Singing-Blocks: Considerations for a Virtual Reality Game to create chords and progressions

Harmony and Chord progressions are the foundational architecture of a number of genres of Western music, from Classical, to Jazz, to popular music. For any musician, mastering the rules can be an important step in learning the skills of composition. The rules are difficult to learn, however. There have been efforts to create innovative educational software displays but to date Virtual Reality (VR) systems have not been investigated. The innately physical nature of VR creates an immersive experience that is impossible with other approaches. This work explains our concept of a VR educational game for young adult learners upwards of certain Western music genres. It draws subtle analogies to the architecture of harmony by presenting a number of levels in which the user builds chords and progressions. The aim is that they journey towards interacting creatively with the harmonics representation. Suggestions are also given as to how an effective evaluation procedure may be carried out in the future

Singing-Blocks: Considerations for a Virtual Reality Game to create chords and progressions

Harmony and Chord progressions are the foundational architecture of a number of genres of Western music, from Classical, to Jazz, to popular music. For any musician, mastering the rules can be an important step in learning the skills of composition. The rules are difficult to learn, however. There have been efforts to create innovative educational software displays but to date Virtual Reality (VR) systems have not been investigated. The innately physical nature of VR creates an immersive experience that is impossible with other approaches. This work explains our concept of a VR educational game for young adult learners upwards of certain Western music genres. It draws subtle analogies to the architecture of harmony by presenting a number of levels in which the user builds chords and progressions. The aim is that they journey towards interacting creatively with the harmonics representation. Suggestions are also given as to how an effective evaluation procedure may be carried out in the future

Visualization of low dimensional structure in tonal pitch space

In his 2001 monograph Tonal Pitch Space, Fred Lerdahl defined a distance function over tonal and post-tonal harmonies distilled from years of research on music cognition. Although this work references the toroidal structure commonly associated with harmonic space, it stops short of presenting an explicit embedding of this torus. It is possible to use statistical techniques to recreate such an embedding from the distance function, yielding a more complex structure than the standard toroidal model has heretofore assumed. Nonlinear techniques can reduce the dimensionality of this structure and be tuned to emphasize global or local anatomy. The resulting manifolds highlight the relationships inherent in the tonal system and offer a basis for future work in machine-assisted analysis and music theory. 1

Applications de la théorie des graphes à des objets musicaux : modélisations, visualisations en hyperespace

At the frontier between music and mathematics, this study presents an original geometrical musical space used for musical analysis and pedagogy.Using different schemes, mathematicians and music theorists have demonstrated that the tempered twelve tones pitch space can be considered as a combination of minor and major thirds. We use the Cartesian product of two circular graphs C3□C4 to build the Planet graph that matches this concept. Since the decomposition involves two sets and each pitch class being a unique combination of these two sub-groups, we use a graph coloration based on complex numbers and introduce the concept of bi-dimensional ideograms. We perform a spectral analysis of the Planet graph to determine its Eigen spaces and obtain geometrical coordinates. The resulting model, called Planet-4D, grants each symbol and equivalent physical position, and involves more symmetries than any discrete 3D model. From there, we build a four dimensional chordal space where perfect chords lie on a hypersphere. We finally extend this concept to display any set of pitches in an atonal context. In the second section we construct the graphs of some existing musical objects such as keyboards, tone networks (Tonnetze), chordal spaces or modulation schemes. We apply spectral projections to visualize the symmetries that are inherent to these objects. This work concludes with musical studies of tonal and atonal pieces, performed with the help of the visualization tolls designed in this study.A la frontière entre musique et mathématiques, cette étude présente un espace musical géométrique original utilisé pour l'analyse et la pédagogie.En utilisant différentes méthodes, les mathématiciens et théoriciens de la musique ont démontré que notre espace des hauteurs tempéré à douze notes peut être considéré comme une combinaison de tierces mineurs et majeures. Nous utilisons le produit cartésien de deux graphes circulaires C3□C4 pour construire le graphe Planet qui répond à ce concept. Comme la décomposition implique deux ensembles et que chaque classe de hauteur est la combinaison unique de ces deux sous-groupes, nous utilisons une coloration en termes de graphes par des nombres complexes et introduisons le concept d'idéogrammes à deux dimensions. Nous effectuons une analyse spectrale du graphe Planet pour déterminer ses espaces propres et obtenir des coordonnées géométriques. Le modèle qui en résulte est appelé Planet-4D, il offre à chaque symbole une position physiquement équivalente. Il comporte plus de symétries que tout modèle discret 3D. A partir de ce modèle, nous construisons une représentation en quatre dimensions où les accords parfaits se trouvent en surface d'une hypersphère. Nous étendons enfin le concept principal pour afficher n'importe quel agrégat de notes sur l'hypersphère dans un cadre atonal. Dans une seconde partie, nous modélisons sous forme de graphes des objets musicaux existants : claviers, réseaux de notes (Tonnetze) ou d'accords ainsi que des schémas de modulation. Nous appliquons des projections spectrales afin de visualiser les symétries inhérentes à ces objets et terminons par des études d'œuvres tonales et atonales, effectuées avec le système de visualisation inventé