Alto!Saxophone!

230 Pages·2014·5.69 MB·English

!
!
!
!
!
!
!
!
!
!
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!