Musical Harmony Research Articles

Fractal and Complex Patterns Existing in Music: Application to the Composition DIAPHONIES of Michael Paouris

This paper reports fractal patterns identified in the complex musical composition DIAPHONIES by Michael Paouris via power-law fractal analysis with sliding-windows of size 1024. From 7,647,232 analysed musical segments of DIAPHONIES, 3,222,832 (42.4%) are fractional Brownian motion (fBm) fractal segments and 4,424,400 (57.6%) are fractional Gaussian noise (fGn) stochastic ones. From the fBm fractal segments 295,294 (9.1%) exhibit strong persistency-P with power-law segments in the range of 2.3≤b≤3. These are the very strong fractal areas in DIAPHONIES. Numerous segments with strong antipersistency 1.7≤b<2 are reported together with segments with AP changes (1.7≤b<2.3). In DIAPHONIES continuous fractal fBm areas are dipped in non-fractal fGn areas of deterministic music. The results are within the fBm fractal areas reported in existing papers. Very importantly, the simple composition called Nocturnal-Angel by Michael Paouris, exhibited limited fBm areas of average b¯=1.98 (σ=0.3), namely of pure statistical, deterministic music, while simultaneously, the fractal analysis profile was completely different from the profiles of DIAPHONIES, hence reinforcing, the fractal findings of DIAPHONIES in relation to trivial music harmony.

Musical Color Harmony: Application of the Principles of Musical Harmony to Produce Color Hue Sets

Abstract Aesthetic response to the visual harmony of color combinations is a very personal and widely differing subjective experience. To the contrary, musical harmony - consonance and dissonance - are mathematically defined and certain combinations of notes exhibit near universal aesthetic agreement across the globe. Although numerous metaphysicians, philosophers, scientists, poets, artists, and musicians have speculated on the existence of a relationship between color and music for over 2000 years, the establishment of a correlation between color and musical harmony has been elusive. The author describes a framework, Musical Color Hue Harmony (MCHH), initially developed for video display systems, that correlates musical and color harmonic consonance and dissonance by applying the physics of aural harmonic resonance and theories of musical harmony to produce sets of “harmonious” color hues based on the mathematically defined frequency relationships between two or more musical pitches. The methodology is applicable to any musical tuning system and any color hue wheel configuration. Color attributes of brightness/luminance and saturation/chroma are presently beyond the scope of the framework.

Music as incarnated beauty in J.R.R. Tolkien’s The Silmarillion: a neoplatonic reading

Abstract In this study I examine key conceptual parallels between J.R.R. Tolkien’s literary imagination and a Neoplatonic mythopoetic. Specifically, I discuss how Tolkien’s Silmarillion deploys a transcendental conception of Beauty that, I argue, suggests similarities with the notion of Beauty discussed by Plotinus in his Enneads. Following the scholarship of Lisa Coutras (2016) and Michael John Halsall (2020), this study analyzes key sections from Tolkien’s work to demonstrate a Neoplatonic influence. This influence, I argue, is best understood via an incarnational logic that understands musical harmony and tonal beauty to be signs that signal an ultimate transcendent source in Tolkien’s legendarium. Falling short of arguing for a direct influence of the Neoplatonic tradition on Tolkien, this study seeks to demonstrate only a plausible link between Neoplatonic sources and Tolkien’s work.

Manifestations of Stylistic Dichotomy in the Harmony of 20th Century Music: General Tendencies andSeveral Case Studies

Manifestations of Stylistic Dichotomy in the Harmony of 20th Century Music: General Tendencies andSeveral Case Studies

Theperception of emotion in music by people with hearing loss and people withcochlear implants.

Music is an important part of life for many people. It can evoke a wide range of emotions, including sadness, happiness, anger, tension, relief and excitement. People with hearing loss and people with cochlear implants have reduced abilities to discriminate some of the features of musical sounds that may be involved in evoking emotions. This paper reviews these changes in perceptual abilities and describes how they affect the perception of emotion in music. For people with acquired partial hearing loss, it appears that the perception of emotion in music is almost normal, whereas congenital partial hearing loss is associated with impaired perception of music emotion. For people with cochlear implants, the ability to discriminate changes in fundamental frequency (associated with perceived pitch) is much worse than normal and musical harmony is hardly perceived. As a result, people with cochlear implants appear to judge emotion in music primarily using tempo and rhythm cues, and this limits the range of emotions that can be judged. This article is part of the theme issue 'Sensing and feeling: an integrative approach to sensory processing and emotional experience'.

Terminological Issues and Propositions in the Search for an Ontology of Harmonic Structures

This article presents a fragment from a larger research with the intention of anticipating some of its main topics, which aim to assemble a pedagogical theoretical body for music harmony in the context of the globalized and diverse world of the 21st century. The research fragment presented discusses terminological issues and propositions for an ontological study of harmonic structures that concerns itself with the definition of what types of musical sound objects of definite pitch do exist, how many are there, which properties they possess and their musical consequences, all organized in a logical taxonomical system referred to by means of an adequate terminology. The text first establishes the need for such an ontology, and proceeds with a description of the terminological issues involved in a secondary term formation action, a subsequent renaming effort that is all the more challenging when dealing with a field with a huge lifetime such as music theory. The methodology used in the terminological recreation is then described, explaining its preference for terms that, regardless of their lexicographic origins and prevalence, are single-words that provide biunivocal association, that avoid ambiguity by synonymy and polysemy, that are self-explanatory, and that are of easy translation using same-lexeme words similar in graphical form. It is then given a brief summary of the structure of the created ontology, followed by the definitions, lexicographic origins, and neologism-creating derivational strategies for all its main proposed terms, including those to be used in the classifications of harmonic structures according to the criteria of cardinality, chirality, azimuth, triadic intrinsicality, monadic, triadic, and transpositional proclivities, limiting characteristics, and modalization, superset and subset relationships. To close the text, a schematic view of the organizational structure of the ontology is shown, together with its translation into three different languages.

Musical harmonies and its relationship with emotional processing: An ERP study in young adults

Music has been used to express and communicate emotional states through its different dimensions such as tone, rhythm, melody, and harmony. Consonant harmonies consistently are rated as pleasant whereas dissonant are considered unpleasant. The aim of this study was to explore the effect of consonant and dissonant musical harmonies used as prime on the emotional classification of images, as indexed by event-related potentials. Thirty volunteers (ages 21–27, 50 % women) were presented with a task consisting of 4 musical intervals in the C major scale, divided into consonant and dissonant harmonies, followed by 180 positive, negative, or neutral images from the International Affective Picture System (IAPS). Participants had to rate the images as pleasant or unpleasant. We found a bias effect on negative images rated as positive when preceded by a consonant musical interval. A N200 component, non-sensible to the valence of the images, was found. On the other hand, a significant difference was found in the amplitude of the P300 component, with a greater amplitude in the consonant-positive images condition compared to the dissonant-positive images. Lastly, a late positivity component around 500–700 ms was found in both negative conditions dissonant and consonant, but with a larger amplitude for the consonant condition when followed by a negative image. These results indicate that additionally to the P300 processing the relevance of the stimulus there are processes like recognition memory involved. As part of the novelty effect this late positive activity may also be related to the emotional content integration of the relevant stimulus.

Evidence for a universal association of auditory roughness with musical stability.

We provide evidence that the roughness of chords-a psychoacoustic property resulting from unresolved frequency components-is associated with perceived musical stability (operationalized as finishedness) in participants with differing levels and types of exposure to Western or Western-like music. Three groups of participants were tested in a remote cloud forest region of Papua New Guinea (PNG), and two groups in Sydney, Australia (musicians and non-musicians). Unlike prominent prior studies of consonance/dissonance across cultures, we framed the concept of consonance as stability rather than as pleasantness. We find a negative relationship between roughness and musical stability in every group including the PNG community with minimal experience of musical harmony. The effect of roughness is stronger for the Sydney participants, particularly musicians. We find an effect of harmonicity-a psychoacoustic property resulting from chords having a spectral structure resembling a single pitched tone (such as produced by human vowel sounds)-only in the Sydney musician group, which indicates this feature's effect is mediated via a culture-dependent mechanism. In sum, these results underline the importance of both universal and cultural mechanisms in music cognition, and they suggest powerful implications for understanding the origin of pitch structures in Western tonal music as well as on possibilities for new musical forms that align with humans' perceptual and cognitive biases. They also highlight the importance of how consonance/dissonance is operationalized and explained to participants-particularly those with minimal prior exposure to musical harmony.

ChoCo: a Chord Corpus and a Data Transformation Workflow for Musical Harmony Knowledge Graphs

Various disconnected chord datasets are currently available for music analysis and information retrieval, but they are often limited by either their size, non-openness, lack of timed information, and interoperability. Together with the lack of overlapping repertoire coverage, this limits cross-corpus studies on harmony over time and across genres, and hampers research in computational music analysis (chord recognition, pattern mining, computational creativity), which needs access to large datasets. We contribute to address this gap, by releasing the Chord Corpus (ChoCo), a large-scale dataset that semantically integrates harmonic data from 18 different sources using heterogeneous representations and formats (Harte, Leadsheet, Roman numerals, ABC, etc.). We rely on JAMS (JSON Annotated Music Specification), a popular data structure for annotations in Music Information Retrieval, to represent and enrich chord-related information (chord, key, mode, etc.) in a uniform way. To achieve semantic integration, we design a novel ontology for modelling music annotations and the entities they involve (artists, scores, etc.), and we build a 30M-triple knowledge graph, including 4 K+ links to other datasets (MIDI-LD, LED).

Theoretical Musicology in Bukovyna (on the Example of S. Vorobkevych’s Harmony Textbook)

The purpose of the work is to characterise the state of theoretical musicology in Bukovyna in the late nineteenth and early twentieth centuries on the basis of Sydir Vorobkevych’s work “Musical Harmony”. Research methodology. The article is based on the following research methods: historical, biographical, cultural, and theoretical generalisation. The systematic approach of scientific research helped to analyse the work, which became one of the attempts to adapt the theoretical foundations of musical harmony to the needs of the multinational environment of the Bukovyna region. Scientific novelty is that for the first time, the article thoroughly analyses the music-theoretical work that became the basis for theoretical training of music specialists in Bukovyna, and draws conclusions about the peculiarities of musicology in the region. Conclusions. One of the first theoretical works in Bukovyna to appear during the period of Austro-Hungarian rule in the region was a textbook on harmony by Sydir Vorobkevych. Despite the fact that the vast majority of imported books and works of local artists were written in German, S. Vorobkevych’s “Musical Harmony” was written in Romanian, as the majority of the region’s population was Romanian. The need for such a textbook was extremely relevant among the musicians of Bukovyna and Chernivtsi. S. Vorobkevych created one of the first works of theoretical musicology in Bukovyna, which became the basis of musical education in the region. Sydir Vorobkevych’s work is fully in line with the traditions of the second half of the nineteenth century and confirms the idea that the terminology and methodological explanation of the foundations of music theory, in particular musical harmony, were at the stage of development at that time and underwent changes already in the next century. S. Vorobkevych’s “Musical harmony” is a source of information about the basic postulates of theoretical musicology, related to the principles of harmonic thinking, which, according to the author of the textbook, is an indispensable basis for successful composing.
 Key words: art of Bukovyna, musicology, musical education of Bukovyna, musical harmony, music theory.

Expectation adaptation for rare cadences in music: Item order matters in repetition priming

Humans make predictions about future events in many domains, including when they listen to music. Previous accounts of harmonic expectation in music have emphasised the role of implicit musical knowledge acquired in the long term through the mechanism of statistical learning. However, it is not known whether listeners can adapt their expectations for unusual harmonies in the short term through repetition priming, and whether the extent of any short-term adaptation depends on the unfolding statistical structure of the music. To explore these possibilities, we presented 150 participants with phrases from Bach chorales that ended with a cadence that was either a priori likely or unlikely based on the long-term statistical structure of the corpus of chorales. While holding the 50–50 incidence of likely vs. unlikely cadences constant, we manipulated the order in which these phrases were presented such that the local probability of hearing an unlikely cadence changed throughout the experiment. For each phrase, participants provided two judgements: (a) a prospective rating of how confident they were in their expectations for the cadence, and (b) a retrospective rating of how well the presented cadence matched their expectations. While confidence ratings increased over the course of the experiment, the rate of change decreased as the local probability of an unexpected cadence increased. Participants' expectations favoured likely cadences over unlikely cadences on average, but their expectation ratings for unlikely cadences increased at a faster rate over the course of the experiment than for likely cadences, particularly when the local probability of hearing an unlikely cadence was high. Thus, despite entrenched long-term statistics about cadences, listeners can indeed adapt to unusual musical harmonies and are sensitive to the local statistical structure of the musical environment. We suggest that this adaptation is an instance of Bayesian belief updating, a domain-general process that accounts for expectation adaptation in multiple domains.

Parsimonious sequences of finite sets and their applications to chord progressions and music composition

Parsimony is a broad concept with applications in music theory and composition. Two sets A and B of finite cardinality n (n-sets) are in parsimonious relation if there exists a (n–1)-set C that is included in both A and B. A sequence of n-sets is parsimonious if any two successive sets in the sequence are in parsimonious relation. This work demonstrates that for any set of finite cardinality p, there exist sequences of its n-subsets (n ≤ p) that are circular, non-redundant, exhaustive and parsimonious, and it describes the corresponding algorithm. The image of such a sequence by a bijection and the retrograde sequence keep the same four properties. The consequences of these results for the pitch class (pc) subsets of cardinality n (or n-chords) of a pc set of finite cardinality p (p-tonic scale) are derived and discussed in the context of music harmony, microtonality and composition.

Liturgical Aesthetics of Archpriest Sergei Protopopov

The article is devoted to the analysis of the treatise “On the Artistic Element in Orthodox Church Singing: (Thoughts and Observations)” (1901) by archpriest S. Protopopov as the fi rst experience of aesthetic research of church music in the period of the Silver Age. The author examines the ontological foundations of the archpriest’s understanding of the nature of aesthetic perception and the specifi cs of sacred music (church singing). It is shown that Sergei Protopopov succeeded in substantiating the principles of the revival of canonical church singing on the basis of the laws of musical harmony of later epochs.

МУЗЫКА, УНИВЕРСАЛИИ ГЕНОМНЫХ ДНК, ГЕНЕТИЧЕСКИЙ ИНТЕЛЛЕКТ И ПРЕДСТАВЛЕНИЕ О СТОХАСТИЧЕСКОЙ СИСТЕМЕ ПРОТОРЕГУЛЯЦИИ

This work is devoted to the structural links between the musical harmony of the Pythagorean fifth scales and the system of hydrogen bonds in genetic molecules DNAs. Hidden regularities in the stochastic organization of hydrogen bond sequences in the genomic DNAs of higher and lower organisms have been discovered. The regularities described are candidates for the role of universal regularities of biological evolution. An idea is advanced on the fundamental role of stochastic regularities in the genetically inherited organization of biological bodies. In the presented study, the author's method of binary stochastics hierarchy for genetic and physiological studies was used.

Automatic note generator for Javanese gamelan music accompaniment using deep learning

Javanese gamelan is a traditional form of music from Indonesia with a variety of styles and patterns. One of these patterns is the harmony music of the Bonang Barung and Bonang Penerus instruments. When playing gamelan, the resulting patterns can vary based on the music’s rhythm or dynamics, which can be challenging for novice players unfamiliar with the gamelan rules and notation system, which only provides melodic notes. Unlike in modern music, where harmony notes are often the same for all instruments, harmony music in Javanese gamelan is vital in establishing the character of a song. With technological advancements, musical composition can be generated automatically without human participation, which has become a trend in music generation research. This study proposes a method to generate musical accompaniment notes for harmony music using a bidirectional long-term memory (BiLSTM) network and compares it with recurrent neural network (RNN) and long-term memory (LSTM) models that use numerical notation to represent musical data, making it easier to learn the variations of harmony music in Javanese gamelan. This method replaces the gamelan composer in completing the notation for all the instruments in a song. To evaluate the generated harmonic music, note distance, dynamic time warping (DTW), and cross-correlation techniques were used to measure the distance between the system-generated results and the gamelan composer's creations. In addition, audio features were extracted and used to visualize the audio. The experimental results show that all models produced better accuracy results when using all features of the song, reaching a value of around 90%, compared to using only 2 features (rhythm and note of melody), which reached 65-70%. Furthermore, the BiLSTM model produced musical harmonies that were more similar to the original music (+93%) than those generated by the LSTM (+92%) and RNN (+90%). This study can be applied to performing Javanese gamelan music.

Philosophical Conversations about Music in Simple Language. Pythagoras: the Divine Number and World Musical Harmony

The article is written on the basis of a conversation on the philosophy of music by Professor G.G. Kolomiets, author of the book Value of music: philosophical aspect, with a musician from France, Dmitry Rasul-Kareev, Clarinet solo of Orchestra de la Suisse Romande. The dialogue gives a detailed and simple understanding of the philosophical view of music on the example of the ancient philosopher Pythagoras. His cosmological teaching saw the kinship of music, mathematics and philosophy and stated that the divine perception of the world is contained in the divine Number permeating the entire cosmos and our life. Music is made of numerical proportions and acts as a substance that exists even without a person, yet this unchanging principle of divine harmony, can be felt, experienced and expressed in musical art. Cosmologists believed there is a comprehensive law, according to which objects obey the divine mind, the great Rhythm. Music seemed to be the embodiment of the rhythm of the universe and harmony. The essence of the harmony of the spheres is that the cosmos is a harmoniously arranged and musical-sounding body. The movement of the starry sky creates the music of the cosmic spheres, which is refracted when playing musical instruments, and this lends itself to precise mathematical calculations. The intervals between the cosmic spheres are mathematically correlated with each other like the intervals of tones in music. The Pythagorean understanding of the numerical harmony of the structure of the universe largely determined the path of development of music theory, forming the main musical categories: fret, rhythm, interval, modulation and others. The modern philosophy of music deepens the Pythagorean ideas of harmony of spheres, putting forward the principles of functionality and processivity as properties of music, and allows us to talk about the law of cyclicity on a global scale. For example, following Pythagoras, music outside of the actual musical art is interpreted as a reflection of the vibrations of a complex communicative system: man-society-nature-cosmos.

Increasing the complexity of isolated musical chords benefits concurrent associative memory formation

The effects of background music on learning and memory are inconsistent, partially due to the intrinsic complexity and diversity of music, as well as variability in music perception and preference. By stripping down musical harmony to its building blocks, namely discrete chords, we explored their effects on memory formation of unfamiliar word-image associations. Chords, defined as two or more simultaneously played notes, differ in the number of tones and inter-tone intervals, yielding varying degrees of harmonic complexity, which translate into a continuum of consonance to dissonance percepts. In the current study, participants heard four different types of musical chords (major, minor, medium complex, and high complex chords) while they learned new word-image pairs of a foreign language. One day later, their memory for the word-image pairs was tested, along with a chord rating session, in which they were required to assess the musical chords in terms of perceived valence, tension, and the extent to which the chords grabbed their attention. We found that musical chords containing dissonant elements were associated with higher memory performance for the word-image pairs compared with consonant chords. Moreover, tension positively mediated the relationship between roughness (a key feature of complexity) and memory, while valence negatively mediated this relationship. The reported findings are discussed in light of the effects that basic musical features have on tension and attention, in turn affecting cognitive processes of associative learning.

Examining Emotion Perception Agreement in Live Music Performance

Current music emotion recognition (MER) systems rely on emotion data averaged across listeners and over time to infer the emotion expressed by a musical piece, often neglecting time- and listener-dependent factors. These limitations can restrict the efficacy of MER systems and cause misjudgements. In a live music concert setting, fifteen audience members annotated perceived emotion in valence-arousal space over time using a mobile application. Analyses of inter-rater reliability yielded widely varying levels of agreement in the perceived emotions. A follow-up lab study to uncover the reasons for such variability was conducted, where twenty-one listeners annotated their perceived emotions through a recording of the original performance and offered open-ended explanations. Thematic analysis reveals many salient features and interpretations that can describe the cognitive processes. Some of the results confirm known findings of music perception and MER studies. Novel findings highlight the importance of less frequently discussed musical attributes, such as musical structure, performer expression, and stage setting, as perceived across different modalities. Musicians are found to attribute emotion change to musical harmony, structure, and performance technique more than non-musicians. We suggest that listener-informed musical features can benefit MER in addressing emotional perception variability by providing reasons for listener similarities and idiosyncrasies.

탄둔의 ‘무협영화 3부작’ 음악의 ‘중서융합’ 요소 연구

Tan Dun, a representative composer of modern Chinese music, has been producing the most notable achievements in the field of Chinese film music by working on “Three Trilogy of Martial Arts” such as “Crouching tiger Hidden Dragon”, “The Heroes” and “The Banquet”. He is famous for his characteristics of actively giving traditional Chinese ideas by exquisitely converging Chinese and Western music elements. These works need to be emphasized in that they can explore strategies to communicate with the international community through Chinese culture. Tandun, who composed three film music, represents consistency in creative style in terms of composition technique, while showing some difference in specific music arrangement depending on the content and form of the film narrative. Therefore, this research focuses on the music theme design of “Crouching tiger Hidden Dragon”, “The Heroes” and “The Banquet”, which are referred to as “Musical Movie Trilogy”, analyzes and compares the film's narrative and music harmony firstly, then discusses how Western music was fused and embodied with the elements of traditional Chinese music.

A Preliminary Analysis of Sang Tong’s Composition: ‘The Vocal Works’

Sang Tong (1923-2011), a well-known composer had made great contributions to the development of Chinese music culture. He combined western traditional and modern harmony techniques with Chinese music theory and musical forms to build a harmony theoretical system with Chinese characteristics. His most representative work, ‘The Theory and Application of Harmoniousness, is widely applied in Chinese professional music teaching and has laid a solid foundation for the development of Chinese music theory. Although he has provided an extensive contribution to the modern Chinese musicology, little research is devoted to understanding his music compositions, especially from the perspective of piano coaching. Hence, this study is designed to provide an analysis of Sang Tong’s eleven compositions of ‘The Vocal Works’ from the piano coaching perspective. This study employed a qualitative research design focusing on the analysis and interpretation of musical contents of eleven works of Sang Tong based on the digital resources in the form of audio and video recordings. The findings revealed that his compositions comprised of varieties of genres and styles ranging from Chinese national-style to ancient and modern poem art songs that include the elements of nature, mountain, labour, nationalism and the ethnic minority's tones. The lyrics used are more connotative and closely integrated with artistic and literary qualities. The piano accompaniment part of Sang Tong's vocal work has rich expressiveness in the prelude, interlude, and end, which are closely related to the theme of the music and vividly set off the artistic conception of the music. He often combine traditional Chinese harmony with western modern music harmony theory in his compositions that set a precedent in the Chinese musicology. The findings of this study anticipated to fill the research gaps regarding the contribution of Sang Tong to modern Chinese music and therefore warrant more studies to investigate different aspects of his compositions as well as promote the development of music culture in the Asian context.