A Thousand Bells: Acoustical implementation of bell spectra using the finite element method and its compositional realization

Lee, Dongryul

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https://hdl.handle.net/2142/108427 Copy

Description

Title

A Thousand Bells: Acoustical implementation of bell spectra using the finite element method and its compositional realization

Author(s)

Lee, Dongryul

Issue Date

2020-06-23

Director of Research (if dissertation) or Advisor (if thesis)

Taube, Heinrich

Doctoral Committee Chair(s)

Taube, Heinrich

Committee Member(s)

• Armando Duarte, Carlos
• Taylor, Stephen Andrew
• Tharp, Reynold
• Tipei, Sever

Department of Study

Music

Discipline

Music

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

A.Mus.D.

Degree Level

Dissertation

Keyword(s)

• Spectral Music
• Spectralism
• Microtonal Music
• Microtonality
• Just Tuning
• Just Intonation
• Tuning
• Bell
• Bells
• Carillons
• Bell Acoustics
• Bell Optimizagion
• Campanology
• Virtual Bells
• Virtual Instruments
• Virtual Musical Instruments
• Physical Modelling
• FEM
• Finite Element Method
• Acoustics
• Eigenfrequency
• Vibrational Modes
• Modal Theory
• Optimization
• Modal Synthesis
• Sound Synthesis
• Physical Modelling Synthesis
• Jonathan Harvey
• Toshiro Mayuzumi
• Tristan Murail

Abstract

This dissertation focuses primarily on the analysis of acoustical models of bell sounds and the modelling of virtual bell shapes and their spectra using the Finite Element Method (FEM) technique. The first chapter provides a brief introduction of pre and post-spectral music that is inspired by or employs bell sounds from which it derives its central materials. The second chapter introduces bell acoustics and the creation of new spectral profiles of optimal bell tone colors based upon just tuning ratios. In this chapter, I discuss how the concepts of consonance and Just Noticeable Difference in psychoacoustics are applied to use the 96 tone equal temperament tuning system for bell harmonic profiles. The third chapter includes the theoretical basis of the FEM and its application to the isoparametric 2-D quadrilateral elements, which are the fundamental theories of how bell harmonies are mathematically calculated. This includes the central concepts of the FEM, such as the Principle of Virtual Work/Displacement, master to global coordinate transformation, FE shape functions, usages of Jacobian matrices, numerical integration of the stiffness matrix and the equivalent nodal force vector for the element by using the Gauss-Lagrange quadrature. In the fourth chapter, I create bell model geometry by using 2D bell nominal curve and adjustable design variables. Physical parameters, such as the Poisson ratio, Young’s modulus, and material properties are also adopted from previous bell design research. Based upon the aforementioned prototypes, I create 24 different 3-D bell geometries, and analyze the spectra of these virtual bells. These bell models are analyzed, optimized and tuned to create tone colors that are defined in Chapter 2. After a validating process of the bell model, the general backgrounds of optimization theory are also introduced and analyzed for the purpose of creating 3-D virtual bells. For a general background of campanology, I use André Lehr’s Campanology textbook to provide the brief history, types, mechanism, casting, forms and parts, and tones of different bells. For acoustical and computational realizations of virtual bells, the analysis focuses on the research of Albertus Johannes Gerardus Schoofs and his follower PJM Roozen-Kroon on the FEM bell optimization, upon which the first prototype of the major-third bell was designed and cast.

Graduation Semester

2020-08

Type of Resource

Thesis

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Copyright 2020 Dongryul Lee

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