Rhythmic Transformation Research Articles

В поисках подлинной реальности: специфика жанра и драматургии в опере Пера Нёргора «Сиддхартха»

The article focuses on the peculiarities of genre and dramaturgy of the opera Siddharta (1974‒1979, revised 1984, libretto by Ole Sarvig) by Danish composer Per Nørgård. Its plotline is based on the story of young Buddha, his birth, growing up and encounter with human sufferings, from which the prince had been artificially shielded by his father. The author of the article connects the opera’s singularity of genre with its character of modulation from a mystery to a drama, which is confirmed by the changes occurring in the libretto’s lexical structure, in the chronotope of the composition, which reflects consistently the various models of time (the mythological, the artistic, and the psychological), in the choice of different opera forms for each act, and in the dramaturgical process directed from the outward eventful plane to the inward psychological dimension. The article reveals the compositional strategies that helped Nørgård manifest the conflict between the genuine and the inauthentic world on a musical level: the rhythmic transformation and the metric reaccentuation of the themes, the combination of the overtone and the undertone pitch sets, the rejection of the hierarchical system at the end of Act III, symbolizing the main protagonist’s estrangement from the world of his past. In connection with the artistic crisis experienced by Nørgård after he composed Siddharta, the author presumes that the opera may be interpreted as a self-reflection of artistic activity.

MoMusic: A Motion-Driven Human-AI Collaborative Music Composition and Performing System

The significant development of artificial neural network architectures has facilitated the increasing adoption of automated music composition models over the past few years. However, most existing systems feature algorithmic generative structures based on hard code and predefined rules, generally excluding interactive or improvised behaviors. We propose a motion based music system, MoMusic, as a AI real time music generation system. MoMusic features a partially randomized harmonic sequencing model based on a probabilistic analysis of tonal chord progressions, mathematically abstracted through musical set theory. This model is presented against a dual dimension grid that produces resulting sounds through a posture recognition mechanism. A camera captures the users' fingers' movement and trajectories, creating coherent, partially improvised harmonic progressions. MoMusic integrates several timbrical registers, from traditional classical instruments such as the piano to a new ''human voice instrument'' created using a voice conversion technique. Our research demonstrates MoMusic's interactiveness, ability to inspire musicians, and ability to generate coherent musical material with various timbrical registers. MoMusic's capabilities could be easily expanded to incorporate different forms of posture controlled timbrical transformation, rhythmic transformation, dynamic transformation, or even digital sound processing techniques.

Fishing for complements with chord, scale, and rhythm nets

The aim of this paper is to argue that complementation is an operation similarly fundamental to music theory as transposition and inversion. We focus on studying the chromatic complement mapping that translates diatonic seventh chords into 8-note scales which can also be interpreted as rhythmic beat patterns. Such complements of diatonic seventh chords are of particular importance since they correspond to the scales popularized by the Jazz theorist Barry Harris, as well as to rhythms used in African drum music and Steve Reich's Clapping Music. Our approach enables a systematic study of these scales and rhythms using established theories of efficient voice leading and generalized diatonic scales and chords, in particular the theory of second-order maximally even sets. The main contributions of this research are (1) to explicate the correspondence between voice leadings and rhythmic transformations, (2) to systematize the family of Barry Harris scales, and (3) to describe classes of voice leadings between chords of different cardinality that are invariant under complementation.

Chinese Piano Music: the Role of Composer Chu Wanghua in the Evolution of Modern Piano Traditions in China (the Case of the ‘Sounds of the Temple’ Capriccio Suite)

Chinese piano music is based on folk songs, Chinese poetry, and the ethnic style, which contribute to the expressiveness of the sound and refinement of the intonation and tonal system. The paper addresses the Chinese piano music and the role of composer Chu Wanghua in shaping contemporary piano traditions, using the ‘Sounds of the Temple’ capriccio suite as an example. Based on the direct method of standardization, the paper determined the significance of the parts of the ‘Sounds of the Temple’ suite. The second part (0.93) is most significant for displaying the piano music, because it involves the use of polyphonic sounds, imitating other instruments. The first part of the suite (0.87) is based on a linear representation of sounds, imitating the sounds of bells. The third part (0.69) centers around the use of slow tempo as well as major tone deviations. Significant elements of the suite (mirror reprise, rhythmic transformation, monotonous repetition of phrases and sounds, application of guó huà techniques, texture elements) were determined on the basis of the measured complexity and harmony of performance, as well as their influence on national traditions. A comparison of performance using standard deviation suggested that the differences were based on monotonous repetition of phrases and sounds (1.07), which is attributed to a greater emphasis on the difficulty of performance than on other parameters. The paper’s practical implications involve the possibility of preserving expressiveness and ethnic elements while playing the piano, based on Chu Wanghua’s ‘Sounds of the Temple’ suite. Further studies might compare the elements that contribute to the expressiveness of performance in the ‘Sounds of the Temple’ suite by Chu Wanghua and ‘Flower Drum’ by Qu Wei.

Valentyn Bibik: reaching artistic maturity

The object of research is the works of V. Bibik written at the beginning of his mature period. The aim of the research is to reveal the main features of Bibik’s style. Methods of research include technical analysis of the works in the context of the innovative tendencies in the Ukrainian music of 1960–70s, as well as comparative research. Research results. Outstanding Ukrainian composer Valentyn Bibik (1940–2003) wrote over 150 works. Mostly they are large-scale symphonic, choral, vocal, and chamber pieces. Among them are 11 symphonies, over 20 concerti for various instruments with orchestra, vocal and choral cycles, chamber compositions (the last group includes 5 string quartets, 3 piano trios, sonatas for string instruments both solo and with piano), 10 piano sonatas, piano solo works (two sets of preludes and fugues – 24 and 34 total, Dies Irae – 39 variations). The composer was born in Kharkiv. In 1966 he completed studies at Kharkiv Conservatory, where he attended the composition class of D. Klebanov. Since 1994, he had been living in St.-Petersburg, and since 1998, in Israel where he died in 2003. Bibik’s formative period coincided with a substantive modernization of Ukrainian culture in the 1960s. During those years, members of the “Kyiv avantgarde” group (L. Hrabovsky, V. Sylvestrov, V. Godziatsky, et al.) sought to utilize modernistic idioms and techniques, such as free atonality, dodecaphony, sonoristic and aleatoric textures, cluster harmony, etc. Unlike the others, Bibik started with a more conservative style, which bore the influences of Shostakovich, Prokofiev, and Bartók. Bibik’s mature period started several years later in the early 1970s with Piano Trio No. 1 (1972) and the composition Watercolors for soprano and piano (1973). Together with his next piano work 34 Preludes and Fugues, these compositions show extremely individual features of Bibik’s style, such as: 1. Special treatment of the sound, which is considered not just a material for building certain musical structures but a self-valuable substance (Bibik has an original manner of organizing sound). Hence, timbral and textural aspects draw special attention to the composer. 2. The pitch and rhythmic structure of the themes is quite simple. A combination of several simple motives becomes the starting point of long and sophisticated development. These motives are derived from folk music, however, due to rhythmic transformation, they have lost their direct connection with the folk source. 3. Rhythmic structures areal so very simple. They often include sequences of equal rhythmic values (usually crotchets or eights). However, the composer avoids monotony dueto due to variable time signatures and permanent rubato, as well as significant flexibility in phrasing. 4. The development relies mostly on melodic and polyphonic elaboration of initial simple motives. The composer utilizes various kinds of polyphony, such as canonic imitations, various combinations of the main and supportive voices, heterophony, hyper-polyphony. In fugues he employs both traditional and new methods of thematic and tonal distribution. 5. The harmony in Bibik’s works is mostly modal, as well as a combination of modality with free atonality and extended tonality. The structure of the dense chords is close to clusters, while more transparent chords include mostly seconds and fourths (as well as their inversions). He almost never used traditional tonal harmony and chords built up from thirds, and was interested in their color aspect rather than their tonal functionalism. 6. The sonoristic texture is very important. It does not diminish the importance of the melody but gets into special collaboration with it (“singing sonority”). A special “mist” around a clear melodic line is one of Bibik’s most typical devices. Due to special “pedal” orchestration, both the line and the “surrounding” sounds become equally important. 7. Elements of limited aleatoric music may be found in his rhythm and agogics, and sometimes inpitch structures (passages and figurations with free choice of the pitches). His favorite technique is a superposition of two rhythmically and temporally independent textural layers (for instance, a combination of the viola solo and the sonoristic orchestral background in the third movement of the Fourth Symphony). 8. Sonata for mand the fugue were significantly reinterpreted within free atonality and modal harmony. These provisions are the scientific novelty of the study.

Музыка - ожившая архитектура: готический собор как модель совершенной музыкальной композиции глазами Венсана Д'энди

Vincent d’Indy developed his own understanding of the ideal algorithm of constructing musical forms. In support of his concept, he took a general artistic perspective. His aim, apparently, was to confirm the special status of the suggested compositional strategies as universal for different kinds of art. These strategies are grounded in such categories as rhythm, order, proportionality, and symmetry inherent to any kind of spatial/temporal art with architecture and music representing the extremes of the spatial/temporal continuum. D’Indy established the correlations between the spatial/temporal arts by embracing the ideas of Hegel, Ruskin, and Lévesque. To explore these ideas, the article resorts to the cultural and historical analysis. D’Indy argues that the “cyclic principle” is the most mature historically and the most perfect constructively. The principle applied exclusively to multimovement compositions has its basis in the translational symmetry of the initial pattern-cell together with its variant renewal. The “cyclic principle” finds its supreme realization in the “cyclic sonata” and the Gothic cathedral. The article is the first attempt to analyse how the “cyclic principle” is used per se, while its particular implementation in music has repeatedly been discussed. The latter was initiated by d’Indy himself in his Cours de Composition Musicale. A step-by-step method of putting the cyclic principle into practice, regardless of the artistic material, is derived by applying the comparative analysis, which helps to develop universal models for working with repetitive patterns in spatial and temporal arts. The analysis revealed the following: first, a “cyclic element” is represented by a syntactically articulated structure which may function as an initial compositional unit (from musical cells to sculptural details); second, the elaboration on the artistic material in music and architecture is done through rhythmic transformations of patterns resulting in the new internal structure with the core preserved. The latter ensures the implementation of the aesthetic maxim “unity in diversity”, seen by d’Indy as crucial in constructing the artistic whole.

Aceleração, desaceleração, tortura sônica e inércia: temporalidades de partidas de futebol

Este artigo explora as relações temporais da disputa futebolística, buscando evidenciar como o controle da passagem do tempo e das mudanças de andamento da partida – o que introduz transformações rítmicas a partir de eventos e lances do jogo – tanto por parte dos jogadores quanto da torcida por meio do som são fundamentais para a constituição do resultado esportivo. A pesquisa da qual parte o trabalho visa compreender como torcida e jogo constroem-se mutuamente no espetáculo futebolístico por meio da manipulação de sonoridades, compreendidas como mediações técnicas entre corpos diferentes. Aqui, quatro destas técnicas são delimitadas e exploradas: a aceleração, a desaceleração, a inércia e a tortura sônica. As observações partem de trabalho de campo realizado em partidas do Clube Atlético Mineiro, entre 2008 e 2015, nos Estádios Independência e Mineirão, em Belo Horizonte.

Інноваційні технології розвитку чуття ритму у студентів на заняттях сольфеджіо

The article reveals one of the topical issues of modern musical and pedagogical education, concerning the usage of innovative technologies in the musical-theoretical preparation of art university students. The author of the article emphasizes that modern scientific and pedagogical thought is one of the efficient means of increasing the efficiency of the educational process recognizing the application of pedagogical technologies. Accordingly, the author analyses the existing approaches to understanding the concept of «pedagogical technology» and concludes for all, the focus is on the guaranteed learning outcomes due to the teacher’s consistent actions in achieving the set learning goals.The author considers the development of the sense of the rhythm of students in solfeggio classes as an active process, the result of which is a deep, active understanding of the organization of the musical composition in time. A brief methodical review of exercises from the development of the sense of rhythm in classes solfeggio allowed the author to choose those of them, which compose the basis of pedagogical technology. They include: rhythmic sketches; rhythmic dictations; conducting and timing; different ways of rhythmization, rhythm-solmization; rhythmic transposition; rhythmic canons; rhythmic accompaniment with using the simplest shock and noise instruments; rhythmic transformation; rhythmic improvisation; warehouse-rhythmization and others.For today, the author of the article notes that the processes of informatization and computerization are actively implemented in the educational space. This affects the active use of innovative technologies in the learning process. In particular, the author outlines a number of computer programs for the development of a sense of rhythm, which can be used in classes solfeggio in higher art educational institutions. Among them: the MusicGoals Rhythm program, GNU Solfege, Ear Master and Sibelius Auralia 4. According to the author, only an organic combination of innovative technologies with traditional methods of training allows you to get optimal results in this direction.

The Mutable Subject

Among the many qualities that set Bach apart from his contemporaries is his manner of transforming his thematic material—most notably his fugue subjects. Bach himself believed that all good fugue writers should know how and when to change (or mutate) their subjects. The consequences of such changes are most often purely tonal in nature, giving rise to modulations that would otherwise take place during episodes. Much less frequently, tonal and rhythmic transformations of the subject may occur simultaneously, as in the fugue from the Sinfonia that opens Partita no. 2 in C minor for keyboard. It turns out that the subject of this fugue is so marked in rhythm and contour that it seems to motivate—and even demand—its own transformation as the fugue unfolds. One consequence of such transformation is a series of metric shifts from triple hypermeter during expositions to duple hypermeter during episodes.

Rhythmic shape change of a vesicle under a pH gradient

A vesicle that exhibits oscillatory structural changes under a pH gradient is reported. This vesicle is composed of oleic acid and sodium oleate and appears to exhibit a stomatocyte-type or a seemingly double spherical shape initially. The inner water is located at one side of the double spherical structure (i.e., the swollen part). The other side of the vesicle is nearly free of water. When the diffusion of hydroxide anions causes a pH gradient, the double spherical structure rotates such that its swollen part faces the higher-pH side. After this event, a small hole in the center of the swollen part begins to open. The vesicle changes to a torus-like structure: the swollen part is formed at the periphery, and a disk-like part is formed in the central part of the torus. The shape change proceeds via the torus-like shape, and the vesicle closes again to form a double spherical shape with a curvature opposite to the initial curvature. At this stage, the swollen part faces the lower-pH side. After this event, the vesicle rotates back to its initial state, where the swollen part faces the higher-pH side. This rhythmic transformation repeats numerous times. The size of the vesicle remains nearly constant during these numerous transformations. Thus, this vesicle continuously generates mechanical work from a pH gradient. In this study, experimental observations under an optical microscope and a model for the transformation are reported.

The Progress of a Motive in Brahms’s Intermezzo op. 119, no. 3

Brahms’s Intermezzo op. 119, no. 3 is structured around a motive with two components—one melodic, one harmonic—that operate sometimes separately and sometimes together. The global harmonic trajectory of the piece is embodied in the combination of these two components; local harmonic motion proceeds through an expanded LR-cycle, with periodic short cuts from one zone of the cycle to another. The A section unfolds a double-tonic complex while introducing chromatic pitch classes in a carefully planned order; the B section is densely chromatic, featuring interlocking transpositions of the harmonic component. Rhythmic transformations of the motive are also addressed, including a previously unnoted motivic connection with op. 119, no. 2.

When Fibre Meets Fibre

When Fibre Meets Fibre

‘Funky Drummer’: New Orleans, James Brown and the rhythmic transformation of American popular music

The singular style of rhythm & blues (R&B) that emerged from New Orleans in the years after World War II played an important role in the development of funk. In a related development, the underlying rhythms of American popular music underwent a basic, yet generally unacknowledged transition from triplet or shuffle feel (12/8) to even or straight eighth notes (8/8). Many jazz historians have shown interest in the process whereby jazz musicians learned to swing (for example, the Fletcher Henderson Orchestra through Louis Armstrong's 1924 arrival in New York), but there has been little analysis of the reverse development – the change back to ‘straighter’ rhythms. The earliest forms of rock 'n' roll, such as the R&B songs that first acquired this label and styles like rockabilly that soon followed, continued to be predominantly in shuffle rhythms. By the 1960s, division of the beat into equal halves had become common practice in the new driving style of rock, and the occurrence of 12/8 metre relatively scarce. Although the move from triplets to even eighths might be seen as a simplification of metre, this shift supported further subdivision to sixteenth-note rhythms that were exploited in New Orleans R&B and funk.