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Interactive Music System Based on Pitch Quantization and Tonal Navigation
Interactive music system based on pitch quantization and tonal navigation Leonardo Aldrey MASTER’S THESIS UPF / 2011 Master in Sound and Music Computing September 3, 2011 Sergi Jordà Puig - Supervisor Department of Information and Communication Technologies Universitat Pompeu Fabra, Barcelona 1 Abstract Recent developments in the field of human computer interaction have led to new ways of making music using digital instruments. The new set of sensors available in devices such as smartphones and touch tablets propose an interesting challenge in the field of music technology regarding how they can be used in a meaningful and musical way. One to one control over parameters such as pitch, timbre and amplitude is no longer required thus making possible to play music at a different level of abstraction. Lerdahl and Jackendoff presented in their publication “Generative theory of tonal music” a perspective that combines Heinrich Schenker’s theory of music and Noam Chomsky linguistics to eXplain how tonal music is organized and structured. This idea opens up the possibility of investigating ways to manipulate a “wider” aspect of music through an assisted interactive musical system that takes into account the “principles” or common knowledge used in music composition and performance. Numerous publications exist in the field of music theory regarding how the tonal aspect of music works. Due to aspects related to psychoacoustics and cultural inheritance, there is a certain common base on how to form and use chords and scales, and how they are organized in terms of hierarchies, movement tendencies and tonal functions. This project deals with the design of a graphical representation about the use of tonality in jazz and popular music, organizing chords and scales in a hierarchical, semanticall and practical way. -
The Geometry of Tonal Space
BRIDGES Mathematical Connections in Art, Mnsic, and Science Hearing With Our Eyes: The Geometry of Tonal Space Julian L. Hook School of Music Penn State University University Park, PA 16802-1901 E-mail: [email protected] There is no intrinsic reason why musical structures should be represented graphically. Music is, after aU, an auditory phenomenon. It consists of vibrations transmitted through the air as sound waves, received by our ears and processed by our brains as acoustic data. Visual aspects of music-the arrangement of musicians on a stage or of notes on a page, the gyrations of the conductor, the shine of the piano-are of secondary importance in our understanding and appreciation of a musical work. Most human beings, however, are visually oriented. We rely on our eyes more than our ears or any of our other sense organs in finding our way around, identifying other people and objects, and learning new information. Because of this dependence on the visual world, most people find abstract concepts easier to grasp if they can somehow be visualized: if some sort of graphical, geometric representation can be devised showing, if only metaphorically, the important elements of the conceptual framework and their relationships with each other. Even if these elements exist in sound and time rather than in light and space, such a representation may help us to get our bearings and to interpret what we hear. Pitches, chords, and key areas are examples of musical elements that lend themselves well to graphical depiction. Many music theorists through the centuries have drawn diagrams showing the appearance of "tonal space" from various perspectives. -
Towards a Perceptually–Grounded Theory of Microtonality: Issues in Sonority, Scale Construction and Auditory Perception and Cognition
Towards a Perceptually–grounded Theory of Microtonality: issues in sonority, scale construction and auditory perception and cognition Brian Bridges Thesis submitted to the National University of Ireland, Maynooth, for the degree of Doctor of Philosophy Volume 1 of 2 Department of Music National University of Ireland, Maynooth October 2012 Head of Department: Prof. Fiona M. Palmer Supervisor: Dr Victor Lazzarini Table of Contents List of Figures 6 Acknowledgements 11 Abstract 14 Relevant Concert Presentations by the Author 15 Chapter 1: Introduction, Aims and Structure, Definitions and a Historical Survey of Tuning and Scale Construction in Western Music 17 1.1 Introduction 17 1.2 Outline of Aims and Thesis Structure 18 1.3 Preliminary Definitions 21 1.3.1 Defining and Delineating Microtonality and Related Terms 21 1.3.2 Defining Pitch as a Psychophysical Attribute 25 1.3.3 Relationships Between Pitches and Concepts of Consonance and Dissonance 27 1.3.4 Models of Relationships Between Stimulus and Cognition 32 1.4 A History of Interval Definition: Music, Measurements and Mathematics 38 1.4.1 Ancient Sources and the Pythagorean Scale 39 1.4.2 Pythagorean and Just Diatonic Scales Compared 42 1.4.3 Generating the Just Diatonic Scale 45 1.4.4 Modulation, Tuning Inconsistencies and Meantone Temperament 46 1.4.5 Enharmonic Distinctions and Proto–microtonal Intervals 53 1.4.6 Towards Equal Temperament 55 1.4.7 Standardisation and Fragmentation in Scale Construction Methodologies 58 1.5 Chapter Summary 59 Chapter 2: Tempered Microtonality and -
Template for Computing in Musicology/H1
4 Out of the Grid and Into the Spiral: Geomet- ric Interpretations of and Comparisons with the Spiral-Array Model Elaine Chew Epstein Department of Industrial and Systems Engineering Hsieh Department of Electrical Engineering Viterbi School of Engineering University of Southern California Los Angeles, CA, USA [email protected] Abstract We present a geometric interpretation of the Spiral-Array model of harmonic rela- tions and compare it Lerdahl’s concept of tonal pitch space and Krumhansl’s spatial representation of pitch relations. The Spiral-Array model is derived from a three- dimensional configuration of the Harmonic Network (Tonnetz). The fundamental idea underlying the model is the representing of higher-level objects in the spiral’s interior as convex combinations of the representations of the lower level components. By using the interior of the spiral, the original discrete space is relaxed to one that is continuous. Geometric mappings are demonstrated among Lerdahl’s tonal pitch space, Krumhansl’s, and Krumhansl and Kessler’s, spatial representations of pitch- class and key relations, and the Spiral-Array model. The interior-point approach is shown to generate higher-level structures that are consistent with the results of these other approaches. The advantages of the interior-point approach are that it facilitates comparisons across different hierarchical levels, and problems that were previously combinatorial in nature can be modeled more efficiently and robustly, mathemati- cally and computationally, using the continuous space in the interior. Tonal Theory for the Digital Age (Computing in Musicology 15, 2007), 51–72. CHEW: OUT OF THE GRID AND INTO THE SPIRAL 51 4.1 Introduction Tonality is the system of relationships that generates a hierarchy among pitches, re- sulting in one pitch being the most stable. -
The Origin and Well-Formedness of Tonal Pitch Structures
The Origin and Well-Formedness of Tonal Pitch Structures Aline Honingh The Origin and Well-Formedness of Tonal Pitch Structures ILLC Dissertation Series DS-2006-05 For further information about ILLC-publications, please contact Institute for Logic, Language and Computation Universiteit van Amsterdam Plantage Muidergracht 24 1018 TV Amsterdam phone: +31-20-525 6051 fax: +31-20-525 5206 e-mail: [email protected] homepage: http://www.illc.uva.nl/ The Origin and Well-Formedness of Tonal Pitch Structures Academisch Proefschrift ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magnificus prof.mr. P.F. van der Heijden ten overstaan van een door het college voor promoties ingestelde commissie, in het openbaar te verdedigen in de Aula der Universiteit op vrijdag 20 oktober 2006, te 12.00 uur door Aline Klazina Honingh geboren te Broek in Waterland Promotores: Prof.dr. R. Bod Prof.dr. H. Barendregt Faculteit der Natuurwetenschappen, Wiskunde en Informatica This research was supported by the Netherlands Organization for Scientific Research (NWO) in the context of the Innovation Impulse programme \Towards a Unifying Model for Linguistic, Musical and Visual Processing". Copyright c 2006 by Aline K. Honingh Printed and bound by PrintPartners Ipskamp. ISBN-10: 90-5776-156-4 ISBN-13: 978-90-5776-156-0 Contents Acknowledgments ix 1 Introduction and musical background 1 1.1 Questions to address in this thesis . 1 1.2 Perception of musical tones . 2 1.2.1 Beats . 3 1.2.2 Critical bandwidth and just noticeable difference . 4 1.2.3 Virtual pitch . -
Music, Space and Performance in Grid Music Systems
The HarmonyGrid: Music, space and performance in Grid Music Systems by Roland Adeney A thesis submitted to the Music and Sound Discipline, Creative Industries Faculty, Queensland University of Technology in partial fulfilment of the requirements for the degree of Doctor of Philosophy 2011 Abstract This research explores music in space, as experienced through performing and music-making with interactive systems. It explores how musical parameters may be presented spatially and displayed visually with a view to their exploration by a musician during performance. Spatial arrangements of musical components, especially pitches and harmonies, have been widely studied in the literature, but the current capabilities of interactive systems allow the improvisational exploration of these musical spaces as part of a performance practice. This research focuses on quantised spatial organisation of musical parameters that can be categorised as grid music systems (GMSs), and interactive music systems based on them. The research explores and surveys existing and historical uses of GMSs, and develops and demonstrates the use of a novel grid music system designed for whole body interaction. Grid music systems provide plotting of spatialised input to construct patterned music on a two-dimensional grid layout. GMSs are navigated to construct a sequence of parametric steps, for example a series of pitches, rhythmic values, a chord sequence, or terraced dynamic steps. While they are conceptually simple when only controlling one musical dimension, grid systems may be layered to enable complex and satisfying musical results. These systems have proved a viable, effective, accessible and engaging means of music-making for the general user as well as the musician. -
Chapter 1: Lerdahl's Model of Tonal Pitch Space
LERDAHL’S SURFACE TENSION RULE: VALIDATION OR MODIFICATION DEBORAH LENORE HENRY A DISSERTATION SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY GRADUATE PROGRAM IN MUSIC YORK UNIVERSITY TORONTO, ONTARIO April 2017 © Deborah Lenore Henry, 2017 ii ABSTRACT Lerdahl’s Tonal Pitch Space (2001) combines music theory with current understanding of music perception and cognition creating of model of tonal pitch space. Lerdahl’s goals include quantification of areas of tension and relaxation perceived by listeners experienced in Western tonal music. Tension is associated with instability, distance, uncommon tones, and weak attractional force; relaxation with stability, proximity, common tones, and strong attractional force. Quantification requires creation of a time-span segmentation derived from the metrical grid and grouping analysis of the score. The time-span segmentation is necessary for creating the time-span reduction. The time-span reduction removes structurally less significant elements from the musical surface through a series of steps not unlike the layers of Schenkerian analysis. The ultimate goal is the prolongational reduction accompanied by prolongational tree. Global tension is quantified by summing values obtained when considering the region in which an event occurs, distance between successive chords revealed by their position on the chordal circle-of-fifths, number of distinct pitch classes between successive chords, tension inherited by subordinate chords from superordinate chords, melodic and harmonic attraction, and surface dissonance. Lerdahl’s Surface Tension Rule assigns tension added values due to chord Inversion, chord note in the top voice (Melody), and nonharmonic chord tones. This study tested the validity of assigned tension added values for Inversion and Melody asking 82 participants familiar with Western tonal music to rate perceived tension of Major and minor four-note chords heard devoid of tonal and musical contexts.