University of New Orleans ScholarWorks@UNO University of New Orleans Theses and Dissertations Dissertations and Theses 8-5-2004 Byzantine Music Intervals: An Experimental Signal Processing Approach Kyriakos Michael Tsiappoutas University of New Orleans, [email protected] Follow this and additional works at: https://scholarworks.uno.edu/td Recommended Citation Tsiappoutas, Kyriakos Michael, "Byzantine Music Intervals: An Experimental Signal Processing Approach" (2004). University of New Orleans Theses and Dissertations. 470. https://scholarworks.uno.edu/td/470 This Thesis is protected by copyright and/or related rights. It has been brought to you by ScholarWorks@UNO with permission from the rights-holder(s). You are free to use this Thesis in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights- holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/or on the work itself. This Thesis has been accepted for inclusion in University of New Orleans Theses and Dissertations by an authorized administrator of ScholarWorks@UNO. For more information, please contact [email protected]. BYZANTINE MUSIC INTERVALS: AN EXPERIMENTAL SIGNAL PROCESSING APPROACH A Thesis Submitted to the Graduate Faculty of the University of New Orleans in partial fulfillment of the requirements for the degree of Master of Science in Applied Physics by Kyriakos Tsiappoutas B.S. University of New Orleans, 2002 August 2004 ACKNOWLEDGEMENTS First I want to thank my Thesis Committee Members for their valuable and insightful comments and guidance both throughout the course of this Thesis and as my Professors in various courses these last years: my Committee Chair Dr. George E. Ioup, and the three members Dr. Juliette W. Ioup, Dr. Ashok Puri from the Department of Physics (University of New Orleans), and Dr. James G. May, from the Department of Psychology (University of New Orleans). Without their priceless supervision this Thesis would not have been possible. I want to thank and dedicate this Thesis to my wife and best friend Dr. Elisabeta Pana for her patience and love; to my mother Georgia, my father Michael and my brother Chris for their financial and moral support over the last seven years; to my grandfather and Byzantine Music teacher Hatzisavvas Psaltis, arch-chanter of the Metropolis of Keryneia, Cyprus, for transfusing me the music. I also want to thank my friends and chanters Dr. Constantine Lagouros, arch- chanter of the Metropolis of Canada and Professor of physics, Dr. Nikos Giannoukakis, arch-chanter of the Metropolis of Pittsburg, Pennsylvania, and Mr. Andreas Koraes, chanter in Cyprus, for their valuable comments over numerous conversations on the theory and physics of Byzantine Music, as well as for sending me Byzantine Music manuscripts used in this thesis. I also thank Louisiana taxpayers for making my assistantship possible. ii TABLE OF CONTENTS List of Figures.................................................................................................................... iv Abstract................................................................................................................................v Chapter 1..............................................................................................................................1 Introduction......................................................................................................................1 Chapter 2..............................................................................................................................6 Themes.........................................................................................................................6 Notation........................................................................................................................6 Scales, Modes and Intervals.........................................................................................7 Fourier analysis Techniques ......................................................................................15 Scope..........................................................................................................................22 Methodology..............................................................................................................22 Chapter 3............................................................................................................................22 Section 3-1 .................................................................................................................35 Section 3-2 .................................................................................................................38 Section 3-3 .................................................................................................................49 Section 3-4 .................................................................................................................67 Section 3-5 .................................................................................................................70 Chapter 4............................................................................................................................73 Discussion..................................................................................................................73 Frequency Ratios .......................................................................................................73 Pitch Discrimination ..................................................................................................78 Chapter 5............................................................................................................................84 Conclusions................................................................................................................84 Suggested Future Research........................................................................................85 References..........................................................................................................................87 Appendices.........................................................................................................................88 Appendix A: Sound Files .............................................................................................88 Appendix B: Byzantine Music Manuscript....................................................................89 Vita.....................................................................................................................................92 iii LIST OF FIGURES Figure 1 ..............................................................................................................................12 Figure 1-a...........................................................................................................................26 Figure 2 ..............................................................................................................................32 Figure 3 ..............................................................................................................................39 Figure 4 ..............................................................................................................................42 Figure 5 ..............................................................................................................................44 Figure 6 ..............................................................................................................................50 Figure 7 ..............................................................................................................................53 Figure 8 ..............................................................................................................................56 Figure 9 ..............................................................................................................................62 Figure 10 ............................................................................................................................64 Figure 11 ............................................................................................................................68 Figure 12 ............................................................................................................................72 iv ABSTRACT A Byzantine Music piece performed by a well recognized chanter is used in order to derive experimentally the mean frequencies of the first five tones (D – A) of the diatonic scale of Byzantine Music. Then the experimentally derived frequencies are compared with frequencies proposed by two theoretical scales, both representative of traditional Byzantine Music chanting. We found that if a scale is performed by a traditional chanter, it is very close in frequency to the frequencies proposed theoretically, except tone F. An allowed frequency deviation from the mean frequencies for each tone is determined. The concept of allowed deviation is not provided by theory. Comparing our results to the notion of pitch discrimination from psychophysics it is further established that the frequency differences are minute. The Attraction Effect is tested for a secondary tone (E) and the effect is quantified for the first time. The concept of the Attraction Effect has not been explained in theory in terms of frequencies