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A New Tonal World: the Bohlen-Pieree Seule

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A New Tonal World: the Bohlen-Pieree Seule ·' A New Tonal World: The Bohlen-Pieree Seule by Amy Advocat Schulich School of Music McGill University, Montreal ~cG\l1 UniverSity August 2010 A paper submitted to McGill University in partial fulfillment of the requirements of the degree of D.Mus. Performance Studies • © Amy Advocat, 2010 A New Tonal World: The Bohlen-Pierce Scale • Table ofContents Table of Contents...................................................................................................... i Abstract. .................................................................................................................. iv Abrégé...................................................................................................................... v Acknow ledgements .................................................................................................vi List of Figures.......................................................................................................viii List ofTables............................................................................................................x List of Musical Examples ....................................................................................... xi Introduction.............................................................................................................. 1 Chapter 1 - New Scales, New Possibilities .............................................................. 2 1.1 -Alternative tuning systems ...........................................................................2 1.2 -Just Intervals and the Harmonic Series ........................................................ 3 1.3 -The Seventh Partial. ..................................................................................... 5 1.4 -19- and 31-Equal Temperaments ................................................................. 6 1.5 -Just Intonation .............................................................................................. 8 1.6 -24-Equal Temperament. ............................................................................. 10 1.7 -72-Equa1 Temperament.. ............................................................................ Il 1.8 -18- and 36-Equa1 Temperaments ............................................................... 12 1.9 -Wendy Carlos' Scales ................................................................................. 12 Chapter 2 - The Bohlen-Pierce Scale ..................................................................... 14 • A New Tonal World: The Bohlen-Pierce Scale • 2.1 -A Thirteen Step Scale ................................................................................. 14 2.2 -The Discovery of the Bohlen-Pierce Scale ................................................ 15 2.2.1 -Heinz Bohlen's Search for a New Scale ............................................. 15 2.2.2 -John Pierce's Discovery of the P3579 scale ....................................... 20 2.2.3 -The Scale Studies of Kees van Prooijen ........................................... 22 2.3 -The Just Bohlen-Pierce Scale .................................................................... 25 2.4 -The Equal-tempered Bohlen-Pierce Scale ................................................. 26 2.5 -Closer Just Ratios to the Bohlen-Pierce-Equal Scale ................................27 2.6 -Continued Fractions ................................................................................... 29 2.7 -The Diatonic Bohlen-Pierce Scale ............................................................. 33 2.8 -Bohlen-Pierce Modes ................................................................................. 35 2.9 -Is there a Bohlen-Pierce Harmonie Theory? ............................................. 36 2.10 -Bohlen-Pierce Notation ............................................................................38 Chapter 3 - Instruments and Timbres .................................................................... .42 3.1 -Heinz Bohlen's Organ ................................................................................ 42 3.2 -Timbre and the Bohlen-Pierce Scale ......................................................... .43 3.3 -Instruments with Odd and Even Timbres ..................................................44 3.4 -Triadalizer. ................................................................................................. 45 3.5 -Bohlen-Pierce Keyboards .......................................................................... 45 3.6 -Tritave Equivalence: John Pierce and Max Matthews .............................. .48 3.7 -Timbre Study: William Sethares ................................................................ 49 • 11 A New Tonal World: The Bohlen-Pierce Scale • 3.8 -Instruments for Other Alternative Scales ................................................... 54 3.9 -The Bohlen-Pierce Clarinet.. ..................................................................... 57 3.1 0 -The Bohlen-Pierce Tenor Clarinet.. ......................................................... 59 Chapter 4 - Bohlen-Pierce Music ...........................................................................61 4.1 -Composing in a New Language ................................................................. 61 4.2 -A Bohlen-Pierce Christmas CaroL ............................................................ 62 4.3 -Bohlen-Pierce Pop Songs ...........................................................................65 4.4 -Katarina Miljkovic's For Amy ................................................................... 70 4.5 -Georg Hajdu's Opera, Der Sprung ............................................................. 73 4.6 -Hajdu's Beyond the Horizon ...................................................................... 74 4.7 -Julia Werntz's Imperfections ...................................................................... 77 Conclusion............................................................................................................. 82 Bibliography.......................................................................................................... 85 Appendix - Bohlen-Pierce Compositions .............................................................. 89 • 111 A New Tonal World: The Bohlen-Pierce Scale • Abstract This paper compares the Bohlen-Pierce scale to other octave and non­ octave-based tuning systems, drawing parallels between it and the widely used 12-equal temperament. These parallels lead to the hypothesis that there can be a set ofharmonic mIes applicable to the Bohlen-Pierce scale that are analogous to the CUITent musical practice. Those theorized mIes are then applied to some examples of the growing body of musical compositions wrÏtten in the Bohlen­ Pierce scale. Aiso included are supportive arguments for a preference of the use of odd-partial timbres in performance of this scale, which make the invention of the Bohlen-Pierce clarinet a major tuming point in the scale's development. Sorne of the musical works studied were written specifically for this author's performance on the Bohlen-Pierce clarinet. • IV A New Tonal World: The Bohlen-Pierce Scale • Abrégé Ce document compare la gamme Bohlen-Pierce à d'autres systèmes d'accord octave et non-octave-basés, établissant des parallèles entre soi et le système la plus utilisé, tempérament de I2-égal. Ces parallèles mènent à la possibilité qu'il peut être des règles harmoniques applicables à la gamme Bohlen­ Pierce qui sont analogues à la pratique musicale courante. Ces règles théorisées sont alors appliquées à quelques exemples du corps croissant de compositions musicales écrites à la gamme Bohlen-Pierce. Il-y-a aussi inclus des arguments qui support la préférence d'utilisation des timbres impair-partiels dans la performance de cette gamme, qui ferait l'invention de la clarinette Bohlen-Pierce un point tournant majeur dans la développement de cette gamme. Certains compositions etudié a été ecris pour la pérformance sur clarinet Bohlen-Pierce par cette auteure . • v A New Tonal World: The Bohlen-Pierce Scale • Acknowledgements This paper represents more than a product of research, it also represents the culmination of a performance project. At the instigation of James Bergin of the Boston Microtonal Society and with the financial assistance ofthe McGill University Schulich Scholarship, 1 purchased a Bohlen-Pierce clarinet and began finding composers interested in working with this strange new scale. The result was six new works for the instrument, aIl of which were premiered in March 2010 at the first ever Bohlen-Pierce Symposium in Boston. My thanks go out to those composers: Julia Werntz, Roger Feria, Stratis Minakakis, Katarina Miljkovic, Anthony De Ritis and James Bergin. rd like to especially thank Stephen Fox for his innovation and dedication to the Bohlen-Pierce Clarinet Project. His work is always on demand in the clarinet world and yet he found the time to construct these instruments, which are a joy to play. Also, 1 must thank Georg Hajdu who first approached Stephen to build the horns, and who coordinated the entire Bohlen-Pierce Symposium. He tirelessly organized this three-day event with composers, researchers and performers spanning three countries: Canada, Germany and the United States. Because of his brainchild, 1 was able to meet and work with many other artists specializing in Bohlen-Pierce performance: Nora-Louise Müller, Âkos Hoffmann, Tilly Kooyman and Todd Harrop, just to name a few. These artists and our • VI A New Tonal World: The
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