerging evidence has shown effectiveness of music interventions for several motor tasks in stroke rehabilitation. Additionally, music has been found effective for increasing exercise performance in athletes and clinical populations. It is postulated that the therapeutic effects of music in physical exercise are modulated by preference and task-specificity of the music. Methods We tested this hypothesis in a pilot study using a three-arm randomized cross-over design comprising the following auditory conditions during cycle ergometry cardiorespiratory exercise sessions: (a) a group-tailored music playlist, (b) radio music, and (c) a non-music control condition. Participants (n = 19) were inpatient stroke survivors undergoing rehabilitation between 2 and 12 weeks post infarct. Results Our results demonstrate that clinical characteristics are an important determinant for identifying patients who can benefit from music. Specifically, participants with a higher level of gait functioning experienced no benefit, whereas participants with a low level of gait functioning showed an increase in both exercise duration (M = 4.46 minutes) and time spent in the recommended heart rate intensity (M = 6.39 and M = 2.49 minutes for the playlist and radio condition, respectively). Discussion The findings suggest a beneficial role of music in rehabilitation of stroke patients with low gait functioning. Future studies should ultimately disentangle which musical parameters are more likely to induce the putative ergogenic effects. Trial registry number: NCT05398575.

Beyond (the cave of) pitch/loudness-equalization: A Commentary on Reymore (2021)

Traditional approaches in timbre research have often equalized sounds according to pitch, loudness, duration in order to study timbral differences across instruments. In a compact case study of the semantic qualities of the oboe and French horn, Reymore (2021) takes a different approach and considers timbral differences within musical instruments, which arise due to the covariation of timbre with the musical parameters of fundamental frequency (pitch) and playing effort (dynamic level). The study constitutes a timely contribution to a growing body of work on the covariation between timbre, pitch, and loudness. After providing a background and summary of important aspects of the target article, I elaborate on results from a recent complementary study that analyzed acoustical signal properties regarding that matter. Finally, I address three important issues in this context that appear to be worthy of future research.