! ! ! ! ! ! ! ! ! ! A!Multiphonic!Reappraisal!and!the!Alto!Saxophone!Concerto!Radial! ! ! Keith!Moore! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! Submitted!in!partial!fulfillment!of!the!! requirements!for!the!degree!of!! Doctor!of!Musical!Arts! in!the!Graduate!School!of!Arts!and!Sciences! ! ! COLUMBIA!UNIVERSITY!! ! 2014! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ©!2014! Keith!Moore! All!rights!reserved! ABSTRACT! A!Multiphonic!Reappraisal!and!the!Alto!Saxophone!Concerto!Radial! Keith!Moore! ! This!dissertation!analyzes!the!original!composition!Radial,!which!is!scored!for!alto! saxophone!solo,!small!orchestra!and!live!electronics.!Multiphonics!are!a!common!feature!on! the!aural!surface!of!Radial.!This!analysis!will!show!that!alto!saxophone!multiphonics!are!also! a!primary!structural!element!in!the!work,!hierarchically!organizing!the!timbres,!harmonies,! instrumental!interactions!and!largeTscale!form!of!the!score.!Interestingly,!no!source!suggests! how! multiphonics! can! be! an! independent! organizational! force.! Numerous! book! length! multiphonic!catalogues!for!diverse!instruments!give!fingerings!for!these!sounds!and!describe! them!as!harmonies!so!that!they!can!be!fitted!into!harmonic!contexts,!and!a!small!but! significant!scientific!literature!on!multiphonics!discusses!the!acoustic!principles!underlying! these! sounds,! but! no! document! considers! their! independent! structural! potential.! After! providing!a!general!account!of!multiphonics!and!their!relation!to!harmonic!and!inharmonic! sounds,! this! dissertation! will! propose! an! answer! to! that! problem! by! drawing! together! concepts!from!American!experimental!music,!spectralism!and!cognitive!music!theory,!with! Radial!reviewed!as!an!example!of!this!method!in!action.!Historical!issues!and!a!broad!range! of!implications!for!this!research!will!also!be!discussed.! ! ! TABLE OF CONTENTS List of Figures iv Acknowledgements viii Dedication ix 1 Introduction . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Practical and Theoretical Backgrounds of Radial . . . 3 2 A Preliminary Definition of Multiphonics . . . . . . . . 8 2.1 Acoustic, Psychoacoustic and Stylistic Boundaries . . 8 2.2 Energy, Resonant Systems, Multiresonant Systems, Coupled Resonators and Radiators . . . . . . . . . . 10 2.3 Five Basic Types of Multiphonics . . . . . . . . . . 14 2.3.1 Collateral multiphonics . . . . . . . . . . . . 14 2.3.2 Harmonic series-based multiphonics . . . . . . 20 2.3.3 Radiated multiphonics . . . . . . . . . . . . . 25 2.3.4 Multi-driver multiphonics . . . . . . . . . . . 26 2.3.5 Non-coincident multiphonics . . . . . . . . . . 28 2.4 General Remarks . . . . . . . . . . . . . . . . . . . 29 3 Theoretical and Practical Literature on Multiphonics . . 33 3.1 A Multiphonic Theoretical Retrospective . . . . . . . 33 3.2 Multiphonic Theoretical Studies After 1950 . . . . . 34 3.3 General Theoretical Discussions Relevant to Multiphonic Theory . . . . . . . . . . . . . . . . . 38 3.4 Multiphonic Catalogues After 1960 . . . . . . . . . . 39 ! i! 4 Structural and Analytical Perspectives in Radial . . . . 42 4.1 Creating Multiphonic Space . . . . . . . . . . . . . 43 4.1.1 The scalar levels . . . . . . . . . . . . . . . 46 4.1.2 The multiphonic prototype sonority . . . . . . . 62 4.1.3 An independent collateral resonance zone . . . . 67 4.1.4 Subtones and the instability continuum . . . . . 70 4.1.5 Reflections on the basic space . . . . . . . . . 72 4.2 The Basic Space at Work in Radial . . . . . . . . . . 82 4.2.1 Radial’s structure and harmonic background . . . 82 4.2.2 The three harmonic and timbral strands . . . . . 85 4.2.3 The ascending and descending harmonic strands. . 87 4.2.4 Inharmonicity in the ascending and descending harmonic strands . . . . . . . . . . . . . . . . 92 4.2.5 Harmonic and timbral hierarchies in the ascending harmonic strand . . . . . . . . . . . 97 4.2.6 Harmonic and timbral hierarchies across the ascending and descending harmonic strands . . . 104 4.2.7 The centricity-fusion strand . . . . . . . . . 108 4.2.8 Timbral and harmonic grouping through delays, beating patterns, orchestration and ensemble interaction . . . . . . . . . . . . . . . . . . 116 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . 134 References . . . . . . . . . . . . . . . . . . . . . . . 139 A Global and Historical Perspectives on Multiphonics . . . 166 ! ii! A.1 Perspectives on a Global History . . . . . . . . . 166 A1.1 Towards a comprehensive model . . . . . . . . 173 A.2 Multiphonics in Early Classical Music and Jazz . . . 175 A2.1 Benade’s first evolutionary period . . . . . . 175 A2.2 First virtuosos . . . . . . . . . . . . . . . . 176 A2.3 Benade’s second and third evolutionary periods and the French horn . . . . . . . . . . . . . . 179 A2.4 French horn postlude . . . . . . . . . . . . . 185 A2.5 Early jazz . . . . . . . . . . . . . . . . . . 185 A.3 Multiphonics After 1950 . . . . . . . . . . . . . . 189 A3.1 Landmarks and reservations: 1957—1959 . . . . . 189 A3.1.1 Interlude: narrative problems . . . . . 193 A3.2 1957—1959: Musicians . . . . . . . . . . . . . 195 A3.3 1957—1959: Further influences . . . . . . . . . 197 B Key Terms and Issues for the Study of Multiphonics . . . 200 B.1 Combination Tones . . . . . . . . . . . . . . . . . 200 B.2 Nonlinearity . . . . . . . . . . . . . . . . . . . . 202 B.3 Amplitude Modulation and Frequency Modulation . . . 204 B.4 The Cochlea . . . . . . . . . . . . . . . . . . . . 207 B.5 The Nonlinearity of Musical Instruments . . . . . . 211 B.6 Cognition and Waves: Another Look at Subjective and Objective Tones and Constructive and Destructive Interference . . . . . . . . . . . . . . 214 ! iii! List of Figures 4.1 All pitches used in alto saxophone multiphonics ordered in an ascending scale . . . . . . . . . . . 48 4.2 Eighteen multiphonics below C4 that could but do not create low difference tones . . . . . . . . . . 52 4.3 Eighteen multiphonics between C4 and D#4 that create low difference tones . . . . . . . . . . . . 53 4.4 Preliminary quantitative resonance curve for the alto saxophone multiphonics . . . . . . . . . . . . 56 4.5 The scalar levels of alto saxophone multiphonic space . . . . . . . . . . . . . . . . . . . . . . . 59 4.6 The prototype alto saxophone multiphonic (Pr0) . . 63 4.7 The prototype multiphonic (Pr0) in detail . . . . . 64 4.8 The wider central region of the prototype multiphonic (PrDi0-Pr0-PrCm0) . . . . . . . . . . . 65 4.9 The full inharmonicity continuum of the prototype multiphonic (PrDi4-Pr0-PrCm6) . . . . . . . . . . . 66 4.10 Various sonorities from the independent collateral resonance zone . . . . . . . . . . . . . . . . . . 69 4.11 The “subtone” multiphonics . . . . . . . . . . . . 71 4.12 The alto saxophone multiphonics transposed to C4 . . 73 ! iv! 4.13 The scalar levels of alto saxophone multiphonic space with voice position ranges and independence markings . . . . . . . . . . . . . . . . . . . . . 77 4.14 Alto saxophone multiphonic timbral space . . . . . 80 4.15 Resonance range Db4 in time bracket 8:20-8:40 of the alto saxophone solo . . . . . . . . . . . . . . 84 4.16 The three harmonic strands in time bracket 0:00-0:20 of the alto saxophone solo . . . . . . . 86 4.17 Ranges and bass positions of the descending and ascending harmonic strands converging on Db4 . . . 89 4.18 Bass positions of Radial’s nine-stage progression of double leading-tone harmonies . . . . . . . . . 90 4.19 Surface reduction of the outer voices of the ascending and descending and harmonic strands . . . 93 4.20 Process from resonance range to surface . . . . . . 98 4.21 Branching structure for example in the final staff of Figure 4.20 . . . . . . . . . . . . . . . . . . 101 4.22 Complete branching structure for the ascending harmonic strand with time span reduction levels (TSR) for each level of the tree . . . . . . . . . 103 4.23 The complete multiphonics and basic timbral divisions of the descending and ascending harmonic strands . . . . . . . . . . . . . . . . . . . . . . 105 ! v! 4.24 Level b time span reduction for the descending and ascending strands . . . . . . . . . . . . . . . . . 107 4.25 Informal “level b” time span reduction for all three harmonic strands . . . . . . . . . . . . . . 108 4.26 The prolongational background and perceptual functions of the centricity-fusion strand . . . . . 110 4.27 Materials of centricity-fusion strand prolongational background synopsized in time brackets 8:00-8:20 and 8:20-8:40 of the alto saxophone solo . . . . . . . . . . . . . . . . . . 112 4.28 Reduction of centricity-fusion strand across the large-scale form . . . . . . . . . . . . . . . . . 113 4.29 Formant frequencies in the centricity-fusion strand . . . . . . . . . . . . . . . . . . . . . . 115 4.30 Surface grouping structures for the third major section of Radial . . . . . . . . . . . . . . . . . 118 4.31 Spectral opacity in the first orchestral event of Figure 4.30 . . . . . . . . . . . . . . . . . . . . 122 4.32 Fundamentals and prominent difference tones in the first orchestral event of Figure 4.30 . . . . . 125 4.33 “Beating key” for the centricity-fusion strand and Radial’s large-scale form . . . . . . . . . . . . . 127 4.34 Large-scale grouping structures of the mixed orchestral groups . . . . . . . . . . . . . . . . . 130 ! vi! 4.35 Orchestral grouping structures annotating the time span reduction levels of Figure 4.22 . . . . . . . 132 A.1 Three common long fingerings on the baroque one-key flute . . . . . . . . . . . . . . . . . . . 179 A.2 Three fully vented fingerings on the Boehm 1847 cylindrical flute . . . . . . . . . . . . . . . . . 181 B.1 The basic equation for a simple harmonic oscillator . . . . . . . . . . . . . . . . . . . . 202 B.2 Ring modulation output example . . . . . . . . . . 205 B.3 Frequency analysis analogy: an action-based description of a square drawn by a pen plotter . . 216 ! vii!