Copyright by Trent William Hanna 2003 The Dissertation Committee for Trent William Hanna certifies that this is the approved version of the following dissertation:
Concerto for Piano and Orchestra
Committee:
______Kevin Puts, Supervisor
______Donald Grantham
______Russell Pinkston
______Stefan Kostka
______Thomas J. O’Hare Concerto for Piano and Orchestra
by
Trent William Hanna, B.M., M.M.
Dissertation
Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of
Doctor of Musical Arts
The University of Texas at Austin May 2003 Dedication
My Concerto for Piano and Orchestra is dedicated to Dr. John Paul, my piano instructor for many years. Acknowledgements
First, I would like to thank the members of my committee: Kevin Puts, Donald Grantham, Russell Pinkston, Stefan Kostka, and Thomas O’Hare. I am grateful for their patience. I would also like to thank Dan Welcher, with whom I studied composition for two years before starting my dissertation. It would be impossible to mention everyone who has supported me through this dissertation and degree. I would, however, like to thank Beth Hiser, David Diers, David Patton, Kyle Kindred, and Mike Vernusky for their friendship these past few years. Thanks also to Tanya Weisheit, who not only helped with proofreading the paper, but also showed her support in so many caring ways. Thanks to my grandfather and my father, Ray and John Hanna. They both received Doctoral degrees and I am proud to continue in this tradition. I would also like to thank my daughter, Symphony, for being as patient as a seven-year-old can be when her father is too busy completing his dissertation to play with her every waking hour (as I would prefer). Most importantly, thank you to my mother and step dad, Victoria and Joe Courtney, for their constant, loving support throughout my educational pursuits.
v Concerto for Piano and Orchestra
Publication No.______
Trent William Hanna, D.M.A. The University of Texas at Austin, 2003
Supervisor: Kevin Puts
The Concerto for Piano and Orchestra is a one-movement work. Symmetry and simple mathematical formulae are used throughout the work as compositional tools and structural framework. This dissertation consists of the full score for the concerto, followed by a discussion of the formal, symmetrical, thematic, and mathematical elements of the music.
vi Table of Contents
MUSICAL SCORE: CONCERTO FOR PIANO AND ORCHESTRA 1
ANALYSIS 62
Introduction ...... 62
Analysis...... 65 Opening Section...... 65 Rehearsal Letters A Through C ...... 72 Rehearsal Letter A ...... 72 Rehearsal Letter B ...... 74 Rehearsal Letter C ...... 76 Rehearsal Letter D...... 78 Rehearsal Letters E and F...... 85 Rehearsal Letter E ...... 85 Rehearsal Letter F ...... 86 Rehearsal Letter G...... 88 Rehearsal Letters H Through K ...... 94 Rehearsal Letter H ...... 94 Rehearsal Letter I ...... 94 Rehearsal Letter J ...... 94 Rehearsal Letter K ...... 94 Rehearsal Letters L Through P ...... 96 Rehearsal Letter L ...... 96 Rehearsal Letter M ...... 97 Rehearsal Letter N ...... 98
vii Rehearsal Letter O ...... 98 Rehearsal Letter P ...... 98 Closing Section ...... 99 Rehearsal Letter Q ...... 99 Rehearsal Letter R ...... 100 Rehearsal Letter S ...... 100 Rehearsal Letter T ...... 100 Rehearsal Letter U ...... 101 Rehearsal Letter V ...... 101 Rehearsal Letter W ...... 101 Rehearsal Letter X ...... 102 Rehearsal Letter Y ...... 102 Rehearsal Letter Z ...... 104 Rehearsal Letter AA ...... 105 Rehearsal Letter BB...... 105 Rehearsal Letter CC...... 106 Rehearsal Letter DD ...... 107
Conclusion ...... 108
Vita ...... 109
viii Concerto for Piano and Orchestra
Score in C Trent Hanna (ASCAP)
With Intensity h = 72 poco rit.
Piccolo
1 Flute 2
1 Oboe 2
English Horn
1 Clarinet in Bb 2 3
1 Bassoon 2
Contrabassoon
1 Horn in F 2
3 Horn in F 4
1 Trumpet in Bb 2 3
1 Tenor Trombone 2
Bass Trombone
Tuba
5 Timpani
Percussion 1 Percussion 2 Percussion 3
Percussion 4
Harp MMLOMMMM
Piano ff cadenza
With Intensity h = 72 poco rit.
Violin I
Violin II
Viola
Violoncello
Contrabass
© 2003 Trent Hanna 1 h = 60 Pno. fff
molto accel. Tam-Tam Perc. 2 pp
Bass Drum Perc. 4 pp
Pno. p p p f
2 Powerful q = 112 Senza misura 2 Picc. ff 1 Fl. 2 ff 1 Ob. 2 ff Eng. Hn. ff Cl. 1 ff 2 Cl. 3 ff stagger breathing 1 Bsn. 2 ff p stagger breathing Cbsn. ff p 1 Hn. 2 ff 3 Hn. 4 ff 1 Tpt. 2 3 ff stagger breathing Tbn. 1 p ff stagger breathing Tbn. 2 p ff stagger breathing B. Tbn. ff p stagger breathing Tba. ff p Timp. f p Anvil Perc. 1 ff Perc. 2 f Brake Drum Perc. 3 ff Perc. 4 f
5 5 6 7 cresc. Pno. (cadenza) f
Powerful q = 112 Senza misura div. Vln. I ff div. Vln. II ff div. Vla. ff div. ( ) Vc. p ff div. ( ) Cb. ff p
3 1 Bsn. 2
Cbsn. Tbn. 1
Tbn. 2
B. Tbn.
Tba. Timp.
Tam-Tam Perc. 2 pp
Bass Drum Perc. 4 pp
9 9 9 9 12 12 12 12 ff Pno. cresc. Vc.
Cb.
4 (q = 112) Senza misura 5 Picc. ff 1 Fl. 2 ff 1 Ob. 2 ff Eng. Hn. ff Cl. 1 ff 2 Cl. 3 ff 1 Bsn. 2 ff p Cbsn. ff p 1 Hn. 2 ff 3 Hn. 4 ff 1 Tpt. 2 3 ff Tbn. 1 ff p Tbn. 2 p ff B. Tbn. ff p
Tba. ff p Timp. p f Perc. 1 ff Perc. 2 f Perc. 3 ff Perc. 4 f
6 6 6 6 33 Pno. fff (cadenza) f cresc. 3 3 (q = 112) Senza misura Vln. I ff Vln. II ff Vla. ff unis. div. ( ) Vc. ff p unis. div. ( ) Cb. p ff
5 As before q = 112 accel. 8 Picc. 6 6 3 mf ff 1 a2 Fl. 2 6 6 3 mf ff a2 1 Ob. 2 mf mf mf ff 3 3 Eng. Hn. mf ff a3 1 Cl. 2 3 mf mf mf ff 3 2 1 Bsn. 2 mp cresc. ff 3 3 Cbsn. mp cresc. ff 1 a2 3 Hn. 2 ff mf mf mf 3 a2 3 Hn. 4 ff mf mf mf a3 1 Tpt. 2 3 mf ff 3 1 Tbn. 2 3 mf mf mf ff 3 B. Tbn. mp cresc. mf ff 3 Tba. mp cresc. ff Timp. cresc. mp f 3
Tom Toms 3 Perc. 2 f 3 Perc. 4 f
6 6 3 Pno. mf mf mf ff cresc. 3
As before q = 112 accel. div. Vln. I ff 3 mf mf mf div. Vln. II ff 3 mf mf mf div. Vla. ff mf mf mf 3 unis. div. 3 Vc. mp cresc. ff 3 Cb. mp cresc. ff
6 13 Picc. 3 cresc. 35fff 1 Fl. 2 3 cresc. 35fff 1 Ob. 2 35 3 cresc. fff 3 35 Eng. Hn. cresc. fff 1 Cl. 2 3 35 3 cresc. fff 1 Bsn. 2 3 cresc. 35fff 3 3 5 Cbsn. cresc. fff 1 3 35 Hn. 2 cresc. fff 3 3 35 Hn. 4 cresc. fff 1 Tpt. 2 3 cresc. 3 3 5 fff fp 1 Tbn. 2 3 cresc. 35 fff fp 5 3 3 B. Tbn. cresc. fff fp 3 35 Tba. cresc. fff Timp. D-E , A-G , B-B cresc. b b b 3 35fff Play toms randomly 3 3 5 as fast as possible Perc. 2 cresc. fff 3 35 Perc. 4 cresc. fff
3 56cresc. Pno. fff 56
Vln. I 3 cresc. 35fff Vln. II 3 cresc. 35fff Vla. 35 3 cresc. fff 3 35 Vc. cresc. fff 3 35 Cb. cresc. fff
7 A Sedate q = 72 17 Picc. p p p ppp
Ob. 1 p p p ppp Cl. 1 p p p ppp
Cbsn. p p p ppp con sord. Hn. 1 p p p ppp Triangle Perc. 1 p Hp. mp F# B§ A
Sedate q = 72 ( ) solo four players 1/2 section Vln. I p p p solo four players 1/2 section Vln. II p p p ppp four players 1/2 section solo Vla. p p p ppp solo four players 1/2 section Vc. p p p ppp ( ) solo three players 1/2 section Cb. p p p
As before q = 72 (a tempo) molto rall. 26 solo Cl. 1 mp cresc. mp mf mp con sord. Hn. 1 p con sord. Hn. 3 p con sord. Tbn. 1 p con sord. Tbn. 2 p
(a tempo) As before q = 72 molto rall. Vln. I pp ppp tutti Vln. II pp tutti Vc. pp
Cb. pp ppp
8 B poco accel. Calm q = 104 34 Cl. 1 ppp senza sord Hn. 1 p ppp senza sord Hn. 3 p ppp senza sord Tbn. 1 p ppp senza sord Tbn. 2 p ppp mp p mp Pno. p mp p
B poco accel. Calm q = 104 div. Vc. pp mp
41 senza sord Hn. 1 mf
3 7 3 3 3 mp p mp Pno. p mf p mp mp p tutti Vln. I mp mf tutti Vln. II mf tutti div. Vla. p mf div. Vc. ppp p mf tutti Cb. mp ppp
9 47 Hn. 1
Tbn. 1 mf Pno. Vln. I
Vln. II unis. Vla.
Vc.
Cb.
52 Picc. mf a2 1 Fl. 2 mf Tbn. 1 f Bb-B§ Timp. mf Suspended Cymbal Perc. 2 ppp mf
9 9 6 f 6 Pno. mp Vln. I f decresc. mf ( ) div. Vln. II mf f decresc. ( ) Vla. f decresc. mf ( ) Vc. f decresc. mf ( ) Cb. f decresc. mf
10 (no rit.) 57 Picc. ppp
1 Fl. 2 ppp
Eng. Hn. mp ppp 1 Cl. 2 mf dim. mp ppp
Bsn. 1 mp ppp Timp. mp
Hp. MLLOLLML mp gliss.
Pno. p p pp 4:3 4:3
(no rit.) Vln. I ppp Vln. II decresc. mf mp ppp Vla. decresc. mp Vc. decresc. mp
Cb. decresc. mp
11 Steady and Relaxed q = 120 C 62 Eng. Hn. p ppp
Bsn. 1 p ppp l.v. Bb - B, Gb - A, Eb - F Timp. p bell tree Perc. 4 p
Hp. gliss. mp
Pno. pp cresc. mp ppp
C Steady and Relaxed q = 120 Vln. I ppp Vln. II ppp Vla. p ppp ppp
Vc. p ppp ppp
Cb. p ppp
12 70 3 Fl. 1 3 mf f 3 Fl. 2 3 mf f 1. 1 Ob. 2 mp mf f Cl. 1 mp f Cl. 2 mp mf f
Cl. 3 f 1. 1 Bsn. 2 mp mf f Cbsn. f
Hp.
3 3 Pno. mp mp mf f 3 3
Vln. I mp f Vln. II mp f
Vla. mp f
Vc. mp f pizz. arco Cb. mp f
13 76 Fl. 1 3 3 3 mp mp 3 Fl. 2 3 3 mp mp 3 1. 1 Ob. 2 mp 3 3 mp mf
Eng. Hn. mp mp 3 3 3 Cl. 1 3 mp mp 3 3 3 3 3 Cl. 2 3 mp mf mp
Cl. 3 1 1. Bsn. 2 mp mp
Cbsn. mp
Timp. mp
LMLONNML Hp. mp
3 3 3 3 3 3 Pno. mp mf mp 3 3 3 3 3 3 div. Vln. I mp div. Vln. II mp div. Vla. mp div. Vc. mp pizz arco Cb.
14 81 Picc. 7 mf f mf Fl. 1 cresc. mf 6 f mf Fl. 2 cresc. mf 1 Ob. 2 cresc. f p
Eng. Hn. cresc. f p Cl. 1 cresc. mf f mf mf Cl. 2 cresc. mf 1. 1 Bsn. 2 cresc. f p mf Cbsn. cresc. f p F - E Timp. mf Hp. f decresc.
7 cresc. f decresc. Pno. 6 Vln. I cresc. f unis. Vln. II cresc. f unis. Vla. cresc. f unis. Vc. cresc. f Cb. cresc. f
15 87 Picc. mf 5 Fl. 1 3 5 mp mf f Fl. 2 f 3 3 Eng. Hn. 3 p mp mp mf 3 3 Cl. 1 3 3 mf f mf mp Cl. 2 f 3 3 Bsn. 1 p 3 3 3 mf Bsn. 2 3 3 3 3 mp 3 p 3 Cbsn. 3 3 3 mp 3 p bell tree Perc. 4 mf MNMOMNMM Hp. 3 333 3 3 3 3 5 Pno. cresc. 3 p 33 3 3 3 5 3 3 unis. Vln. I ppp decresc. Vln. II decresc. ppp Vla. decresc. ppp Vc. decresc. ppp pizz Cb. decresc. ppp
16 D Shimmering (q = 120) 92 Picc. ff decresc. poco a poco (to m. 96) f
Fl. 1 ff decresc. poco a poco (to m. 96) f
Fl. 2 ff decresc. poco a poco (to m. 96) f
Cl. 1 ff decresc. poco a poco (to m. 111) Cl. 2 ff decresc. poco a poco (to m. 111)
Cl. 3 ff decresc. poco a poco (to m. 111) Triangle Perc. 1 f decresc. poco a poco (to m. 121) Vibraphone Perc. 2 ff decresc. poco a poco (to m. 119) Vibraphone
Perc. 3 ff decresc. poco a poco (to m. 121) l.v. Perc. 4 Glockenspiel f decresc. poco a poco (to m. 121)
ff Hp. decresc. poco a poco (to m. 121) C§ C#
ff decresc. poco a poco (to m. 120) Pno.
D Shimmering ( = 120) q 1/2 Vln. I ff decresc. poco a poco (to m. 124)
div. Vln. II ff decresc. poco a poco (to m. 124)
div. Vla. ff decresc. poco a poco (to m. 124) 1/2 Vc. ff decresc. poco a poco (to m. 124)
17 97 Ob. 1 f decresc. poco a poco (to m. 116) Ob. 2 f decresc. poco a poco (to m. 116)
Eng. Hn. f decresc. poco a poco (to m. 116)
Cl. 1 ( f )
Cl. 2 ( f )
Cl. 3 ( f ) Perc. 1 ( f ) Perc. 2 ( f )
Perc. 3
( f ) Perc. 4 ( f ) Hp. ( f ) C§ C#
( f ) Pno.
div. Vln. I ( f ) 1/2 Vln. II ( f ) 1/2 Vla. ( f ) div. Vc. ( f )
18 102 Ob. 1 ( mf )
Ob. 2 ( mf )
Eng. Hn. ( mf )
Cl. 1 ( mf )
Cl. 2 ( mf ) Cl. 3 ( mf ) Perc. 1 ( mf ) Perc. 2 ( mf )
Perc. 3 ( mf ) Perc. 4 ( mf )
Hp. ( mf ) C§ C #
Pno. ( mf ) Vln. I
( mf ) Vln. II
( mf ) Vla.
( mf ) Vc.
( mf )
19 107 Ob. 1 ( mp )
Ob. 2
( mp ) Eng. Hn. ( mp )
Cl. 1 ( mp ) p
Cl. 2 ( mp ) p
Cl. 3 (mp ) p Perc. 1 ( mp ) Perc. 2
( mp )
Perc. 3 ( mp ) Perc. 4 ( mp )
Hp. ( mp ) C C# §
Pno. ( mp ) 1/2 Vln. I ( mp ) div. Vln. II ( mp ) div. Vla.
( mp ) 1/2 Vc. ( mp )
20 112 Ob. 1 ( p ) pp
Ob. 2 ( ) p pp
Eng. Hn. ( p ) pp
Bsn. 1 p decresc. poco a poco (to m. 120)
Bsn. 2 p decresc. poco a poco (to m. 120)
Cbsn. p decresc. poco a poco (to m. 120) Perc. 1 ( p ) Perc. 2
( p )
Perc. 3 ( p ) Perc. 4 ( p )
Hp. ( p ) C§ C#
Pno. ( ) p div. Vln. I
( p ) 1/2 Vln. II
( p ) 1/2 Vla.
( p )
div. Vc. ( p )
21 rit. q = 60 rit. 117 solo Eng. Hn. mp Bsn. 1
( pp ) ppp Bsn. 2 ( pp ) ppp Cbsn. ( ) pp ppp con sord Tbn. 1 pp decresc. poco a poco ppp con sord Tbn. 2 pp decresc. poco a poco ppp con sord B. Tbn. pp decresc. poco a poco ppp Timp. ppp
Perc. 1 ( pp ) ppp
Perc. 2
( pp ) motor on Perc. 3 ( pp ) ppp
Perc. 4 ppp ( pp )
ppp Hp. ( pp )
Pno. ( pp ) ppp
rit. q = 60 rit. ppp Vln. I ppp ppp Vln. II div. tutti div. 1/2 Vla. ppp 1/2 div. 1/2 div. Vc. ppp
E Peaceful q = 60 126 Eng. Hn. Pno. p solo con.
22 3 slowly decelerate trill 136 3 mp Pno.
solo Vc. pp
poco rall.
3 144 1 Fl. 2 mp 3 3 3 mf pp
1 Cl. 2 mp mf pp
poco rall. 3 3 3 3 3 3 3 3 Pno. 3 3 3 3 3 3 3 3 poco rall.
1/2 Vla. mf pp 1/2 Vc. mf pp
F (q = h.) Regal h. = 60 As before q = 60 148 con sord. Hn. 1 p
6669 6 6 9 Pno. p mf mp f 6 9 6 6 6 6 9
F (q = h.) Regal h. = 60
As before q = 60 tutti sul pont. naturale Vln. I p mp mp sul pont. pizz. Vln. II mp p mp tutti sul pont. pizz. Vla. mp mp p tutti sul pont. pizz. Vc. p mp mp pizz. Cb. mp
23 158 Eng. Hn. mp Hn. 1 ppp
Pno. mp mf
Vln. I
Vln. II
Vla. Vc. Cb.
171 Fl. 1 mf ppp
Eng. Hn. mf ppp Bsn. 1 mp mf ppp
Timp. p mf
Hp. f f f
f ff Pno. 3
sim. Vln. I f arco sim. Vln. II f arco sim. Vla. f arco sim. Vc. f pizz. arco Cb. f
24 181 Fl. 1 mp cresc. 3 3
Fl. 2 cresc. mp 3 Cl. 1 mp cresc. 3 Cl. 2 mp cresc.
Vibraphone Perc. 3 mf Hp. mf cresc. mp Pno. dim.
Vln. I mp dim. pp pizz. Vln. II mp pp Vla. mp dim. pp pizz. Vc. mp pp Cb.
accel.
192 Picc. mf Fl. 1 f ppp mf Fl. 2 f ppp mf Cl. 1 f ppp mf Cl. 2 mf f ppp 1 a2 Bsn. 2 mf Cbsn. mf
33 33 Pno. mf mf 33 3 3 accel. Vln. I mf mf arco Vln. II mf mf Vla. mf arco Vc. mf mf Cb. mf
25 G q = 192 200 Picc. f
1 Fl. 2 f 5:6 ff Ob. 1 f pp
Ob. 2 f pp 5:6 Cl. 1 pp f ff 5:6 Cl. 2 pp f ff Bsn. 1 pp 5:6 Bsn. 2 pp f ff Cbsn. f 5:6 ff 5:6 1 Hn. 2 f ff 5:6 3 Hn. 4 f ff 5:6 F-A, A-C, B-D Timp. mf ff
Suspended Cymbal dampen Perc. 2 ff Glockenspiel Perc. 4 f 5:6 ff
Pno. f G q = 192 Vln. I 5:6 f ff pp 5:6 Vln. II f ff pp
Vla. f Vc. f 5:6 pp ff arco Cb. f 5:6 pp ff
26 210 Picc. p cresc. poco a poco mp
Ob. 1 mp
Ob. 2 p Cl. 1 pp pp p Cl. 2 pp p p Bsn. 1 pp pp p Bsn. 2 pp p p
Glockenspiel Perc. 4 p
Vln. I p Vln. II p Vc. p Cb. p mp
27 220 Picc. mf Fl. 1 mf mf Fl. 2 mf mf
Ob. 1
Ob. 2 mf Cl. 1 mp mp mf Cl. 2 mp mf mf Bsn. 1 mp mp mf Bsn. 2 mp mf mf
con sord. Tpt. 1 mf mf con sord. Tpt. 2 mf mf senza sord. Tbn. 1 mp mp mf senza sord. Tbn. 2 mf senza sord. mp
B. Tbn. mp mp mf
Perc. 4 mp mf
Vln. I mp mf Vln. II mp mf Vc. mp mf Cb. mf
28 229 Picc. f f Fl. 1 mf f f f Fl. 2 mf f f f
Ob. 1 f
Ob. 2 f decresc. Cl. 1 f f mf Cl. 2 f f Bsn. 1 f f mf Bsn. 2 f f
Cbsn. ff
Tpt. 1 mf f f f Tpt. 2 mf f f f
Tbn. 1 f f
Tbn. 2 f f f
B. Tbn. f f
Tba. ff ff
Timp. f Perc. 4 f mf
Pno. f
Vln. I f ppp Vln. II f ppp Vc. f ppp Cb. f ppp
29 238 Picc. mf p Fl. 1 f mf mp Fl. 2 f mf mp
Ob. 1 p
Ob. 2
Cl. 1 p Cl. 2 mp Bsn. 1 p Bsn. 2 mp
Cbsn. f mp
Tpt. 1 f mf mp
Tpt. 2 f mf mp
Tbn. 1
Tbn. 2
B. Tbn.
Tba. mf
Timp. Tom Toms Perc. 2 ff
Perc. 4 mp
Pno. cresc. ff
Vln. I
30 247 Fl. 1 p
Fl. 2 p
Cbsn. ppp
Tpt. 1 p
Tpt. 2 p
Tba. p ppp
Timp.
Perc. 2
Pno.
H 254 rit. Picc. ff Fl. 1 ff f Fl. 2 ff f Ob. 1 ff Ob. 2 f Cl. 1 f Cl. 2 ff
rit. Timp. ff D-Db, C-B, E-Eb, G-C Crotales Perc. 1 ff Perc. 2 ff Suspended Cymbal Perc. 3 ff Bass Drum Perc. 4 ff
Pno. fff
31 264 Fl. 1 mf Fl. 2 mp
Ob. 1 mf
Ob. 2 mf mp
Cl. 1 mp
Cl. 2 mf p
Cl. 3 p
I Senza misura q = 80 poco accel.
274 Cl. 1 ppp
Cl. 2 ppp
Cl. 3 ppp
Pno. p cresc.
(q = 160) molto rit. 274 Pno.
32 J Brash q = 100 accel. 275 Cbsn. f 7:8 Hn. 1 f 3 3 3 3 Hn. 2 f 5:4 3 Hn. 3 f
Hn. 4 f senza sord. 3 Tpt. 1 f 5 senza sord. Tpt. 2 f 3 3 3 senza sord. 3 Tpt. 3 f
Tbn. 1 f Tbn. 2 f B. Tbn. senza sord. f Tba. f f accel. Ratchet Perc. 3
Pno. ff
K q = 160 284 Picc. ff Fl. 1 ff Fl. 2 ff
Ob. 1 ff Ob. 2 ff Eng. Hn. ff Cl. 1 ff Cl. 2 ff Cl. 3 ff
Slap Stick Perc. 4 ff ff Pno.
33 (no decresc.) 289 Picc. 3 3 3 3 3 3 Fl. 1 3 3 3 3 3 3 3 3 Fl. 2 3 3 3 3 3 3
Ob. 1 3 3 3 3 3
Ob. 2 3 3 3 3 3
Eng. Hn. 3 3 3 3 Cl. 1 3 3 3 3 3 3 3 3 Cl. 2 3 3 3 3 3 3 Cl. 3 3 3 3 3 3 3 3
Pno.
294 ( ) Picc. fp ( ) Fl. 1 fp ( ) Fl. 2 fp ( ) Ob. 1 3 fp Ob. 2 ( ) 3 3 3 fp ( ) Eng. Hn. 3 3 fp ( ) Cl. 1 fp ( ) Cl. 2 fp ( ) Cl. 3 3 fp
chromatic cluster 3 56 7 Pno.
34 L Pulsating q = 120 298 Picc. fff Fl. 1 fff Fl. 2 fff Ob. 1 fff
Ob. 2 fff
Eng. Hn. fff Cl. 1 fff Cl. 2 fff Cl. 3 fff
1 Bsn. 2 f p Cbsn. f p
Use q. duration to open harmon mute 1 Tpt. 2 3 f 3 con sord. Tbn. 2 p con sord. f B. Tbn. p con sord. f Tba. f p Bass Drum Perc. 4 mf gliss. 5 5 5 Pno. fff gliss. 5 5 5 5 5 5 5 5 5 5 con 5 L Pulsating q = 120 pizz Vc. (non div.) pizz f Cb. f
305 5 5 5 5 5 5 5 5 Pno. 5 5 5 5 5 5 5 5
313 5 5 5 Pno. 5 5 5 5 5 5 5 5 6 5
35 320 6 6 5 5 5 6 5 5 5 6 5 Pno. 5 5 5 5 5 5 5 ff 5 5
327 5 5 5 5 5 6 Pno. 5 5 5 5 5
331 5 5 5 5 5 5 5 5 5 Pno. 5 5 5 5 5
M 336 a2 1 Tbn. 2 3 f 3 B. Tbn. f
5 5 5 5 5 5 5 3 5 5 5 3 5 5 Pno. 5 5 5 5 5 5 5 3 5 5 5 3 5 5 M Vc. 3 f Cb. 3 f
36 342 a2 1 Fl. 2 3 f 3 1 a3 Cl. 2 3 f
senza sord. 3 1 Tbn. 2 f senza sord. 3 B. Tbn. f
3:2 3:2 3:2 3:2 6 4:3 4:3 4:3 4:3 4:3 4:3 4:3 4:3 4:3 4:3 5 5 5 5 5 5 3 5 5 5 5 Pno. 5 5 5 5 5 5 3 5 5 5 5 6 Vln. I f 3 3 Vln. II f Vc. 3 f Cb. 3 f
347 1 Fl. 2 3 f 3 1 Cl. 2 3 f Hn. 1 f Hn. 3 f senza sord. Tpt. 1 f 1 Tbn. 2 3 f 3 B. Tbn. f
3:2 3:2 3:2 3:2 3:2 3:2 4:3 6 3 4:3 6 3 4:3 6 4:3 4:3 4:3 5 5 5 5 5 Pno. 5 6 5 5 5 5 5 5 6 3 6 3 Vln. I f 3 3 Vln. II f div. Vla. f Vc. 3 f Cb. 3 f
37 350 1 Fl. 2 3 f
1 3 Cl. 2 3 f 1 Hn. 2 f 3 Hn. 4 f 1.2. senza sord. 1 Tpt. 2 3 f 1 Tbn. 2 3 3 f 3 3 B. Tbn. f
3:2 3:2 3:2 3:2 6 66 6 4:3 4:3 4:3 4:3 5 5 5 5 Pno. 6 6 6 6 5 5 5 5 Vln. I 3 f 3 Vln. II f Vla. f Vc. 3 3 f Cb. 3 3 f
38 352 Fl. 1 5 5 Fl. 2 5 5
5 5 1 Cl. 2 3 1 5 5 Hn. 2
3 5 5 Hn. 4 a3 senza sord. 1 Tpt. 2 3 f 5 5
1 Tbn. 2 5 5
5 5 B. Tbn.
senza sord. 5 5 Tba. f
3:2 3:2 3:2 3:2 6 6 66 4:3 4:3 6 4:3 4:3 5 5 5 5 Pno. 6 6 6 6 6 5 5 5 5 Vln. I 5
5 Vln. II Vla. 5
Vc. 5
Cb. 5
39 molto rit. 354 Picc. 333333 f cresc. Fl. 1 333333 cresc. Fl. 2 3 3333 3 cresc. 3 3 3 1 33 3 Ob. 2 f cresc.
Eng. Hn. f cresc. 1 Cl. 2 3 cresc. 1 Bsn. 2 f cresc. Cbsn. f cresc. 1 Hn. 2 cresc. 3 Hn. 4 cresc.
1 Tpt. 2 3 cresc. 1 Tbn. 2 cresc.
B. Tbn. cresc.
Tba. cresc.
3:2 3:2 3:2 3:2 4:3 4:3 664:3 4:3 5 5 5 5 Pno. 6 6 5 5 5 5
molto rit. div a3 Vln. I cresc.
div a3 Vln. II cresc.
Vla. cresc.
div Vc. cresc.
div Cb. cresc.
40 N
Powerful q = 112 355 Picc. ff a2 1 Fl. 2 ff a2 1 Ob. 2 ff Eng. Hn. ff 1 a3 Cl. 2 3 ff 1 Bsn. 2 ff Cbsn. ff 1 Hn. 2 ff 3 Hn. 4 ff 1 Tpt. 2 3 ff 1 Tbn. 2 ff B. Tbn. ff Tba. ff Timp. f
Anvil Perc. 1 ff Brake Drum Perc. 3 ff
Bass Drum Perc. 4 ff
7
5 6 3:2 3:2 5 4:3 4:3 Pno. 5 ff 5 5 N
Powerful q = 112 div. Vln. I tutti ff
tutti div. Vln. II ff
Vla. ff Vc. ff Cb. ff
41 molto rit. 358 Picc. sfp 1 Fl. 2 sfp 1 Ob. 2 sfp Eng. Hn. 1 Cl. 2 3 1 Cl. 2 sfp Cl. 3 sfp 1 Bsn. 2 Cbsn. 1 Hn. 2 Hn. 1 sfp 3 Hn. 4 1 Tpt. 2 3 Tpt. 1 sfp
Tpt. 2 sfp Tpt. 3 sfp 1 Tbn. 2 B. Tbn. Tba. Timp. ppp Perc. 1 Suspended Cymbal Perc. 2 ppp Perc. 3 Perc. 4
Hp. f gliss. LMLOLMML cresc. 8:6 20 12 ff Pno.
molto rit. tutti div. gliss. tutti Vln. I ppp tutti div. tutti gliss. Vln. II ppp tutti gliss. Vla. ppp tutti Vc. gliss. ppp Cb. 42 O Soaring q = 80 361 rit. l.v. Timp. Db-D, Eb-A f l.v. Perc. 2 ff gliss. Hp. ff
Pno. fff
O
Soaring q = 80 rit. gliss. div. Vln. I ff fff ff f gliss. Vln. II ff fff ff f gliss. Vla. ff fff ff f
Vc. ff fff ff f tutti Cb. ff fff ff f
Q P Senza misura Driving q = 160 369 ca. 20" Pno. f
one by one (on conductor's cue) Q players gliss to D4 P taking 2"-4". gliss freely - unsteady rhythm gliss. q = 120-200 - bow as necessary ca. 20" Sul G gliss. Vln. I p gliss. Sul G Vln. II gliss. p
gliss. Vla. p
Sul A gliss. Vc. gliss. p Sul G gliss. Cb. gliss. p
43 374 Timp. mp
Pno.
Vln. I ppp
Vln. II ppp
Vla. ppp
pizz Vc. ppp f pizz Cb. f
380 Timp.
Pno.
Vc.
Cb.
R 385 a2 1 Ob. 2 mf a2 1 Cl. 2 mf Marimba Perc. 1 ff
Pno.
cresc. R pizz. Vln. I mf f f
Vln. II mf f Vla. mf f Vc. mf f
44 389 1 Ob. 2 1 Cl. 2
Perc. 1
Pno. mf
Vln. I pizz. Vln. II f
S 393 Picc. 6 mf f Fl. 1 mf 6 f 1 Ob. 2 6 f 1 Cl. 2 6 f
Perc. 1
6 6 Pno. f f 6 S arco Vln. I 6 f arco 6 Vln. II f Vla. 6 f Vc. 6 f
397
Hp.
6 6 6 6 6 6 6 Pno. mp
arco Vc. mp arco Cb. mp
45 T 401 1 Fl. 2 f Timp. mf f Pno. mf mf T Vln. I f Vln. II f arco f Vla. mf f Vc. mf f Cb. 3 3 3 mf f 3 404 Picc. f 1. 1 Fl. 2 f
a2 1 Cl. 2 f f Timp. Xylophone Perc. 2 f Vibraphone Perc. 3 f
7 Pno. 7
Vln. I f Vln. II f
Vla. Vc. Cb.
46 U 408 Picc.
a2 1 Fl. 2 mf a2 1 Ob. 2 mf 3 3 3 3 Cl. 1 mf Cl. 2 a2 1 Bsn. 2 mf Tbn. 1 mf
Pno. ff
U Vln. I mf
Vln. II mf Vla. mf 3 3 3 3
413 Picc. mf 1 Fl. 2 1 Ob. 2 3 3 3 3 3 3 3 3 3 333 3 3 Cl. 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 Cl. 2 mf 1 Bsn. 2 gliss. Tbn. 1 Timp. f Xylophone Perc. 2 mf Vln. I Vln. II
Vla. 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
47 V 418 Picc. f 1 Fl. 2 f 1 Ob. 2 f Cl. 1 f Cl. 2 f 1 Bsn. 2 f Tbn. 1 Timp. A-Gb Perc. 2 Pno. f V Vln. I
Vln. II
Vla.
W 423 a3 1 Cl. 2 3 f 1 con sord. Hn. 2 f 3 con sord. Hn. 4 f a3 1 con sord. Tpt. 2 3 f
Pno. ff W Vln. I f Vln. II f Vla. f
48 428 1 Cl. 2 3 1 Hn. 2 3 Hn. 4 1 Tpt. 2 3
Pno. Vln. I Vln. II Vla.
X 432 1 Cl. 2 3 senza sord. 1 Hn. 2 ff ff 3 senza sord. Hn. 4 ff ff 1 Tpt. 2 3 1 a2 Tbn. 2 ff ff B. Tbn. ff ff Tba. ff ff Timp. ff Crotales Perc. 1 ff Bass Drum Perc. 4 4:3 4:3 4:3 4:3 ff Pno. ff X Vln. I Vln. II Vla. Vc. f
49 436 1 Hn. 2 ff ff ff
3 Hn. 4 ff ff ff 1 Tbn. 2 ff ff ff B. Tbn. ff ff ff Tba. ff ff ff
Timp.
Perc. 1 Perc. 4
Pno.
Vln. I Vln. II Vla.
Vc.
50 Y 441 a2 1 Bsn. 2 ff Cbsn. ff
Hn. 1 ff Hn. 2 ff Hn. 3 ff Hn. 4 ff senza sord a3 1 Tpt. 2 3 ff a2 1 Tbn. 2 ff B. Tbn. ff Tba. ff
Timp. f Suspended Cymbal l.v. Perc. 1 ppp ff Chimes Perc. 2 ff Chimes Perc. 3 ff Bass Drum Perc. 4 f
gliss. Pno. gliss. fff cresc.
Y
Vln. I Vln. II Vla.
Vc.
Cb. ff
51 Z (x = x) 447 Eng. Hn. f 1 Bsn. 2 ppp
Cbsn. ppp
Hn. 1 ppp Hn. 2 ppp Hn. 3 ppp Hn. 4 ppp 1 Tpt. 2 3 ppp 1 Tbn. 2 ppp B. Tbn. ppp Tba. ppp Timp. B-B , A-F, C-A ppp b b Marimba Perc. 1 f Perc. 2 Perc. 3
Snare Drum Perc. 4 f ppp Z (x = x) Vln. I ppp Vln. II ppp Vla. ppp Vc. ppp
Cb. ppp
52 454 Ob. 1 f
Eng. Hn. Cl. 2 f
Bsn. 1 f
Bsn. 2 f
Tpt. 2 f
Tbn. 2 f
Perc. 1
Vln. II f
Vc. f
53 461 Picc. f Fl. 1 f Fl. 2 f Ob. 1
Ob. 2 f
Eng. Hn. Cl. 1 f Cl. 2 Cl. 3 f Bsn. 1
Bsn. 2
Cbsn. f Hn. 1 f Hn. 2 f Hn. 3 f Hn. 4 f Tpt. 1 f
Tpt. 2
Tpt. 3 f Tbn. 1 f Tbn. 2
B. Tbn. f
Tba. f
Timp. p Crotales Perc. 1 ff Tam-tam Perc. 2 p Chimes Perc. 3 ff Glockenspiel Perc. 4 ff Vln. I f f Vln. II f Vla. f f Vc.
Cb. f
54 (no rit.) 467 Picc. Fl. 1 Fl. 2
Ob. 1 Ob. 2
Eng. Hn. Cl. 1 Cl. 2 Cl. 3 Bsn. 1 Bsn. 2
Cbsn. Hn. 1 Hn. 2 Hn. 3 Hn. 4 Tpt. 1 Tpt. 2
Tpt. 3
Tbn. 1 Tbn. 2 B. Tbn. Tba. Timp.
Perc. 1 Perc. 2
Perc. 3 Perc. 4 (no rit.) Vln. I Vln. II Vla. Vc. f
Cb.
55 AA Triumphant q = 80 471 Picc. ff 1 Fl. 2 ff 1 Ob. 2 ff
Eng. Hn. ff 1 Cl. 2 3 ff 1 Bsn. 2 ff
Cbsn. ff 1 Hn. 2 ff
3 Hn. 4 ff Tpt. 1 ff
Tpt. 2 ff Tpt. 3 ff 1 Tbn. 2 ff
B. Tbn. ff
Tba. ff Timp. f p
Perc. 1
Perc. 2 ff
Perc. 3
Perc. 4 11 11 11 11 Pno. ff
AA Triumphant q = 80 Vln. I ff Vln. II ff Vla. ff
Vc. ff
Cb. ff
56 473 Picc.
1 Fl. 2
1 Ob. 2
Eng. Hn.
1 Cl. 2 3 1 Bsn. 2
Cbsn. 1 Hn. 2
3 Hn. 4
Tpt. 1 Tpt. 2 Tpt. 3 1 Tbn. 2
B. Tbn.
Tba.
Timp. f
11 11 11 11 Pno.
Vln. I Vln. II
Vla.
Vc.
Cb.
57 molto rit. 475 Picc. cresc. 3 1 Fl. 2 cresc. 3 1 Ob. 2 cresc.
Eng. Hn. cresc. 1 Cl. 2 3 cresc.
1 Bsn. 2 cresc. Cbsn. cresc. 1 Hn. 2 cresc. 3 Hn. 4 cresc. Tpt. 1 Tpt. 2 Tpt. 3
Tbn. 1 cresc. Tbn. 2 cresc. 3 3 B. Tbn. cresc. Tba. cresc. 3 Timp. ff D-Db, F-Eb
Chimes Perc. 2 3 ff Chimes Perc. 3 3 ff 12 9 12 12 9 9 3 Pno. 3 molto rit.
Vln. I cresc. 3 Vln. II cresc. 3 3 Vla. cresc. Vc. cresc. Cb. cresc.
58 BB Relentless q = 160 478 Pno. mf cresc.
CC 482 Picc. ff 6 6 6 1 Fl. 2 ff 666 Ob. 1 6 6 6 ff Cl. 1 ff 666 fp Cl. 2 ff 666 Cl. 3 6 6 6 ff Bsn. 1 fp Cbsn. fp Hn. 1 gliss. fp 1 Tpt. 2 3 ff gliss. Tbn. 1 ff gliss. Tbn. 2 ff B. Tbn. gliss. ff fp Timp. mp gliss. Flexatone gliss. Perc. 1 ff Tam-Tam Perc. 2 p Slapstick Perc. 4 ff
Hp. LMLOLNLL ff Pno. fff ff CC
sul A gliss. (l.h. pizz) Vln. I ff sul A gliss. (l.h. pizz) Vln. II ff gliss. sul A (l.h. pizz) Vla. ff gliss. sul A (l.h. pizz) arco Vc. ff div a4 Cb. p
59 486 Fl. 1 fp Fl. 2 fp Ob. 1 fp fp Ob. 2 fp Eng. Hn. fp Cl. 1 Cl. 2 fp Cl. 3 fp Bsn. 1 fp fp Bsn. 2 fp Cbsn.
Hn. 1 fp Hn. 2 fp Hn. 3 fp Hn. 4 fp
Tpt. 1 fp Tpt. 2 fp Tpt. 3 fp Tbn. 1 fp Tbn. 2 fp B. Tbn.
Tba. fp
Timp. Perc. 2
Hp. Pno. div a4 arco Vln. I p arco div a4 Vln. II p ( ) arco div a4 Vla. p ( ) div a4 Vc. p ( ) Cb.
60 DD Chaotic q = 144 490 Picc. fff 3 1 Fl. 2 3 fff 3 1 Ob. 2 fff 3 Eng. Hn. fff 1 Cl. 2 3 3 fff a2 1 3 3 3 Bsn. 2 fff 3 3 3 Cbsn. fff
1 Hn. 2 fff 3 3 Hn. 4 fff 3 1 Tpt. 2 3 3 fff 3 3 1 3 a2 Tbn. 2 3 fff 3 3 B. Tbn. fff 3 3 3 Tba. fff 3 Timp. Db-D§ ff Anvil 3 3 3 fff Perc. 1 ff Tom-toms 6 l.v. Perc. 2 3 6 ff fff Brake Drum 3 dampen tam-tam Perc. 3 ff 3 3 3 Bass Drum Perc. 4 ff
forearm cluster - chromatic palm cluster - white notes 6 6 3 Pno. fff sfffz 3 Chaotic q = 144 DD non div. 3 Vln. I fff non div. fff 3 non div. fff 3 Vln. II non div. fff 3 non div. Vla. fff 3 non div. 3 fff 3 3 3 non div. fff Vc. 3 3 non div. 3 fff 3 3 non div. 3 fff Cb. 3 3 non div. 3 fff March 2003 61 INTRODUCTION
I have long had the desire to compose a piano concerto. As a piano performance major during my undergraduate and masters years I competed in several piano concerto competitions and was fortunate enough to win a few of them. This, in time, led to the opportunity of performing piano concerti with several orchestras. All this experience helped me gain an appreciation for well-written “competition-winning” piano concerti. My experience playing Gershwin’s Rhapsody in Blue and Concerto in F, Corigliano’s Concerto for Piano and Orchestra, Ravel’s Piano Concerto in G Major, and Ginastera’s Concerto for Piano and Orchestra left wonderful impressions on my mind, sparking the aspiration to compose a piano concerto of my own some day. Before I began working on the concerto, I knew from my competition experience how exciting and rewarding a powerful ending can be for both the performer and audience. Because I wanted to create such an ending in my concerto, my focus began at the end. For years I had been playing a percussive “ditty” on the piano that had promise as closing material. I am also very interested in symmetry as a compositional tool and decided to use it as an underlying factor in the concerto. This fit in well with my plans, for the little “ditty” possesses symmetry of its own, establishing the core concept for the ending of the concerto. From this foundation, I began conceptualizing the rest of the piece. I became interested in symmetry in the Fall of 2001 while working on my first string quartet (Tetrasomia). Although I was already employing symmetrical ideas in this piece, I became further interested in their use when I began studying Bartok’s Fourth String Quartet and learned of the importance of symmetry therein. Like my string quartet, this piano concerto is symmetrically centered around the pitch D4. This works
62 out well on the piano, for not only are the pitches symmetrical in interval, but are visually symmetrical as well.
Example No. 1
Although symmetry is an important element throughout the concerto, it does not dominate the entire piece. Whereas I use symmetrical sets with varying degrees of consonance, I also “break free” of this symmetry from time to time. My approach to symmetry involves a focus on tonal or modal symmetrical sounds in opposition to the more chromatic “dissonant-sounding” possibilities, which symmetry easily allows. It is perhaps true that during the act of playing simultaneous random sounds at the keyboard, dissonant harmonies are more often encountered than consonant ones. If symmetry is the only guideline for this same practice, much of the same result would occur. My goal was to use symmetrical pitch sets and to search for “pleasant” harmonies and melodies, and contrast them with the more dissonant possibilities. As a result, symmetry replaces the use of a key, so instead of a Concerto in D, for example, I have composed a Concerto in Symmetry, in which D acts as the pitch center. Another concept I focus on in my concerto is the use of proportions, contractions and expansions of both meter and rhythm. Throughout the concerto there are many
63 instances of time signatures expanding or contracting the length of a measure, and additions or subtractions governing the number of chord or pitch repetitions. The first measure of the concerto (the introductory piano cadenza) introduces some of the symmetrical and numerical concepts found throughout the concerto. While most of the numerical processes in this concerto, mostly of addition and subtraction by one, are somewhat simple, the likelihood of the audience hearing (or at least “feeling”) these simpler deviations is far greater than if I used more involved mathematical formulae to create rhythmic variation and development. The orchestration consists of a standard size orchestra. The wind section includes piccolo and two flutes, two oboes and English horn, three clarinets, two bassoons, and contrabassoon. The brass section employs four horns, three trumpets, two tenor trombones, bass trombone, and tuba. The percussion involves the use of four players whose instrumentation includes glockenspiel, xylophone, vibraphone, marimba, two sets of chimes, crotales, bass drum, tam-tam, snare drum, suspended cymbal, tom toms, slap stick, flexatone, anvil, brake drum, ratchet, and bell tree. The instrumentation also includes five timpani, harp, standard strings, and, of course, piano. I have always had a fondness for single-movement works and therefore decided to compose this piano concerto in one movement. Usually I have some sort of programmatic notion in my compositions, but this piano concerto breaks from that practice.
64 ANALYSIS
OPENING SECTION
As I have stated, most of the piece is symmetrical around D, and more specifically D4. The concerto begins with a piano cadenza of intense force, commanding the listener’s attention. The piano introduction, before the entrance of the orchestra, can be divided into three main parts. The first part begins with A0, the lowest possible note on the piano, followed by G7, the symmetrical counterpart of A0. After the pitch A1 is added in the left hand, the right hand mirrors the left with G6. Following this, another octave is added, and both hands are employed to accomplish the addition of symmetrical pitches in both registers. The upper register’s symmetrical imitation of the lower register continues as more and more pitches are added until both hands are playing five-note chords in the extreme registers of the piano (See Example No. 2 below). As a means of creating even greater forcefulness and intensity, grace-note chords are systematically added to the beginning of these chordal outbursts. The lower register has two unanswered instances of this before the upper register responds with its own grace-note chord. Then the systematic repetition continues as both registers add two and three grace-note chords, respectively. Up to this point the only pitches involved have been the white notes excluding B and F – the pentatonic collection. With these two pitches omitted, the two most dissonant intervals – the tritone and the minor second (and major seventh) – have been avoided.
65 Example No. 2
The second part (first system, p. 2) introduces the previously mentioned dissonance. With the grace-note chord count rising to four, the hands separate, and both registers resound together for the first time. However, the grace-note chords are no longer foreshadowing the same chord, but are announcing the arrival of symmetrical dissonance. The left hand moves up to B0 and Bb1 while the right hand goes down to F#6 and F7. Pitches B and F are now introduced as well as the black-note counterparts (Bb and F#). More dissonant intervals (the tritone and the minor second) and the black-note
“realm” are introduced simultaneously.
66 Example No. 3
Following this swift transitional chord is a black-note contrasting gesture to C#4 and D#4 (Example No. 3). This occurs two more times, with the only difference being an additional grace-note chord before each. After the third utterance, the arrival at C#4 and D#4 is not sustained as both hands rise together in diminished-seventh arpeggios a major second apart, ending at the extreme high register of the piano; A#7 and C8 (the
enharmonic equivalent of a major second).
Example No. 4
In the introduction’s third part, the music returns to the middle register of the keyboard. No longer employing C#4 and D#4 as an intervallic center, it is expanded
67 outward by a minor second to C4 and E4. Once again pitches are symmetrically added to each hand. This time, however, the addition of pitches occurs in an outward direction simultaneous in both hands and involves more dissonance than the pentatonic gestures at the outset of the piece.
Example No. 5
These expanding gestures arrive on a chord that contains the previously avoided pitches B and F, as well as the E and C from whence they came. Each chord reaches a total of five notes before beginning again on the same two pitches. This chord is repeated four times before an extra pitch is added to each hand. A written-out accelerando continues as the chord is repeated five times before the final pitch is added to each hand. A bass drum and tam-tam roll join in as the repetition of this chord accelerates and builds intensity into the introduction of the full orchestra.
68 The orchestra makes a powerful entrance and is symmetrical as well. After the initial Ds on the downbeat in the low register, the axis moves up an octave and a tritone for the accented chordal response occurring on beat 3. This is in keeping with a familial axis, D and Ab sharing the same symmetry.
Example No. 6
The low Ds sound again, followed by two chords, which now converge on the D axis by semitone. The low Ds respond in the next measure by expanding by semitones to a sustained Eb and Db dyad as the piano continues with symmetrical virtuosic cadenza
material.
Example No. 7
69 After this display the orchestra part returns with material similar to its entrance. However, this time the accented chords spread outward by semitone, while the low Ds expand even further to a sustained tritone (B and F), over which the piano performs a rather difficult octave section. The next full orchestral entrance imitates a previous part of the piano introduction (2nd system, p. 2) before reaching a repeated chord with a written-out accelerando, much like before. This repeated chord, however, accelerates at three levels.
Example No. 8
The most obvious of these is the actual accelerando indicated in m. 11. The second is the written-out accelerando which involves the orchestra beginning with half notes, followed by half-note triplets. This is imitated twice in diminution, followed by four sixteenths and five sixteenths, respectively, before reaching the measure of fermata (m. 15). While this is going on, the piano part follows a different pattern. Each two beats that pass involve the piano part playing one additional utterance of a chord. The hands are spread at the extreme registers like at the beginning of the concerto, but move inward every two beats to a different, symmetrical chord. Also, pitches are added much like before, reaching five pitches per hand by m. 13. In the final measure before the fermata (m. 14), the repeated chords are replaced by trilled chords that ascend together into the high
70 register of the piano, reaching a highly dissonant, raucous trill as the orchestra also makes its frenzied arrival at the measure of fermata. A measure of rest follows to allow the listener to reflect on what just took place, and to imagine what might possibly lie ahead.
71 REHEARSAL LETTERS A THROUGH C
Rehearsal Letter A
As a means of relief, the following section (Rehearsal Letter A, beginning in m. 17) is quite subdued. The orchestration begins with woodwind quintet, triangle, harp, and solo strings. D4 is the first pitch sounded, followed by C3 and E5. The next two pitches, however, do not follow the usual scheme of symmetry, introducing the first example of what I term “combined symmetry.” This involves a group of notes that do not form symmetry by themselves, but create symmetry when combined with a nearby group of notes. In mm. 18-19, Bb1 and F6 are introduced, but are not symmetrical to D4. In m. 20 D4 returns, followed by E5 and C3. This time, however, F#6 and B1 replace their symmetrical counterparts. These two pairs of pitches are symmetrical to each other.
Example No. 9
I first experimented with this concept of combined symmetry in my string quartet. In it, as a scale is being repeated up and back from A3 to D5, the pitches being employed alternate between those of B-natural minor and Bb major. The B and C# offset the Eb and F, while the Bb and C do the same to the E and F#. Together the two scales form a symmetrical bond.
72 Example No. 10
In the concerto, I use this concept as a way to incorporate some tonal elements while maintaining a symmetrical basis. The main musical theme (Theme 1) of the entire concerto is introduced in mm. 26-28 by the solo clarinet. While the outer pitches (G1 and A6 - an inversion of the beginning pitches of the concerto) are sustained from the previous section, the clarinet begins the main theme on the primary axis of D4. This is a symmetrical theme, using each “white-key” pitch class. The first three measures of this melody contain the thematic material that is used throughout the concerto.
Example No. 11
73 The second part of the melody (mm. 52-56) does not return until Rehearsal Letter AA (m. 471), an intense climatic section of the work. The melody in its entirety radiates a sense of hope as the clarinet searches high and low before eventually locating its resting spot an octave below its beginning pitch.
Rehearsal Letter B
At Rehearsal Letter B (m. 36) the secondary theme (Theme 2) is introduced by the cello section, and the piano makes its first entrance since the cadenza. The piano part acts as an accompaniment, while its pitch content is based on the primary theme.
Example No. 12
The left hand echoes each pitch of the right hand except for the final pitch. At this moment the left hand begins the theme and the right hand imitates, continuing the pattern. The cellos are divisi: the upper part has the melody while the lower is in symmetry. By m. 42 the violins and basses relieve the cellos due to the range considerations caused by the outward expansion of the two lines. The piano part has a small written-out accelerando propelling into m. 46, at which point the string section expands into symmetrical six-note chords. Here, the right hand is relegated to continue a
74 somewhat imitative version of the accompaniment performed previously by both hands. However, as the musical line reaches its valleys and peaks, the intervals between the imitated pitches are reduced each time by one step, resulting in fourths by the middle of m. 51. Also, the piano part avoids playing any Ds throughout this section, and the intervals are altered where necessary to avoid this pitch.
Example No. 13
The piano part throughout Rehearsal Letter B begins with all white notes, but pitches are altered in order to conform to the symmetrical harmony being produced in the strings. I call this “altered symmetry.” The concept of symmetry is still the overriding factor, but rules are bent in order to maintain pitch consistency between the piano and orchestral parts.
75 Rehearsal Letter C
Rehearsal Letter C (m. 62) begins with the piano, in an accompanying role, emerging from the chord being sustained from the previous section. The tempo is slightly faster and the alternating meters of 3/4 and 7/8 add a gentle bounce to the section’s beginning. Both the right hand and left hand parts in the piano use combined symmetry. The piano part alone introduces the accompaniment, but soon fades out as the string section takes over. Beginning in m. 70, three aspects control the piano part. The piano begins with a transposed retrograde version of the primary theme in octaves (A). This is followed by a rising dissonant “push” (B -- a variation on the third part of the piano’s introduction). A transitional flourish of sixteenth notes in stepwise, parallel quintal harmonies (C) returns the piano part to the main theme, no longer in retrograde and harmonizing itself in the left hand at the interval of a major second (m. 77).
Example No. 14
76 Another stepwise sixteenth note flourish follows, this time in quartal harmony (m. 81). Now, in m. 82, the piano part is displayed in thirds and, in m. 89, fourths and fifths. Interval expansion is the overriding factor of the piano part in this section, much like the earlier interval contraction in mm. 46-51. Throughout this section, I also wanted to do something uncommon in piano concertos; coloring the solo line with a woodwind texture. As the melodic line reaches different levels and intensities, the orchestral timbre changes ever so slightly. As the section nears its end, the strings fade out as the music rises up in the woodwinds and piano to the upper register. This is where the next section begins.
77 REHEARSAL LETTER D
Beginning with a bright, shimmering orchestration and diminishing in both range and intensity throughout its length, Rehearsal Letter D (m. 92) employs several methods of organization to control its shape and flow. The section’s main framework consists of two three-note chords of quintal construction in each measure; the lower chord ascends by semitone as the upper chord descends by the same interval. Since the distance between the two sets of pitches is four semitones, the chords exchange positions after five measures. I have numbered the voices of the chords from bottom to top (1 to 6, respectively) for analysis.
Example No. 15
The pattern of beats per measure throughout the section is as follows:
Example No. 16
Mm. Beats per measure 92-96 54321 97-102 45321 102-106 34521 107-111 23451 112-116 12345
78 In the first five measures of the section the high descending quintal chord group consists of piccolo and flutes 1 and 2 (mm. 92-96), while the lower group begins with the clarinets. Following this, the descending chord group drops down an octave, and clarinets replace the flutes and piccolo. The pattern continues as shown below (Example No. 17).
Example No. 17
The strings at Rehearsal Letter D are called upon to play high harmonics following the same chordal pattern described above. However, like the woodwinds, the strings do not maintain the same position in each five-measure grouping. In fact, the strings never repeat the same five-bar pattern, but maintain a structural symmetry as shown below (Example No. 18).
79 Example No. 18
The piano part in this section uses only four of the six notes from the two chords, producing two-note tremolos in each hand. Each five-bar section in the piano part uses a different arrangement of four of the six pitches, each pitch following the same semitone ascent or descent as in the orchestral part. In the piano part, each pitch position is used a total of six times. As the section nears the end in mm. 117-120, a different arrangement of four of the six pitches changes each measure.
Example No. 19
mm. 92-6 97-101 102-6 107-11 112-6 117 118 119 120 666 666 = 6 555555 = 6 4 4444 4= 6 33 3 3 33= 6 222222= 6 111 111= 6
80 Example No. 20
The glockenspiel takes the place of one woodwind instrument per measure (an octave higher), creating both a coloristic effect for this section and a chance for the instrumentalists to breathe. The glockenspiel part changes position each measure, starting in position 1 and continuing in opposite numerical order (i.e. 6, 5, 4, etc.).
Example No. 21
81 In this section I was also searching for a defining, methodical embellishment in the piano part, and my decision was to employ grace notes. The grace notes follow their own numerical layout, while pitch-choice is defined as follows. Each five-bar repetition of the five-chord exchange pattern involves some repetition of pitches identical in both the ascending and descending lines. These pitches are A, B, and Bb, and are excluded as grace notes, while E is also excluded as it is the centrally introduced, non-repetitive pitch. The remaining pitches in order (based on the ascending pattern) are G, D, Ab, Eb, F, C, F#, and C#.
Example No. 22
I avoided using grace notes in every measure for the sake of variety and ease. Each measure of 1/4 is denied grace notes due to the short length of these measures, while the first measure in each five-measure grouping is without embellishment as well, due in part to its following the short measure of 1/4. This leaves fifteen measures to be accounted for. The first of these fifteen measures contains one grace note (m. 93), followed by two in the second, and so on, until the middle of the fifteen measures is reached, which has the highest grace note count of eight (m. 104). Then each following measure reduces the total by one, returning to one grace note by the final measure involved (m. 116). The placement of the grace notes in the right and left hand is as follows: (the vertical lines indicate bar lines and the numbers indicate the order of the grace-note’s appearances)
82 Example No. 23
The pitch order of the grace notes (G, D, Ab, Eb, F, C, F#, C#) is not maintained,
but is altered much like the time signatures’ arrangement in this section is altered. While the time signatures, grouped in five-bar sets, make a complete reversal after five cycles, the order of the grace-note pitches follows the same pattern, but the number eight controls the formula. The chart below demonstrates how each eight-note group involves the use of a new pitch in the hierarchy. In other words, as each new row emerges, the closest pitch to the beginning that has not yet been the first pitch becomes the first pitch for the next row, while the remaining pitches maintain their order. This formula works out so that no matter how many pitches (or time signatures) are being accounted for, it takes that same number of times for the order of the pitches (or time signatures) to be reversed.
Example No. 24
83 A somber English horn solo marks the end of this section (mm. 120-127) and introduces the main theme (Theme 3) for the upcoming slow section.
84 REHEARSAL LETTERS E AND F
Rehearsal Letter E
The slow section of the concerto (Rehearsal Letter E, m. 126) is the most “tonal” sounding of all the sections. The left hand remains symmetrical throughout most of the section, starting with the first two pitches of the concerto – G and A. This repeated accompaniment figure, beginning with a dyad consisting of G3 and A3 followed by D4, expands outward; G3 and A4 expands to F3 and B5, while D5 expands to C5 and E5. The right hand has the melody (Theme 3), which is actually a transformation of the main theme reduced to just five pitches.
Example No. 25
The piano part becomes slightly more involved beginning in m. 136 as a solo cello is called upon to perform a rendition of Theme 2. In mm. 144-145, the piano part maintains octave-equivalent symmetry offset by differing rhythms in each hand, while the flutes imitate the right hand a beat later.
85 Example No. 26
Two dissonant symmetrical flourishes expand outward (mm. 148-149), catapulting the music into virtual chaos.
Rehearsal Letter F
This is interrupted by a light, innocent waltz in the strings, introduced at Rehearsal Letter F (m. 150). The melody in the first violins is a transformed version of Theme 3, while the accompaniment involves pizzicato in the rest of the section. The phrases are five, four, three, and two measures long, respectively, and each contains eight notes that maintain a similar shape. During these measures, the theme attempts to return to its original pitch level (Bb, C, D, E, F) as each of the phrase’s beginning pitches is a minor second higher than the one before.
86 Example No. 27
The piano makes its entrance in m. 164 and sounds as if it will be returning to the original pitch level of Theme 3. This, however, is not the case as the piano part begins on Db just as the first violins had, but eventually does return to the D combined symmetry by m. 174. Following this, the outward expanding flourishes return with woodwind reinforcement, no longer deceiving the listener as they send the music into controlled chaos.
87 REHEARSAL LETTER G
At the beginning of Rehearsal Letter G (m. 200), the harmony from Rehearsal Letter E returns with pitches G and A inverted. The music is no longer subdued (as before), but brash, demanding attention. The dyad of A and G is sounded twice at the dotted half note, followed by the F-B dyad three times in half notes. This pattern of addition by one dyad continues, with four and then five dyads presented, each evenly spaced within six beats.
Example No. 28
This section involves eight different repetitive melodic lines, each a transformation of one of the first three themes. One line at a time is introduced and continues as a new one is added. However, the number of measures before the introduction of a new line lessens by one each time. As soon as all eight of the lines have reached fruition, they each are removed from the texture, one by one, starting with the chordal framework in the strings. The elimination of lines, however, is spaced by beats rather than measures. The basses are the first instruments eliminated following one measure after the introduction of the timpani part (the last of the eight lines being successively added). Following this, the cellos exit two beats after the basses. Then three beats pass before the third part (Vln. II) is eliminated. This pattern continues until every line is gone except the piano and the percussion.
88 Example No. 29
Mm. 87654321
Ob. 1.2, Vla. Cl. 1.2., Bsn. 1.2. Picc., Glock. Tbn. 1.2., B. Tbn. Fl. 1.2., Tpt. 1.2. Piano (Theme from Waltz) Cbsn., Tba. Timp.
Beats 12345678910 Cb. Vc. Vln. II Vln. I Ob. 1.2. Cl. 1.2., Bsn. 1.2. Picc., Glock. Tbn. 1.2., B. Tbn Fl. 1.2., Tpt. 1.2 Cbsn., Tba.
89 Example No. 30
Example No. 31
Group Note Count Note Value Duration (beats) 85 Eighth-note 2 1/2 75 Eighth-note 2 1/2 610 Eighth-note 5 511 Quarter-note 11 4 5*7 1/2 45 r.h. ** 9 4 l.h. 6 212 Dotted quarter 11 1/2 15 Half-note *** 10
* Durations change and follow same pattern used with alteration of time signatures at Rehearsal Letter D. ** See below. *** Pitches change every half-note value, but rhythmic values get systematically added with each repetition.
90 The piano part of Rehearsal Letter G (beginning in m. 229) consists of two main elements. The melody is based on the theme from the waltz section and is presented in octaves in the right hand. While this repeated melody consists of five notes, a symmetrical pattern contained inside the octave melody embodies a four-note pattern. This same four-note pattern is used in the left-hand accompaniment as well. However it neither synchronizes rhythmically with the right hand representation nor is it presented in the same order.
Example No. 32
The melody at the onset lasts for three bars and is repeated twice. The following two times, the melody is reduced to dotted quarters (m. 235), now totaling only five measures compared to the previous six. The next two repetitions of the melody reduce the rhythm of the right hand to alternating quarter and eighth notes (m. 240), decreasing the number
91 of bars once again by one. This is followed by a representation of the melody in eighth- notes (m. 245), repeated six times in order to complete a cycle, synchronizing the beginning of the measure with the beginning of the pitch pattern.
Example No. 33
During this, the left hand accompaniment changes in accordance with the melody, but follows its own patterns. First the left-hand rhythm resembles that of the accompanimental rhythms towards the end of Rehearsal Letter F. The four-note pattern (C#, D#, C, E) cycles through three times in the left hand as opposed to two in the right.
As the rhythm in the right hand reverts to dotted quarter notes (m. 235), the accompaniment avoids coinciding with the melody. As the right hand melody reverts to the use of quarters and eighths (m. 240), the left-hand pitches are each held for the duration of seven eighth notes. When the melody is finally reduced to eighth notes, the left hand’s octaves are held for the duration of five eighth notes (mm. 245-249). This finally culminates in both hands playing alternating sixteenth notes, repeating the melodic
92 pattern six times (once again) in order to synchronize the cyclic pattern with the bar line. Then both hands, in octaves, descend into the low register of the piano, avoiding the target G# until abruptly landing on it with the support of the bombastic percussion. This is quite an important pitch in the piece as it is the other axis of symmetry (Ab).
93 REHEARSAL LETTERS H THROUGH K
Rehearsal Letter H
As the G#s in the piano and crotales diminish, the upper woodwinds emulate the piano’s descent with a brittle rendition of their own in quarter note durations, alternating between the five-note symmetrical pattern around both D and Ab, until finally resting on
D5.
Rehearsal Letter I
An elision in the piano begins a slow solo interlude displaying Theme 1 in all twelve keys (m. 274). A crescendo and accelerando throughout Rehearsal Letter I propel the symmetrical motives downward to low Abs.
Rehearsal Letter J
Following this, the brass section mimics the material from the previous section, but whereas the piano was moving deeper and deeper into the lower register, the brass section rises out of the depths before reaching a climatic dissonant symmetrical chord (m. 283). Also, the theme moves further and further from symmetry and becomes rhythmically more complex.
Rehearsal Letter K
As if reverberating from the biting brass chord, a frantic woodwind section appears (Rehearsal Letter K, m. 284) that foreshadows the closing section’s material. Nine woodwind instruments are used in this section and are divided into three groups by classification (piccolo and flutes, clarinets, and oboes and English horn). Each group has
94 one instrument beginning on either pitch D, Eb, or C#, and every instrument follows the pitch order of C#, D, Eb, D. The woodwinds have six beats of sixteenth notes using these pitches before the piano makes its entrance. The piano part consists of the same pitches as well. The woodwinds return with just five beats before the piano answers with three beats. This pattern is repeated once more before the forces join together. At this moment, the piano’s minor seconds are expanded to major, then minor to major thirds, and so on, until the pianist is dared to attempt such an erratic spread as two minor sevenths in each hand (mm. 290-293). This is all going on as the woodwinds are seemingly running out of “rhythmic” gas. But that is not the case. They are just waiting for their moment to trill – and reintroduce a strong brass downbeat as the piano dissonantly reaches a cluster and glissando.
Example No. 34
95 REHEARSAL LETTERS L THROUGH P
Rehearsal Letter L
The middle cadenza (Rehearsal Letter L, m. 298) begins with a thunderous cluster and a rising glissando in the right hand, quickly answered by a descending glissando in the left. A quintal arpeggiation in the left hand begins at the same time as the cluster and becomes the underlining force throughout the cadenza. An upward arpeggiation of the quintal chord consisting of pitches D3, A3, and E4 is followed by the symmetrical equivalent (C4, G4, and D5). This arpeggiation lasts for seven measures before a new arpeggiated chord and its symmetrical equivalent takes place. This pattern continues two more times, one measure in length shorter each time. The notes being displayed outside of the arpeggiations are also symmetrical and their rhythmic placement is proportional as well.
Example No. 35
Starting in m. 320, Theme 3 is now placed in the left hand in octaves as the right hand arpeggiates both of the quintal harmonies from the first measure of Rehearsal Letter D (m. 92). The left hand, when not playing the melody, supports the right hand with arpeggiations of its own. As the melody ends, the right hand arpeggiation returns to
96 arpeggiating the beginning harmony from Rehearsal Letter D. When the two hands arpeggiate simultaneously, the left hand has B, F#, and C# as the right hand has G, D, and
A, and vice versa.
Rehearsal Letter M
The orchestra makes its return at Rehearsal Letter M (m. 336) with Theme 3 beginning on F#. After the second entrance of this group, woodwinds and violins answer beginning on Eb, the five pitches as a group being symmetrical to the five in the first group. A third group makes an entrance after each has begun again. This group represents the possibilities of combined symmetry between Bb major and B minor simultaneously.
Example No. 36
In mm. 352-354 more pitches get added, producing a cluster-like chord, yet still maintaining its symmetry. The piano part throughout this orchestral conglomeration
97 continues its arpeggiations of the previously mentioned quintal chords as additional pitches get added, producing a much more dissonant effect in the piano part as well.
Rehearsal Letter N
The material at Rehearsal Letter N (m. 355) represents an inverted version of the orchestral entrance at the beginning of the concerto. The low Ds are replaced by high Ds and the clangorous chords are now produced in the low register of the orchestra. This section is much shorter than the beginning’s version because of the absence of a cadenza. The piano, however, still performs some rather virtuosic passagework, but in much more condensed forms. M. 357 displays borrowed material from m. 7 of the beginning cadenza, but now the octaves alternate between both hands and ascend. In m. 360 the material is borrowed from the end of m. 4, while the rhythm is altered to accommodate 8, 12, 16, and 20 pitches, respectively, in each beat.
Rehearsal Letter O
The next section is a rich, lush, shortened version of Rehearsal Letter B (Rehearsal Letter O, m. 361) and remains symmetrical throughout. The section culminates in the strings reaching a Db major seventh chord three times.
Rehearsal Letter P
As the third chord is held, each player is to slowly glissando, one by one, towards D4 on the conductor’s command (m. 369). As each player reaches this pitch, he is to glissando inward and outward from it within a semitone. This sets up the final section of the work.
98 CLOSING SECTION
Rehearsal Letter Q
The closing section of the concerto begins at Rehearsal Letter Q (m. 370). Two new rhythmic transformations of the main theme control most of this section. The first (Theme 4) is presented by the piano beginning in m. 377 and is based on combined symmetry expanding outward, while the rhythm is non-retrogradable. Theme 5 is introduced in m. 387 by the oboes and clarinets and follows the same rhythmic pattern set up by Theme 4. It uses the same pitches as Theme 1, but differs in that it is includes an elided retrograde version.
Example No. 37
The piano part is rather percussive throughout the final section, based on the little “ditty” mentioned earlier. The pianist is called upon to play this section much as a mallet player would play a marimba or xylophone part, except the pianist uses his index fingers
99 instead of mallets. It begins with a rapid succession of repeated D4s. Once again the focus is on the combined symmetry between Bb-F and B-F#.
Rehearsal Letter R
At Rehearsal Letter R (m. 387) the marimba replaces the piano and continues the repeated sixteenth notes, while the repeated pitches now are G and A, sounding simultaneously. Oboes and clarinets, as mentioned above, are called upon to play Theme 5 with the axis moved up to A4. After four measures, the piano joins in, filling the melody in with quartal arpeggiations.
Rehearsal Letter S
As the piano part regains the repeated sixteenth notes (m. 396), the axis returns to D4. The quartal concept remains in the piano part, first punctuating downbeats, then strong beats, and finally taking over every beat. Three measures of transition move the axis of symmetry back up to A4, but this time the marimba is not called upon, as the piano part remains to perform the repeated sixteenth notes, punctuated with arpeggiations.
Rehearsal Letter T
This time the punctuation is on the first beat of each measure, getting closer together as each measure contracts by a beat (mm. 403-406).
100 Rehearsal Letter U
At Rehearsal Letter U (m. 408) the orchestra takes over the melody for the first time with the D4 axis. Four rhythmic transformations of Theme 5 are introduced at two- measure intervals. Only the first and third synchronize at the bar line.
Example No. 38
Rehearsal Letter V
Rehearsal Letter V (m. 418) begins with an axial transposition up a whole step to B4. The pianist is no longer using just his index fingers, as octaves are used to play the moving outer parts of Theme 4.
Rehearsal Letter W
As the orchestra mimics the previous eight bars of the piano (Rehearsal Letter V), it is the piano’s turn to show off by playing some bravura sixteenth note passages, two octaves apart (m. 426).
101 Rehearsal Letter X
Rehearsal Letter X (m. 432) has a return to the D axis. While the material here is similar to the initial entrance of the orchestra (m. 2), the previously symmetrical chords in the orchestra are replaced by only piano and crotales. Furthermore, the chords no longer contain all the pitches from before, but are replaced with the harmony from the first three measures of Rehearsal Letter A. The second chord uses the pitches from mm. 20-22, while the third chord continues this pattern, using the same pitches as in mm. 23-25. Here, the crotales sound the chord once as the piano plays it four times. This chord is repeated again with an additional symmetrical pitch in both hands and is played only three times. This pattern of contraction happens once more before a sixteenth note octave sweep downward in the piano, landing on octave Ds in both hands, followed by a powerful glissando upward to high Ds in octaves, at which the brass makes its entrance (Rehearsal Letter Y).
Rehearsal Letter Y
Here Theme 1 is split into its two symmetrical halves (m. 442), resulting in one ascending and one descending line. This is actually not the first occurrence, for Theme 4 was also split in this way at the previous Rehearsal Letter. However, this is more transparent as both lines sustain the pitches throughout the section. The chimes is the only instrument playing both halves of the theme, but it features the theme with the upper part of the melody as the lowest part and the lowest part as the highest.
102 Example No. 39
Theme 1 is announced four times, and each time the rhythm gets more compact.
Example No. 40
103 Rehearsal Letter Z
At Rehearsal Letter Z (m. 450) the meter suddenly changes to 12/16 as the brass fade out. The accented rhythm is no longer syncopated, but synchronized with the beat. In this section, I wanted Theme 1 introduced in a systematic way. The only parameters being altered for each introduction of the theme are register and rhythmic placement. I used nine separate introductions of the theme throughout this section. The organization of the theme’s entrances concerning register is simple. There are three divisions of register - middle, high, and low – and three groups introduced in order using each of these register placements. This results in nine occurrences of Theme 1. I use three possible orders of register placement that contain no repetition of placement in either of the groups; middle-high-low, high-low-middle, and low-middle-high. My desire was to start out in the middle register and end in the high register, so the order above worked out best. The first group employs one instrument for each of the registers. The second and third groups use a division of the string section, plus two and four instruments for each of the registers, respectively.
Example No. 41
Also, each register placement avoids beginning on the same beat subdivision. Since there are twelve possible subdivisions of the beat in a measure of 12/16, this is formulated in
104 such a way that each register placement begins on a different subdivision of the beat, which leaves three remaining, equally spaced subdivisions of the beat unused. These are the beats on which the pitched percussion parts (chimes, crotales, bells) heroically attempt to introduce the upcoming new focal point of F#.
Example No. 42
Rehearsal Letter AA
In my opinion, Rehearsal Letter AA (m. 471) is the climactic section of the entire concerto. A real test for the listener occurs, as the music of this section has only been heard once before. At Rehearsal Letter A, the clarinet introduced the main theme of the concerto, which was only the beginning part of the melody. This section uses the remainder of this melody, performed here with full orchestral forces as the piano arpeggiates rapidly in the upper register.
Rehearsal Letter BB
At Rehearsal Letter BB (m. 478), the sixteenth-note material returns in the piano, but the material continues to expand outward, much like it did in both hands right before the beginning of the middle cadenza (mm. 290-294). Following this, one measure of erratic, unforeseen material occurs (m. 484), as if shaking the foundations of the piece.
105 Violins, violas, and cellos grace this measure with one long downward glissando. The woodwinds rapidly ascend and descend, while trumpets, flexatone, and slapstick highlight their apex. Trombones enter on the third beat with their own ascending glissando, their accented arrival marking the beginning of Rehearsal Letter CC.
Rehearsal Letter CC
With the foundation now shaken, new material seems to pop out of nowhere (Rehearsal Letter CC, m. 485), the only organizing factor being symmetry. As the right hand part of the piano arpeggiates an A minor seventh chord involving a repeated pattern of five sixteenth notes, the left hand uses quarter notes to play each of the five black notes, alternating fifths and fourths in these two measures.
Example No. 43
As the piano part continues to ascend, the orchestra acts like an amplified sustain pedal for the piano. The strings enter on the white notes as each pattern of five sixteenth notes begins, while the rest of the orchestra sustains the black notes as they are introduced, culminating in a rather intense rush of energy.
106 Rehearsal Letter DD
At Rehearsal Letter DD (m. 490) one measure of primal-sounding clusters in the piano accompanied by bass drum, anvil, and brake drum takes place before the full orchestra joins in. The rhythm is the same as that of the string section beginning in m. 207 of Rehearsal Letter G. The following measure has every instrument playing in a powerful range, repeating the same rhythm. The winds have eleven of the twelve possible tones (excluding D) in both the upper and lower divisions of the sections while maintaining symmetry. Both violins I and II are divisi with triple stops, involving all twelve tones, while violas, cellos, and basses are divisi with double stops, also producing all twelve tones. One lone instrument, the English horn, is relegated to bravely holding D4 for the entire measure while the surrounding bedlam ensues. The final measure begins with all instruments remaining on their previous pitch (minus the D4 from the English horn) being repeated as eighth-note triplets before dropping the upper register to brashly close in the lower register where the piece began. The entire work ends on D in a dramatic forceful flash.
107 Conclusion
As I think back to when I first started composing the concerto, it is hard to believe that I am sitting here, typing a concluding paragraph. I knew that eventually the end would come, but some say compositions are never really completed. I dare to disagree. Though the concerto will likely need minor changes here and there, I believe in looking towards the future and not dwelling on the past. I do not plan on doing revision after revision of any of my works, including this concerto. Instead, I look forward to the next time I am sitting in front of a blank sheet of manuscript paper, wondering what will fill the pages as I begin a new composition. The concerto is roughly 16 minutes long and was completed on March 20, 2003.
108 Vita
Trent William Hanna was born on Williams A.F.B. in Williamson County, Arizona, on April 30, 1969, the son of John William Hanna and Victoria Lynn Hanna. Upon graduation from Bryan High School, Bryan, Texas, in 1987, he entered Sam Houston State University in Huntsville, Texas. He received his Bachelor of Music degree in theory, composition, and piano performance in 1992, and his Master of Music degree in piano performance in 1995. During the following two years he was employed as an adjunct faculty member at Sam Houston State University and taught private and class piano, fundamentals of music, and conducted both of the jazz ensembles. In August 2000 he entered the Graduate School of the University of Texas at Austin. Trent has received awards in both composition and piano performance including first place in the 2001 SCI/ASCAP Student Composition Competition, Region VI, in the 1994 TMTA Collegiate Competition, in the Corpus Christ International Young Artists 24th Concerto Competition, in the 1995 Sorantin Young Artist International Concerto Competition, and in the 1996 Texas Young Artists Concerto Competition.
Permanent Address: 1308 Esther Blvd., Bryan, Texas 77802 This dissertation was typed by the author.
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