The missing fundamentals of harmonic theory: Chord roots and their ambiguity in arrangements of jazz standards

Since Lippius and Rameau, chords have roots that are often voiced in the bass, doubled, and used as labels. Psychological experiments and analyses of databases of Western classical music have not produced clear evidence for the psychological reality of chord roots. We analyzed a symbolic database of 100 arrangements of jazz standards (musical instrument digital interface [MIDI] files from midkar.com and thejazzpage.de ). Selection criteria were representativeness and quality.The original songs had been composed in the 1930s and 1950s, and each file had a beat track. Files were converted to chord progressions by identifying tone onsets near beat locations (±10% of beat duration). Chords were classified as triads (major, minor, diminished, suspended) or seventh chords (major–minor, minor, major, half-diminished, diminished, and suspended) plus extra tones. Roots that were theoretically less ambiguous were more often in the bass or (to a lesser extent) doubled. The root of the minor triad was ambiguous, as predicted (conventional root or third). Of the sevenths, the major–minor had the clearest root. The diminished triad was often part of a major–minor seventh chord; the half-diminished seventh, of a dominant ninth. Added notes (“tensions”) tended to minimize dissonance (roughness or inharmonicity). In arrangements of songs from the 1950s, diminished triads and sevenths were less common, and suspended triads more common, relative to the 1930s. Results confirm the psychological reality of chord roots and their specific ambiguities. Results are consistent with Terhardt’s virtual pitch theory and the idea that musical chords emerge gradually from cultural and historic processes. The approach can enrich music theory (including pitch-class set analysis) and jazz pedagogy.

Symmetry, Combinatorics, Artificial Intelligence, Music and Spectroscopy

Symmetry forms the foundation of combinatorial theories and algorithms of enumeration such as Möbius inversion, Euler totient functions, and the celebrated Pólya’s theory of enumeration under the symmetric group action. As machine learning and artificial intelligence techniques play increasingly important roles in the machine perception of music to image processing that are central to many disciplines, combinatorics, graph theory, and symmetry act as powerful bridges to the developments of algorithms for such varied applications. In this review, we bring together the confluence of music theory and spectroscopy as two primary disciplines to outline several interconnections of combinatorial and symmetry techniques in the development of algorithms for machine generation of musical patterns of the east and west and a variety of spectroscopic signatures of molecules. Combinatorial techniques in conjunction with group theory can be harnessed to generate the musical scales, intensity patterns in ESR spectra, multiple quantum NMR spectra, nuclear spin statistics of both fermions and bosons, colorings of hyperplanes of hypercubes, enumeration of chiral isomers, and vibrational modes of complex systems including supergiant fullerenes, as exemplified by our work on the golden fullerene C150,000. Combinatorial techniques are shown to yield algorithms for the enumeration and construction of musical chords and scales called ragas in music theory, as we exemplify by the machine construction of ragas and machine perception of musical patterns. We also outline the applications of Hadamard matrices and magic squares in the development of algorithms for the generation of balanced-pitch chords. Machine perception of musical, spectroscopic, and symmetry patterns are considered.

Creativity in Generative Musical Networks: Evidence From Two Case Studies

Deep learning, one of the fastest-growing branches of artificial intelligence, has become one of the most relevant research and development areas of the last years, especially since 2012, when a neural network surpassed the most advanced image classification techniques of the time. This spectacular development has not been alien to the world of the arts, as recent advances in generative networks have made possible the artificial creation of high-quality content such as images, movies or music. We believe that these novel generative models propose a great challenge to our current understanding of computational creativity. If a robot can now create music that an expert cannot distinguish from music composed by a human, or create novel musical entities that were not known at training time, or exhibit conceptual leaps, does it mean that the machine is then creative? We believe that the emergence of these generative models clearly signals that much more research needs to be done in this area. We would like to contribute to this debate with two case studies of our own: TimbreNet, a variational auto-encoder network trained to generate audio-based musical chords, and StyleGAN Pianorolls, a generative adversarial network capable of creating short musical excerpts, despite the fact that it was trained with images and not musical data. We discuss and assess these generative models in terms of their creativity and we show that they are in practice capable of learning musical concepts that are not obvious based on the training data, and we hypothesize that these deep models, based on our current understanding of creativity in robots and machines, can be considered, in fact, creative.

The Resolution of Musical Chords: A Physical Paradigm

In any form of music, the fundamental aspect which gives the most of an essence is the tune of the composition. An integral concept in orchestral music is chords. Chords usually follow the notes of the song, making it harmonious with the overall progression of the performance. Chords are often interchangeable within the scale of the song. The mellifluous effect of chords and the harmony it portrays are self-explanatory and pleasant. There lies a mathematical and physical reason behind the working of these chords and the movement shown by them during the piece. In this study, we look at the fundamental tonal frequencies associated with the notes of the chords and analyze the patterns exhibited and draw meaningful conclusions corroborating the scientific relationship with music and its play, while proposing a new musical phenomenon called ‘tonal inertia’ that seems to potentially explain the musical conventions using physical bases.

The Resolution of Musical Chords: A Physical Paradigm

In any form of music, the fundamental aspect which gives the most of an essence is the tune of the composition. An integral concept in orchestral music is chords. Chords usually follow the notes of the song, making it harmonious with the overall progression of the performance. Chords are often interchangeable within the scale of the song. The mellifluous effect of chords and the harmony it portrays are self-explanatory and pleasant. There lies a mathematical and physical reason behind the working of these chords and the movement shown by them during the piece. In this study, we look at the fundamental tonal frequencies associated with the notes of the chords and analyze the patterns exhibited and draw meaningful conclusions corroborating the scientific relationship with music and its play, while proposing a new musical phenomenon called ‘tonal inertia’ that seems to potentially explain the musical conventions using physical bases.

A Deep Learning Approach for Generating Pleasant Music

Advancement in deep neural networks have made it possible to compose music that mimics music composition by humans. The capacity of deep learning architectures in learning musical style from arbitrary musical corpora have been explored in this paper. The paper proposes a method for generated from the estimated distribution. Musical chords have been extracted for various instruments to train a sequential model to generate the polyphonic music on some selected instruments. We demonstrate a simple method comprising a sequential LSTM models to generate polyphonic music. The results of the model evaluation show that generated music is pleasant to hear and is similar to music played by humans. This has great application in entertainment industry which enables music composers to generate variety of creative music.

Making the Unfamiliar Familiar: The Effect of Exposure on Ratings of Unfamiliar Musical Chords

Affective responses to music have been shown to be influenced by the psychoacoustic features of the acoustic signal, learned associations between musical features and emotions, and familiarity with a musical system through exposure. The present article reports two experiments investigating whether short-term exposure has an effect on valence and consonance ratings of unfamiliar musical chords from the Bohlen-Pierce system, which are not based on a traditional Western musical scale. In a pre- and post-test design, exposure to positive, negative and neutral chord types was manipulated to test for an effect of exposure on liking. In this paradigm, short-term (“mere”) exposure to unfamiliar chords produced an increase only in valence ratings for negative chords. In neither experiment did it produce an increase in valence or pleasantness ratings for other chord types. Contrast effects for some chord types were found in both experiments, suggesting that a chord’s affect (i.e., affective response to the chord) might be emphasised when the chord is preceded by a stimulus with a contrasting affect. The results confirmed those of a previous study showing that psychoacoustic features play an important role in the perception of music. The findings are discussed in light of their psychological and musical implications.