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Harmonics: Composing in Extended Just Intonation

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Harmonics: Composing in Extended Just Intonation University of Wollongong Research Online University of Wollongong Thesis Collection University of Wollongong Thesis Collections 2011 Tuning the horn: a composer-performer's perspective on using extended just intonation Michael H. Dixon University of Wollongong Recommended Citation Dixon, Michael H., Tuning the horn: a composer-performer's perspective on using extended just intonation, Doctor of Creative Arts thesis, Faculty of Creative Arts, University of Wollongong, 2011. http://ro.uow.edu.au/theses/3419 Research Online is the open access institutional repository for the University of Wollongong. For further information contact Manager Repository Services: [email protected]. TUNING THE HORN A COMPOSER-PERFORMER’S PERSPECTIVE ON USING EXTENDED JUST INTONATION A thesis submitted in partial fulfilment of the requirements for the award of the degree DOCTOR OF CREATIVE ARTS from UNIVERSITY OF WOLLONGONG by MICHAEL H DIXON, MMus, MPhil FACULTY OF CREATIVE ARTS, SCHOOL OF MUSIC, 2011 Certification I, Michael Hugh Dixon, declare that this thesis, submitted in partial fulfillment of the requirements for the award of Doctor of Creative Arts, in the Faculty of Creative Arts, University of Wollongong, is wholly my own work unless otherwise referenced or acknowledged. The document has not been submitted for qualifications at any other academic institution. 1 March 2011 i Table of Contents List of Tables iv List of Examples v List of Illustrations vii Abstract viii Acknowledgments ix Prologue xi Chapter 1 1 The extended xenharmonic family of labrosones 1.2 3rd harmonic 13 1.3 5th harmonic 18 1.4 7th harmonic 20 1.5 11th harmonic 29 1.6 13th harmonic 40 1.7 17th harmonic and beyond 46 1.8 Summary 53 Chapter 2 55 Labrosone harmonics: composing in extended just intonation 2.1 7-limit just intonation: natural labrosones 57 2.2 11-limit just intonation: natural labrosones 65 2.3 13-limit just intonation: natural labrosones 82 2.4 13-limit just intonation: finger hole labrosones 86 2.5 Brass instruments in 7, 11 & 13-limit just 93 intonation composition 2.6 Standard brass: observations regarding 99 performance in non-standard tunings ii Chapter 3 101 A new repertoire: French horn and close relatives 3.1 Extended just intonation compositions: Group A 111 3.2 Extended just intonation compositions: Group B 153 3.3 Extended just intonation compositions: Group C 179 Epilogue 203 Endnotes 211 References 215 Appendix A 165, 9-note scales A1-8 Appendix B HSIS-13 B1-8 Appendix C Notation: HEWM C1-3 Appendix D Method for horn D1-119 Folio of Compositions Folio 1-170 Track List: Tuning Cribs & Performances Folio 171-174 CDs 1, 2 & 3 after the Folio iii List of Tables Table 1 Classification of labrosones 6 Table 2 Musical scenario summary - Chapter Two 56 Table 3 Alphorn pitches - Chapter Two 84 Table 4 Pitch relations in 3.1.3 121 Table 5 Valve slide settings for 3.3.2 188 Table 6 Valve slide tunings for 3.3.3 196 Table 7 Bassoon pitches in 3.3.3 200 Table 8 Valve slide tunings for 3.3.3 202 iv List of Examples Example 1 Slurring across the grain, Martin’s Ballade 23 Example 2 Harmonics in Britten’s Serenade 35 Example 3 Harmonics for I wouldn’t mind dyin’ 36 Example 4 7th harmonics for quartertone effect 37 Example 5 Multi-crook approach by Ligeti 41 Example 6 Harmonics in Mandelbaum’s Wind Quintet No.2 45 Example 7 High written G, 24th harmonic 47 Example 8 Horn harmonics 1-31 in Chemchok Heruka 52 Example 9 Pitch ratio allocation for each rozhok 88 Example 10 Trombone tuning plan for Scenario Six score 97 Example 11 Scale 1 from the set of 165 103 Example 12 Scale 2 from the set of 165 104 Example 13 Scale 3 from the set of 165 104 Example 14 Scale 165 from the set of 165 104 Example 15 Harmonic series & Derivation 1 (HSIS-13) 108 Example 16 Harmonic series & Derivation 1 (HSIS-13) 109 Example 17 Harmonic series & Derivation 1 (HSIS-13) 109 Example 18 Horn tuning in 3.1.1 113 Example 19 Keyboard tuning in 3.1.1 116 Example 20 Tuning parameters in 3.1.2 118 Example 21 Koto string arrangement in 3.1.3 122 Example 22 Horn entry - harmonics in 3.1.3 123 Example 23 Dyads used in 3.1.4 126 Example 24 Pitch groups in 3.1.5 129 Example 25 Vowel map in 3.1.6 133 Example 26 Ratio 45:28 with harmonisations in 3.1.6 133 Example 27 Chord changes in 3.1.6 134 v Example 28 Feature chord, ratios 6:7:9:11, in 3.1.7 139 Example 29 Vowel map in 3.1.7 140 Example 30 Chord progression in 3.1.7 142 Example 31 Tonic chord in 3.1.8 148 Example 32 Horn entry - 13th harmonic in 3.1.8 151 Example 33 Ratio scales in 3.2.1 155 Example 34 Off-unison, pitch beating in 3.2.1 156 Example 35 Symmetrical 9-note scales in 3.2.2 158 Example 36 Descending line of 24 ratios in 3.2.2 159 Example 37 3 sets of harmonics: 4, 5, 6, 7 in 3.2.3 163 Example 38 9-note scale with 3 tonics in 3.2.3 164 Example 39 Interval scales in 3.2.4 167 Example 40 Harmonic series relations in 3.2.4 169 Example 41 Melodic fragments (harmonics) in 3.2.4 171 Example 42 Pitch beatings in 3.2.4 171 Example 43 Multi-crook use in 3.2.5 176 Example 44 Notation, fingering & harmonics in 3.3.1 184 Example 45 Arpeggios difficult to achieve in 3.3.2 191 Example 46 Converging harmonics in 3.3.3 198 Example 47 Microtonal shift in 3.3.3 199 vi List of Illustrations Illustration 1 Bugle 58 Illustration 2 Russian Horn Capella 66 Illustration 3 Blowing horn 71 Illustration 4 Trutruka 75 Illustration 5 Alphorn & Arkady Shilkloper 82 Illustration 6 Rozhok 88 Illustration 7 Valve slide settings for 3.1.1 114 Illustration 8 Xenophone 125 Illustration 9 Valve slide settings for 3.2.4 169 Illustration 10 Valve slide settings for 3.3.2 188 Illustration 11 Valve slide settings for 3.3.3 201 vii Abstract There is a large repertoire for the (French) horn yet it is mostly confined to standard tuning systems. Development of new repertoire, as demonstrated in this thesis, may assist in bringing non-standard tunings out of the margins and into the mainstream. A significant compositional resource is provided by the available harmonics of the standard double horn, 13-24 on each of 16 tube lengths, along with traditional techniques of lip, right hand and valve slide adjustments. The performance of compositions in extended just intonation is discovered to be within the realm of expertise of players using standard brass instruments. A deeper understanding of the use of harmonics produced on lip- vibrated instruments or labrosones is gained by classifying them according to just intonation prime-limits. The use of harmonics is therefore linked with the long and rich tradition of just intonation and other microtonal exploration. A method specifically for training horn players in extended just intonation completes this thesis. viii Acknowledgments My gratitude goes to my Principal Supervisor Greg Schiemer for his guidance throughout my candidature and in particular for his expert advice regarding the preparation of this thesis. I also acknowledge the suggestions by my Associate Supervisor Stephen Ingham in the early part of my candidature. I had many fruitful discussions concerning instrumental and vocal technique with a number of musicians. In particular: trombone players Will Farmer, Brett Favell, Scott Kinmont, Jack Machin, Greg van der Struik; trumpet players Joshua Clark, John Foster, Andrew Evans, Leanne Sullivan, Julie Waters; tuba player Angus Charlton; euphonium player Matt van Emmerick; bassoon player Matt Ockenden; oboe player Kirsten Barry; singer Wendy Dixon. I am also grateful to Lee Bracegirdle for translating some Spanish text; to Joy Goodsell for proof- reading the main text; to Wendy Dixon for proof-reading the Appendices and to Terumi Narushima for assistance with referencing. For some years a microtonal, diamond shaped metallaphone was housed at UOW. I made use of this xenophone with the kind permission of designer/ builder Christian van der Vyver. The preparation of tuning cribs that allowed for computer generated sound files was an integral part of my work. Warren Burt provided assistance in tuning the Kurzweil K2000. The software Li’l Miss’ ix Scale Oven was an extremely useful tool and the technical support from it’s creator Jeff Scott was most beneficial to me. A number of composers allowed me to include their works in concerts I organised: Michael Barkl, Dennis Bathory-Kitsch, Warren Burt, Hugh Dixon, Kraig Grady, Terumi Narushima, Greg Schiemer. The performances were memorable. None of my work for this DCA would have any meaning without the performances of my compositions. Many performers graciously gave of their time and energy to prepare and present live performances and recordings. They are listed with the commentary on each composition in the portfolio. Also my thanks to Wirripang Pty Ltd for publishing the compositions I selected. The support and understanding of my wife, Lisa Wynne-Allen, was paramount especially in the final year of thesis preparation. x Prologue Over the past 15 years my work as a composer and instrumental performer has been increasingly driven by my interest in exploring and understanding the world of just intonation, an area so often taken for granted or misunderstood by many musicians.
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