Harmonic Progressions Research Articles

Laser harmonic generation with independent control of frequency and orbital angular momentum

The non-linear optical process of laser harmonic generation (HG) enables the creation of high quality pulses of UV or even X-ray radiation, which have many potential uses at the frontiers of experimental science, ranging from lensless microscopy to ultrafast metrology and chiral science. Although many of the promising applications are enabled by generating harmonic modes with orbital angular momentum (OAM), independent control of the harmonic frequency and OAM level remains elusive. Here we show, through a theoretical approach, validated with 3D simulations, how unique 2-D harmonic progressions can be obtained, with both frequency and OAM level tuned independently, from tailored structured targets in both reflective and transmissive configurations. Through preferential selection of a subset of harmonic modes with a specific OAM value, a controlled frequency comb of circularly polarised harmonics can be produced. Our approach to describe HG, which simplifies both the theoretical predictions and the analysis of the harmonic spectrum, is directly applicable across the full range of HG mechanisms and can be readily applied to investigations of OAM harmonics in other processes, such as OAM cascades in Raman amplification, or the analysis of harmonic progressions in nonlinear optics.

Musical Factors Influencing the Perceptual and Cognitive Reality of Schenkerian Hierarchic Structure in Music: A Qualitative Case Study

The Schenkerian hierarchical structure, a fundamental concept in Schenkerian theory, offers a systematic approach to analyzing the underlying organization of tonal music. However, the extent to which listeners perceive and cognitively process these hierarchical structures remains an area of inquiry. This study investigates the influence of various musical factors on the perception and cognition of Schenkerian hierarchical structures. Through a qualitative research approach involving undergraduate music students, the research explores how elements such as harmony, structural position, linear progression, rhythm, meter, and intensified tones shape listeners' understanding of musical hierarchy. The findings highlight the predominant role of harmony, aligning with Schenkerian theory's emphasis on harmonic progression. Additionally, the study underscores the subjective nature of linear progression interpretation, influenced by individual musical backgrounds and training. The results suggest the need for a more comprehensive Schenkerian analysis framework that incorporates rhythm and intensified tones, as these factors were generally ranked lower in importance by participants. Despite limitations in sample size and experimental scope, this study provides a nuanced understanding of how listeners process and comprehend hierarchical structures in music.

Encoding Emotion

The paper Encoding Emotion details an experiment conducted on early 18th-century French recitative to determine how composers relate harmony to sung text, if at all. Although the existence of a relationship between harmony and vocal expression is generally agreed upon, it is rarely properly taught to baroque singers, even though harmony is fundamental to the concept of basso continuo. It is also rarely discussed in continuo or singing treatises, either historical or modern, and, if so, never explicitly. The present experiment aims to fill that gap by examining harmony and text in actual written music. To do so, a harmonic analysis was performed on excerpts of secco recitative from French operas and cantatas written by Campra, Clérambault, Jacquet de la Guerre, and Rameau; the significant chords and harmonic passages were then logged in a spreadsheet with their corresponding text. Over two hundred lines of results were then analysed to determine whether patterns could be found associating certain words to chords or harmonic progressions. In the end, the dataset was too small for any general conclusions to be made with certainty, but patterns still emerged. Most notably, the plagal cadence correlated to feelings of love and tenderness, particularly in a sacred or noble context. It was also noted that, though general patterns could not always be identified, some chords or harmonic progressions appeared to have specific meaning for a certain composer. The V of IV, for example, was strongly associated with pleasure in Clérambault's works. Although there is only limited use for these results outside of this study, the identified patterns show that a more extensive dataset would yield enlightening results and give singers access to a remarkably rich tool with which to inform their interpretation.

Segmenting and Predicting Musical Phrase Structure Exploits Neural Gain Modulation and Phase Precession.

Music, like spoken language, is often characterized by hierarchically organized structure. Previous experiments have shown neural tracking of notes and beats, but little work touches on the more abstract question: how does the brain establish high-level musical structures in real time? We presented Bach chorales to participants (20 females and 9 males) undergoing electroencephalogram (EEG) recording to investigate how the brain tracks musical phrases. We removed the main temporal cues to phrasal structures, so that listeners could only rely on harmonic information to parse a continuous musical stream. Phrasal structures were disrupted by locally or globally reversing the harmonic progression, so that our observations on the original music could be controlled and compared. We first replicated the findings on neural tracking of musical notes and beats, substantiating the positive correlation between musical training and neural tracking. Critically, we discovered a neural signature in the frequency range ∼0.1 Hz (modulations of EEG power) that reliably tracks musical phrasal structure. Next, we developed an approach to quantify the phrasal phase precession of the EEG power, revealing that phrase tracking is indeed an operation of active segmentation involving predictive processes. We demonstrate that the brain establishes complex musical structures online over long timescales (>5 s) and actively segments continuous music streams in a manner comparable to language processing. These two neural signatures, phrase tracking and phrasal phase precession, provide new conceptual and technical tools to study the processes underpinning high-level structure building using noninvasive recording techniques.

Triangles with arithmetic, geometric and harmonic progressions

This article explores the fascinating world of triangles with angle and side sequences in arithmetic, geometric and harmonic progressions. The properties and relationships between these progressions and the corresponding triangle parameters are investigated. The main focus is on proving a series of theorems that provide insights into the conditions under which triangles exhibit these progressions. The proofs are presented with meticulous attention to detail, offering a deep understanding of the results. The presented findings contribute to the field of mathematical education by providing rich material for classroom activities and discussions.

Composing jazz music pieces using LSTM neural networks approach

The domain of artificial intelligence has increasingly extended into the creative arts, aiming to emulate and augment human creativity with automated processes. This is particularly evident in the field of music, where AI's ability to learn and produce intricate compositions has attracted significant attention. This study explores the challenge of generating jazz music using artificial intelligence, specifically focusing on the application of Long Short-Term Memory (LSTM) neural networks for jazz composition. By optimizing the model to address the genre's complexity, the research demonstrates the LSTM's capacity to capture and reproduce jazz's essential harmonic progressions and rhythmic nuances. Quantitative analyses show high accuracy and a deep understanding of musical structures, whereas qualitative feedback confirms the model's efficacy in producing compositions that embody jazz's spontaneity. Despite its achievements, the model's tendency to generate repetitive sequences suggests areas for improvement. This paper advances the field of AI in music, illustrating the potential of LSTM networks to mimic complex musical genres and emphasizing the necessity of ongoing model refinement to foster creativity. It highlights the evolving role of machine learning in music generation, proposing a foundation for future work aimed at diminishing the gap between AI capabilities and artistic expression.

Exploring the neural underpinnings of chord prediction uncertainty: an electroencephalography (EEG) study

Predictive processing in the brain, involving interaction between interoceptive (bodily signal) and exteroceptive (sensory) processing, is essential for understanding music as it encompasses musical temporality dynamics and affective responses. This study explores the relationship between neural correlates and subjective certainty of chord prediction, focusing on the alignment between predicted and actual chord progressions in both musically appropriate chord sequences and random chord sequences. Participants were asked to predict the final chord in sequences while their brain activity was measured using electroencephalography (EEG). We found that the stimulus preceding negativity (SPN), an EEG component associated with predictive processing of sensory stimuli, was larger for non-harmonic chord sequences than for harmonic chord progressions. Additionally, the heartbeat evoked potential (HEP), an EEG component related to interoceptive processing, was larger for random chord sequences and correlated with prediction certainty ratings. HEP also correlated with the N5 component, found while listening to the final chord. Our findings suggest that HEP more directly reflects the subjective prediction certainty than SPN. These findings offer new insights into the neural mechanisms underlying music perception and prediction, emphasizing the importance of considering auditory prediction certainty when examining the neural basis of music cognition.

Approximation of Sum of Harmonic Progression

Approximation of Sum of Harmonic Progression

빌 에반스(Bill Evans)의 “We Will Meet Again” 솔로 피아노에 나타난 아포지아투라와 폴리코드에 관한 연구

This study analyzes the most prominent manifestations of harmonic expansion and tension in Bill Evans’ harmonic techniques, focusing on appoggiatura and polychords. These two techniques represent Evans’ characteristic harmonic progressions that dramatically induce and resolve tension. While Evans employs numerous other idiosyncratic harmonic techniques, these two serve as cornerstones of all Jazz harmonic development, rooted in his assimilation of classical music into Jazz piano. Appoggiatura elucidates Evans’ method of inducing harmonic tension and resolution through the polyphonic use of non-harmonic tones. Polychord is dissected into two categories: one comprising diatonic scales and the other involving altered scales. The study explores how Evans employed diverse Polychords based on harmonic tension and the flow of the musical piece. Through the analysis of Bill Evans’ solo piano composition “We Will Meet Again”, this research examines how harmonic expansion unfolds in compositional music and elucidates how Evans employed these techniques in his performances to actualize and crystallize his unique harmonies.

A study on Bernard Herrmann’s science fiction film music

The early sound film and “classical-style” Hollywood film periods were important representatives in the history of Hollywood films, producing many classic films as well as many famous film music composers. Among them, Bernard Herrmann was a unique and distinctive representative with his own personal compositional style, and was also the representative composer for thriller, horror, mystery and science fiction films during this period. When analyzing film music, especially Bernard Herrmann’s works, using tonal music analysis, many harmonic progressions cannot be accurately expressed. Harmonic function analysis emphasizes the principles of tonality, while neo-Riemannian theory breaks away from the framework of tonality and harmonic functions, emphasizing the spatial progression between chords. For Bernard Herrmann’s music, using neo-Riemannian theory can reasonably analyze the characteristics and patterns of musical progression, and explain many chord progressions that harmonic functions cannot. One of the films that can be given as an example of this situation is The Day the Earth Stood Still (1951). The Day the Earth Stood Still is a Hollywood science fiction film made in 1951. This work played an important role in the development of later science fiction films. Bernard Herrmann chose to abandon the traditional orchestral instrumentation and used a specific instrumental ensemble to form Herrmann’s unique science fiction film music space. Transformational analysis shows that the music uses modes, hexatonic scales and octatonic scales to form melodies and harmonies with ambiguous characteristics, and the use of these modes and scales also provides important color elements for film music of specific styles. Neo-Riemannian theory has been around for less than 50 years. As an emerging music theory system, it is not yet mature and complete, and is still expanding and improving. However, as an analysis tool for nonfunctional tonal film music, it can provide a brand new perspective. This researcher also believes that neo-Riemannian theory can provide theoretical basis for analyzing various styles of film music as an analytical tool.

BELA BARTÓK’S POLYMODAL CHROMATICISM IN CHICK COREA’S CHILDREN SONG NO.5 AND NO.15

This study focuses on the application of Bela Bartók’s theory of polymodal chromaticism in Chick Corea’s selected piano pieces from Children’s Songs, 1984. The selected pieces of Children Song No.5 and No.15 provide examples of the application of Bela Bartók’s theory of polymodal chromaticism as a compositional device in jazz music. Despite the significance of these pieces, there exists a scarcity of musical analyses examining the use of polymodal chromaticism, indicating a need for further research in this area. This study reveals the compositional method, style, and tool that Corea uses in applying the theory of polymodal chromaticism. Integration of polymodal chromaticism with functional harmonic progression and unique combinations of modal and compound scales that Corea employs to achieve polymodal chromaticism is revealed in this study. Qualitative method of music analysis and quasi-`Schenkerian music analysis were applied to highlight modal and compound scales, ostinatos, harmonic progression, and compositional techniques Corea used in developing polymodal chromaticism in the selected pieces. The study led to detailed insights into the compositional techniques used to achieve polymodal chromaticism, as well as the discovery of unique compound scales and combinations of scales that led to chromaticism. The methods of applying polymodal chromaticism are detailed in this study, allowing further exploration of the theory in other areas of jazz and contemporary music.

Embedded Dissonance in Eighteenth- and Nineteenth-Century Harmonic Theory and Practice

Seeking to elucidate aspects of harmonic practice that originated in contrapuntal patterns, this article traces a specific set of voice-leading configurations in which the generative roles of dissonance, counterpoint, and harmonic progression are blurred. These configurations, originating in early eighteenth-century practice, feature upper-voice suspensions, which are notable for their interlocking qualities and for their compatibility with an extended range of thoroughbass patterns and bass motions (Harrison 2003). Segments of such patterns were partially assimilated into later compositional practice and appeared in treatises on fundamental-bass and scale-step systems of harmony, but these configurations revealed a degree of friction between counterpoint-based idioms and the emerging harmonic theories attempting to explain them according to singular principles. The continued appearance of these configurations in subsequent compositional practice raises the question of what aspects of dissonance and counterpoint have been both embedded in harmonic practice and increasingly subordinated to chord structure in the harmonic theories that stretch from Rameau to Schenker. This dialectical engagement between historical theory and compositional practice offers a critique of our inherited harmonic theories, exposing competing conceptions of dissonance and discrepancies over its autonomy relative to harmonic principles. Tracing this history also reveals that the essential connections among rhythm/meter, dissonance treatment, and harmonic progression that are clearly present in eighteenth-century practice—Kirnberger’s “rhythmic harmony” (Aldrich 1970)—become increasingly subordinated to harmonic principles in nineteenth-century theory. The historical path of embedded dissonance appears to exemplify Adorno’s notion of sedimentation, which offers several interesting disciplinary and aesthetic conclusions about harmonic theory.

Simulating Chromatic Harmony in Romantic Era Music using Diophantine Approximation

The Romantic period of music is known for its intricate and emotionally expressive harmonic style. Nevertheless, recreating authentic melodies of the Romantic period in contemporary compositions poses a considerable challenge for composers and musicians. In this paper, we present a method for simulating chromatic harmony in Romantic Era music through the use of Diophantine Approximation. Inspired by the works of renowned composers of that period, such as Richard Wagner, Franz, Liszt, and Frederic Chopin, my transitional model was constructed to preserve the essence of the preceding melody as the harmonic progression unfolds. The model helps with the creation of harmonic progressions that contain the nuances of the preceding harmonic structure and musical style, providing composers with a novel way to explore a wide range of musical possibilities. Experimental validation involving human hearing shows that the model is successful in imitating authentic Romantic-era harmonic structures. This finding suggests that the model is a promising tool that could inspire contemporary composers to create almost authentic chromatic harmonic progressions.

Lutosławski's Mid-Century Harmony

Abstract This article proposes to expand our understanding of Witold Lutosławski's chordal space and its relation to formal processes. It argues that the traditional analytical focus on harmonic colors of isolated chords comes at the expense of understanding how chordal interactions shape form. How do individual chords participate in cogent, expressive, and sensuous long-range harmonic processes? The article explores how the arrangement of intervals in twelve-tone chords (especially the ordering, restriction, and modularity of intervals) not only imprint distinct coloristic qualities to single chordal entities but are also implicated in strategies of harmonic progression, relatedness, complementarity, and contrast. These analytical goals prompt a reconceptualization of chordal elements, which are understood as combinations of pitch class and modal quality rather than simply as pitches in register. The analytical focus is on Lutosławski's harmony of the mid- to late fifties, attending in particular to the Five Iłłakowicz Songs, the composer's inaugural effort in the use of vertical aggregates. Lutosławski's chordal space in these pieces is interpreted through a series of cyclic graphs and transpositional networks, prompting a novel understanding between twelve-tone chordal harmony and form. The study proposes to contribute to the analytical reappraisal of a set of pieces that anchor an influential harmonic practice in twentieth- and twenty-first-century music.

Semiotic Dimension Deconstruction in the First Movement of "Spring" by Vivaldi

Music is a means of expressing feelings and aesthetics in the human mind and heart. Through increasing human creativity, this media for expression comes in many types, one of which is program music, whose compositional construction is based on the composer's imagination to describe a character, atmosphere, or an event. Allegro of “Concerto No. 1 in E major, Op. 8, RV 269: Spring (La primavera)”, as the first movement of the program music The Four Seasons from Vivaldi, is famous for depicting the atmosphere of spring filled with birdsong, the wind blowing, to the sound of the river flowing. Therefore, this study intents to thoroughly examine those representations of this atmosphere through the deconstruction of the semiotic dimension. As an inductive qualitative research, Peirce's semiotic theory and the descriptive analysis data method are applied. Based on Peirce's semiotic theory, the description of the spring atmosphere is present in interpretant through the imitation of bird sounds, river flow, and storms; harmonic progressions, melodic motifs, musical technique ornaments, and collective structures in objects; as well as sonnets in representamen. Thus, it can be summarized that the illustration of the atmosphere in the title and sonnet is closely related to the music notation, meaning they are inseparable. In the past few years, an akin exploration that focuses on Vivaldi's works through the semiotic perspective was absent; hence, this study plays a huge part in its research contribution to the field of knowledge.

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.

Hyperparameters optimization of convolutional neural network based on local autonomous competition harmony search algorithm

Abstract Because of the good performance of convolutional neural network (CNN), it has been extensively used in many fields, such as image, speech, text, etc. However, it is easily affected by hyperparameters. How to effectively configure hyperparameters at a reasonable time to improve the performance of CNNs has always been a complex problem. To solve this problem, this paper proposes a method to automatically optimize CNN hyperparameters based on the local autonomous competitive harmony search (LACHS) algorithm. To avoid the influence of complicated parameter adjustment of LACHS algorithm on its performance, a parameter dynamic adjustment strategy is adopted, which makes the pitch adjustment probability PAR and step factor BW dynamically adjust according to the actual situation. To strengthen the fine search of neighborhood space and reduce the possibility of falling into local optima for a long time, an autonomous decision-making search strategy based on the optimal state is designed. To help the algorithm jump out of the local fitting situation, this paper proposes a local competition mechanism to make the new sound competes with the worst harmonic progression of local selection. In addition, an evaluation function is proposed, which integrates the training times and recognition accuracy. To achieve the purpose of saving the calculation cost without affecting the search result, it makes the training time for each model depending on the learning rate and batch size. In order to prove the feasibility of LACHS algorithm in configuring CNN superparameters, the classification of the Fashion-MNIST dataset and CIFAR10 dataset is tested. The comparison is made between CNN based on empirical configuration and CNN based on classical algorithms to optimize hyperparameters automatically. The results show that the performance of CNN based on the LACHS algorithm has been improved effectively, so this algorithm has certain advantages in hyperparametric optimization. In addition, this paper applies the LACHS algorithm to expression recognition. Experiments show that the performance of CNN optimized based on the LACHS algorithm is better than that of the same type of artificially designed CNN. Therefore, the method proposed in this paper is feasible in practical application.

Mandatory Metal Moments

Through a series of case studies, this article presents a framework of common musical tropes originally only found in heavy metal music. The use of aggressive “double-kick” drum grooves, galloping bass lines, harmonized melodies, and overall fast tempi are all common elements of many styles of metal that first emerged in the 1980s. Video games developed alongside this musical genre; action, platforming, and role-playing games not only embraced these distinguishing characteristics of metal music, but these tropes are now expected in games of various genres. In addition, other extra-musical topics associated with heavy metal’s lyrical themes—such as references to the occult and fantasy—are common archetypes used to build the worlds of these video games. Studies have been conducted that examine the cultural similarities between these two cultures, the relationship of music genre with game genre and function, and the use of rock paired with sacred music specifically in battle themes. By analyzing the arrangements, treatment of melodic contours, rhythmic gestures, and harmonic progressions of these games, this article discusses and demonstrates how metal has disseminated into video game culture. There are strong connections between the fast-paced obstacles in Mega Man with the speed of Iron Maiden, the gothic horror stages of Castlevania and Baroque elegance of Yngwie Malmsteen, and how the themes from fantasy literature made their way into video game design and power metal. The worlds of these games are built on their music, but their music is built on a fusion of tropes used in heavy metal culture.

An Eightfold Taxonomy of Harmonic Progressions, and Its Application to Triads Related by Major Third and Their Significance in Recent Screen Music

Abstract A hybridization of two recent innovations in music theory—a focus on the progression of two triads as a unitary analytical object, and a component-wise formation of a set of equivalence classes—brings together under one conceptual and labeling system eight different approaches to the classification of harmonic progression. A holistic adoption of these eight approaches, each already preexisting within music scholarship in some partial or complete form, affords precise and gradated statements regarding the styles, associative meanings, and hermeneutics of music for recent multimedia. To that end, this article pays particular attention to progressions of like-moded triads a major third apart, as demonstrated through analyses of music for the television series Bridgerton and the movie Ex Machina.

Easing Into Jazz Improvisation With the Blues

Although there is a consensus that it is important to teach jazz and the skill of improvisation inherent within it, many feel unprepared to do so. This article presents a simple way for beginners to improvise through the blues scale and harmonic progression at any present skill level in kindergarten through high school general music coursework. This practical method addresses the Creating pillar of the 2014 Music Standards while enhancing students’ and instructors’ musical skills and leadership skills, and presenting an avenue for live performance. Teachers and students alike can feel empowered to learn jazz improvisation with the “correct notes” provided through these friendly steps that I have been using in my own teaching for over 15 years.