DOCSLIB.ORG

TUE Coding Rules

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
TUE Coding Rules Ein Beitrag zur tonraumbasierten Analyse und Synthese musikalischer Audiosignale Dissertation zur Erlangung des akademischen Grades Doktoringenieur (Dr.-Ing.) vorgelegt der Fakultät für Elektrotechnik und Informationstechnik der Technischen Universität Ilmenau von Dipl.-Ing. Gabriel Gatzsche, geboren am 21.05.1979 in Bad Langensalza von Dipl.-Ing. Markus Mehnert, geboren am 23.01.1976 in Hünfeld Gutachter: Prof. Dr.-Ing. Dr. rer. nat. h.c. Karlheinz Brandenburg Prof. Dr.-Ing. Thomas Sporer Prof. Thomas Krämer vorgelegt am: 25.05.2009 Verteidigung am: 29.04.2011 Verf.-Nr.: EI 240 urn:nbn:de:gbv:ilm1-2011000164 ZUSAMMENFASSUNG Zusammenfassung Das Ziel dieser Arbeit besteht darin, Verbesserungen in der Analyse und Synthese von Audiosig- nalen durch Anwendung von Tonräumen zu erreichen. Im ersten Teil, der die Kapitel 2 bis 6 enthält und von Gabriel Gatzsche verfasst wurde, erfolgt die mathematisch-geometrische Beschreibung der Tonalität auf verschiedenen hierarchischen Ebenen angelehnt an Fred Lerdahls Tonal Pitch Space, David Gatzsches Kadenzkreis und Elaine Chew’s Spiral Array (Berechnung von geometrischen Schwerpunkten in Tonraummodellen). Mit Hilfe zweier Formeln, der Symmetriemodell-Generatorformel und dem SYM-Operator, wird es möglich, die Entstehung der wichtigsten Hauptebenen der abendländischen Tonalität aus einer Quintreihe zu beschreiben, verschiedene, auf eine Tonart bezogene Modelle zu erzeugen und auf den jeweili- gen Symmetrieton zu zentrieren. Damit gelingt es, eine Vielzahl bereits existierender Modelle zu verbinden und in ein einheitliches als Symmetriemodell bezeichnetes Framework zu integrieren. Um auch reale Musiksignale tonraumbasiert analysieren zu können, wird mit dem Summenvektor im kreisförmigen Tonraum ein Feature-Vektor vorgestellt, der wichtige tonale Eigenschaften eines Musiksignals niedrigdimensional repräsentiert. Dazu gehören z.B. funktionstheoretische Eigen- schaften, das Tongeschlecht, Spannungs- und Auflösungsbestreben oder auch harmonische Mehr- deutigkeiten. Weiterhin wird der Tonigkeits-Tonhöhenraum eingeführt, der den unterschiedlichen Oktavlagen von Tonigkeiten geometrische Positionen so zuordnet, dass durch Wahl eines Raum- auschnittes „gut klingende“ Akkorde erzeugt und durch Transformation des Raumausschnittes „günstig“ ineinander übergeblendet werden können. Dies führt zur Entwicklung eines neuartigen Musikinstrumentes, das als HarmonyPad bezeichnet wird. Dieses erlaubt einem Musiker, direkt mit geometrischen Tonräumen zu interagieren und damit Musiksignale zu erzeugen. Markus Mehnert untersucht im zweiten Teil der Arbeit in den Kapiteln 7 bis 12 die Anwend- barkeit des Symmetriemodells auf konkrete Probleme des Music Information Retrieval (MIR). Hier werden sowohl die Tonart- als auch die Akkorderkennung betrachtet. Im Bereich der Tonarterken- nung, die sich derzeit auf die Erkennung von Dur- und Molltonarten beschränkt, wird ein neuer Algorithmus vorgestellt, der auf dem Symmetriemodell basiert. Dieser verbessert den Stand der Technik erheblich. Darüber hinaus wird ein vollkommen neuer Ansatz vorgestellt, der die Tonart- erkennung auf die sechs gebräuchlichsten Kirchentonarten erweitert, da diese besser als die reine Erkennung von Dur und Moll geeignet sind, den Charakter eines Musikstückes widerzuspiegeln. Zusätzlich wird ein neues Bewertungsmaß eingeführt, das den Vergleich mit zukünftigen Verfah- ren ermöglicht. Es wird ein für das MIR neues maschinelles Lernverfahren (HMM/KNN) vorgestellt, das die beiden Verfahren Hidden Markov Models und k Nearest Neighbours verknüpft. Im Bereich der Akkorderkennung werden mit diesem neuen Verfahren bessere Ergebnisse als mit allen vorherge- henden Verfahren erzielt. Dabei zeigt sich auch, dass der Merkmalsvektor des Symmetriemodells in Verbindung mit Akkorderkennung signifikant besser ist als der Chromavektor, der den Stand der Technik repräsentiert. 3 ABSTRACT Abstract The goal of the present work is to improve the analysis and synthesis of musical audio signals by the application of tonal pitch spaces. The first part written by Gabriel Gatzsche consists of the Chapters 2 to 6. It discusses the mathematic-geometrical description of tonality on several hierarchical levels based on Fred Ler- dahl’s Tonal Pitch Space, David Gatzsche’s Cadence Circle and Elaine Chew’s Spiral Array (calcu- lation of geometric centroids within tonal pitch spaces). Using two formulas, the symmetry model generator formula and the SYM operator, it is possible 1.) to describe the emergence of the most important levels of western tonality out of an array of fifths and 2.) to generate several key related models which are centered to the corresponding symmetry tone. With that steps it becomes possi- ble to link several existing pitch spaces into a unified framework called symmetry model. To enable also the analysis of real music signals based on pitch spaces the centroid vector within the circular pitch space is introduced. This feature vector is a low dimensional representation of important tonal properties of musical audio signals. Such properties are functional relationships, the mode, tension and relaxation or harmonic ambiguities. Furthermore the pitch class - pitch height space is introduced. This space assigns geometric positions to different octaves of a given pitch class such that ”well sounding” chords can be created by choosing a simple shaped region of the space. By transforming (rotating, translating, scaling etc.) such a region also well sounding chord transitions are generated. This leads to the development of a new musical instrument, called HarmonyPad. The HarmonyPad allows a musician to create music by interacting with pitch spaces directly. Within the second part of the dissertation consisting of the Chapters 7 to 12 Markus Mehnert investigates the applicability of the symmetry model to concrete problems of music information retrieval (MIR) particularly chord and key recognition. The state of the art in the field of key recogni- tion focuses on the estimation of major and minor keys. Within that work a new symmetry model based algorithm is presented which exceeds the results of current algorithms clearly. Additionally a new approach is proposed which extends key recognition to the estimation of the most often used six church modes. The latter represent the character of a musical piece in a better way then the standard modes ”major” and ”minor” do. Furthermore a new benchmark is introduced which allows the comparison of the current approach with future algorithms. A new machine learning algorithm (HMM/KNN) is proposed. The new algorithm combines the approaches Hidden Markov Models and k Nearest Neighbours. In the field of chord recognition the new approach achieves better results then all of the previous algorithms. It is shown that the symmetry model feature vector leads to significant better chord recognition results then the chroma vector which represents the state of the art. 5 DANKSAGUNG Danksagung Als erstes möchten wir Herrn Prof. Karlheinz Brandenburg als unserem Doktorvater und Betreuer danken. Trotz vielfältiger Aufgaben in der Fraunhofer-Institutsleitung und der Universitätspro- fessur stand Prof. Brandenburg regelmäßig für Gespräche bereit und unterstützte uns mit Rat und Tat. Er gab uns die notwendigen Freiheiten und ein arbeitstechnisch exzellentes Umfeld, das zum Gelingen dieser Arbeit maßgeblich beitrug. Ein großer Dank gilt Herrn Prof. Thomas Krämer. Seine Harmonielehrebücher waren eine hervorragende Grundlage, uns tiefer in die klassische Harmonielehre einzuarbeiten und diese in das Symmetriemodell einzuordnen. Darüber hinaus gab er uns bei persönlichen Treffen wertvolle Hinweise und Anregungen, die wir in die vorlie- gende Arbeit einfließen lassen konnten. Ebenso möchten wir auch Dr. Thomas Sporer danken, der mit seiner Erfahrung und guten Ratschlägen auch dann weiter wusste, wenn der eine oder andere Hör- bzw. Usability-Test nicht ganz nach unseren Wünschen ausfiel. Seine positive Art lädt stets ein, Themen auch mal kontrovers zu diskutieren. Vielen Dank an die Metadaten-Abteilung des Fraunhofer IDMT. Die dort entwickelte Transkription- Toolbox, welche die Grundlage für die Musikverarbeitung (Frontend) beinhaltet, stand uns unein- geschränkt zur Verfügung. Besonders bei Holger Großmann, Christian Dittmar, Matthias Gruhne und Daniel Gärtner möchten wir uns für die gute Zusammenarbeit bedanken. Ein weiterer Dank gilt Herrn Prof. Dr. Eckard Lange von der Hochschule für Musik Franz Liszt, Weimar, dem wir unsere Ideen gerade in der so wichtigen Anfangszeit der Promotion vorstellen konnten. Durch ihn haben wir auch den Kontakt zu Prof. Krämer gefunden. Gemeinsamer Dank gilt allen Studenten, die in Form von Diplomarbeiten, Medienprojekten und Hauptseminaren diese Arbeit unterstützten. Dazu gehören Tina Meyer, Jakob Abeßer, Thomas Mayenfels, Tobias Oeckler, Michael Büttner, Sebastian Schneider, Florian Raschke, Kristin Müller, Antje Storbeck, Arne Taute, Haojin Yang, Christian Stöcklmeier, Sebastian Bube, Jacob Korn, Fabian van de Sand, Daniel Arndt, Ting Zhao, Yawei Wang, Jan Bolz, Benjamin Hudarew, Felix Hirzel, Johannes Post, Michael Stein, Benjamin Schubert und Sascha Grollmich. Persönlicher Dank Gabriel Gatzsche Persönlich großer Dank gebührt meiner direkten Vorgesetzten Frau Dr. Sandra Brix, welche nicht nur mentale Unterstützung durch ihre offene und ermutigende Art bot. Vielmehr ermöglichte und förderte sie durch Entlastung von der täglichen Projektarbeit, durch Finanzierung von wis- senschaftlichen Hilfskräften und Konferenzbesuchen und
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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
    [Show full text]
  • 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.
    [Show full text]
  • 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 .
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]