UBC Theses and Dissertations

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UBC Theses and Dissertations

Camerata Bonaccorso, Jose Carlos 1994

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CAME RAT A by JOSE CARLOS BONACCORSO B.Mus., Faculdade de Artes Alcantara Machado, 1981 M.Mus. , University of Alberta, 1988 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF MUSICAL ARTS (COMPOSITION) in THE FACULTY OF GRADUATE STUDIES (School of Music) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1994 © Jose Carlos Bonaccorso, 1994 ii ABSTRACT This thesis consists of an original composition and an analysis of it. Scored for a small orchestra, the Camerata is approximately 16 minutes in length. The analysis deals with general matters of structure as well as details of harmonic organization that play a specific and prominent role in this work. The piece is to be perceived in four integrated sec-tions. Each section has its own characteristics. However, the sequence from one section to another is functional, so that the piece would not work if the sequence of sections were arranged differently. Section B develops the thematic material of section A. Section C is an outgrowth of section B because of the exchange of the dynamic and static aspects pertaining to harmony and melody. Moreover, as a unifying element, these two central sections show tonal tendencies. Section D rounds off the piece with a concealed texturally decreasing formal design, which balances the crescendo and texturally increasing overall shape of the first section. i i i TABLE OF CONTENTS ABSTRACT i± TABLE OF CONTENTS i i i INSTRUMENTATION iv I . CAMERATA 1 I I . INTRODUCTION 77 I I I . SECTION A 80 i Form and overall content 80 ii Harmonic organization 80 iii Rhythmic structure 82 IV. SECTION B 85 i Form and overall content 85 ii Harmonic organization 85 V. SECTION C 94 i Harmonic structure 94 ii Form and overall content 94 VI. SECTION D 98 i Form and overall content 98 ii Harmonic organization 98 iv INSTRUMENTATION Flute Oboe Clarinet in B-flat Bassoon 2 Horns in F Trumpet in C Trombone Percussion Snare drum 2 Timpani (with pedals) 3 Tom-toms (small, medium and large) Tamburo Temple Blocks (small, medium and large) Suspended cymbal (small) Tam-tam (large) Vibraphone Strings (6/6/4/4/2) Duration ca. 16 minutes CAMERATA 3^£ F l . O b . friV t M [\tm t ff t/- E Cl . (Bb) F g . m m t 4^ m Horn (F : f 6 t m J&E ' >" tf 'K f «0? s p T r p t . i 4k. J f saipre ?^#£ -faa f tY ^ £EEE m rt=f= Tom-tom S. P e r c . Tom-tom M. 4- t- ± h $ t t Sul pont. i MM m ?=ET V I . I V I . I I V i a . i 4-J t Sul pont. [>i i Sul pent. ^ ^ O b . Cl . (Bb) | F g . Horn(F T r p t V I . I I V i a . C I . (Bb) V I . I r >r ft 7 h J' »J. C l . ( B b ) F g . =?=f Horn (F: I I T r p t . ,„ i—^jraj.-I JPr->l i v l . I P •1 £ J± i J= 3f ^ S C I . (Bb) F g . H o r n ( F T r p t . V i a . F l . CI.(Bb) F g . T r p t . V I . I I KSZ V i a . P i . O b . ^m C l . (Bb) F g . ft,,,.- ,__ Hornlr: ^ m m T r p t . T r b n . m JU x^g. ^ m V I . I VI . I I V i a . » i ^ g -P fe WL a ? /• is ^ = ^ f j E ^ ^ FT ^P¥ V I . I I O b . C I . ( B b ) F g . H o r n l F : T r p t . V I . I V I . I I y^-t i ^ rm $£ f(\P Senpre m 27 F l . O b . C I . ( B b ) F g . $f«n" i ? HornfFi I I T r p t . \l l|J.. . . h i ^ ^ ^ ?F [•' ?'-7TFT-it *f—#-^S ^ 3 ^ ^ ^ ^ /• >J >/• ? ^ /• J>J , )* ? ^ * /• i,)j. , )/• E n =f& ^ / > / P 1 * * a i ^ ^ ^ H m " - s e ^ « J- ' * ytM- ^ T f > / E JCU ' ^ - j T ° W * /rf-f Sarpre 30 ^ m ft y f i V ]M 7=*=^ £m ri i i m *=& i ft ? ¥*•& k 11 y vy y 't f *f P ^ T f , / ? y *ft~fr / ? * iiJ * H < w - P C l . (Bb) F g . m^  m y ? ? ? V ^ (i WP £$ y- ? y ^ ^ T> I * ? "tf =* ^ ? f ? /Tp / ^ ^^ /3 ^ ^ HorntF: K4 ^ ^y^4 # F T ^ r f /fi^JLfe ^ & T r p t . rnran bf> y /• £ ? & & ™ i> ^ **. "frry^ /• EE^I ./? /• ^ r ii I* l» ^ ' - *M» ?? /• H.'/ / V I . I V i a . k") f ft ;/? /'ftp y i •JT f f? /- [ * ^ ^ y- in E ?'? / ^ H r ^ F IfiFf-r? /'fifr^E Ffr"p-y?* H ^ 0 $ V / p / / r t / ^ > / ^i? h t\rf%'F <* EPE7EF F l . O b . flvftnK? ^ ^ <nf ^'•myp/-^;/^; f^SJv^ f^ejfe 4 dim. l ip a^'Vb? 'i C I . (Bb) F g . •^/ '^y^' /r JV\Alr- ^ p pi - ^ ^ /»«/ f^ - *kh> \Ul>* * J ^ H o r n ( F : I I Trpt. ^ ^ £ J ^ ) E£ fly-fW^?^ fc,. > „ i ^g»^^ cresc jj-f- bP ^ dim. S.D. Tom-tom S. ? I » r1! ^ w n> f LU f C' •' «tf M P=# m ^ ^ dim. £££ V I . I V I . I I V i a . fc£ Hitti ^ ^ qTF /•'* f i f^T C*f dim. [> ? /• fyt Yiih^^ j/\)n p- ? ^ m * w b^Q. K # 8 ^^^yi * ^ r y'K? U M ^ il '^ f^ - f- y ^J§i i / • ^ dim. *W twvr ^ /• /• ^ff[>i^m !*$• dim. 36 f hi ' W f / Jy * C l . (Bb) F g . f^ # ^s^g P m g i H o r n ( F I I T r p t . ' $ • ? ^ # £ £ ^ ^ ^ S.D. Tom-tomS P e r c . Tom-tom. m^ \*]i}h- m ty t >-WK^gEfi :=£: tf V I . I V I . I I $L^M ifit< ^B S fry g yj»/ - ^ ^ ii l i r i s j^Ek^ff - Sul pent. w a ^ ^EE£ Pizz. « f^ s - * i 4 4-m 15 mk ~w i rt CI.(Bb) F g . .4-w §=p w m u ^ 4= HorntF: I "tf <**<* T r p t . T r b n . m fi^ ^=g= «f<^ ^ i 4 <*£ -f i 3 S V s / ? * . J J. J , J ^ 1,1^ \>ff U l > bJ ^ LJ J J JE ^  F l . C l . ( B b ) F g . Horn (F: I M «p i T r p t . Trbn . i* s V I . I I i 3^5 i 45 Fl . C I . (Bb) F g . m M 3^£ Horn(F fa > J' wm^ i' E E y * / .t > T r p t . T r b n . P ^ P s ? Y ' P y gr 'pr 'J-r r r \._Q"t \ \\ £fe m O b . C I . (Bb) F g . H o r n (Fi T r p t . V I . I V i a . F l . O b . C I . (Bb) F g . Horn(F: T r p t . V I . I V I . I I m s m m Solo :<0J 6 4b "5~ 8 3 ~ 4b 5 4b 6 8 5 4b 5 4b 5 5 4b M^uL 4b y espress. 8 6 4b WL 5 yib JE " T ISE 4 2 14:. z 4 fc^ ift 4 3 4-3 :4-59 F l . O b . C I . (Bb) F g . m Horn (F: I I T r p t . T r b n . I m k < fit 1 Tr f /\>r? w Pizz. hm m m & i K J' f ? ? y V i a . y r fes^^^ ^ EBE m 62 t •f-- ^ H l f C l . (Bb) | F g . m •$.. = y f e = ^ S i ,*r. / ? H o r n ( F l i 'f. y t M 1 K EEE£ T r p t . P^  d = r /• Jj r^f> y_- i ^ S V I . I V I . I I ^ ^ 3 3 fiob. r i t t . . _ iaroo Oil, pont . P i z z . ( ^ ¥ •~ • C3?) *tf O b . CI . (Bb)| F g . S'ltf *f n^ Horn(F I I T r p t . S.Drum Tamburo Small Cymlj P e r c . V I . I V i a . V r f-jfe if ^ /• ^ f" T ^ i -V i>-^« /4^i,J'-ru >• - -J r X ^ L J J ' ^ J fi.i =s; p i^ p— *n-i-~•• (Struck near the dans, always ) 2 Serrpre - delicately **£ > Senpre - delicately IMA * ^pp 3 ^ ^ ^ ' * ,» y • ^ ^ f=£ S ^ ^ ^ ^ 'H^ J^ ]Jj S^ m .i£ r ? E E£ 71 2 5 F l . CI .(Bb) F g . & r yi rt Horn(F) II T r p t . B §§==£ I Hi i t ; ^S £ fe PP S.D. Tamb. Cymb. *K£?H T.Blocks H m n • Ji r> » [ f i ^ ^ ^ ^ ^ fi y > y"TI fe r uu: k:1 'ifl ^ f V I . I V I . I I V i a . T T. y §m s H = * = 3 E CI . (Bb) F g . H o r n ( F ) I I T r p t . T r b n . S . D . Tamb. Cymb. s Tom-toms S. P e r c . M . L. T . B l o c k s M. V I . I I i m i i ? » i _ ^ = _ -J- - -J' ^^r^ ?' . v f ?' p g ss ^f^rn if j y j y ^ : ^n /' ji ^ 7 ^ ^ ^ ^ ^ ^ ^ * t m& ^m ^ ^ ^ m ^r C l . ( B b ) F g . m Horn(F) II T r p t . w S.D. Tamb. Cymb. Tom-toms S-P e r c .M. L T. Blocks V I . I I ii t W i ~W f u r~v v . - . f ' ^ iilii £• « ^ £ d^ * •* Wl T h£-3EEEZ 3 l £ ^ E = E /• r, z mO m£ f fiy *- ' E fcfj Ey' ^ i ^ P ^ ^ u. m 80 O b . CI. (Bb) F g . $ t \h Horn(F) T r p t . % J*£ i- \Mfp n r ^ y ^*-*S 3=£ iFf My/ £ yy ^y^yp ^ L T L T L T * * r^>- ?• t ^>^m tea g ' p i y • .> ' ^ -1 = ^ i / JYfr * i p ^ F 5 ^ S.D. Tamb. Cymb. Tom-toms S. Perc .H. L. / F y_y E y £ p y f> ££/ ££_/ H P ^ g f ^ fry' ^Mfr SSg ^ p Ms / J i m ± > y T I y T l r1 ' y " r V I . I H ^ 83 2 9 F l . $ C I . (Bb) F g . H o r n ( F ) I I T r p t . T r b n . i^F ^ ^ ^m m 4 S . D . Tamb. Cymb. Tom-toms s P e r c -M. L. •t UUffJgJB m P Ul P U P ; / P it t mi "i u a- f i s i y i i i -*—-1 - - • j r n y~n y T3 y ~n j^i^d ^jjp a {> /JV ^ g a 86 30 i C l . (Bb) F g . m Horn(F) I I T r p t . $ m S.D. Tamb. Cymb. T.toms S P e r c -M. L. t fUJ^f gf f \t \s -m t R y«r u i ?*f mm fc^ m ¥^T^ * t A. :»£  ff l t % tng s^ V I . I V I . I I 1§ ^ P I . O b . Cl . (Bb) F g . y. Horn(F) ? / J 1 ! J""j j j J~T ^ ^ 1 wm -» # # T r p t . T rbn . Cymb. T.toms P e r c . M . Timpani WVkilWWt^ s # £2: s-* ard. i»f » > f f f f=f f r r r r r r r r -* Cresc. — - $ - " /nf fe^^ -i * * * • r V I . I I / ^ Cresc. riDlto $ F l . Cl . (Bb) F g . m 'fr i } Horn(F) I I ^ V m ^ # ^ in / g^ yy^r /fryf=*=*p T r p t . «^PP \:ruJrWiil mm 3ft K . -.J 1 X p^¥ rfL Tom-tom P e r c . JiJJJJ-J j j - 5 > , 5 -'—°—"-i d i i i i i i i J j j J J J J J J J Bfeffi J J J J J JJJJJ JJJJJJJJJJ v l . I V I . I I O b . C I . (Bb) \t r ft ^ ^ mf ^P^ift 4_ rr. -5- ins ffln F g . ' l*W J'|,J ' J'jJII, "* fi is ^ U' i i J ^ j ' jU*g^ j Horn(F) U v t.i "r p £ P^P T r p t . T r b n . ^ fr'r--, ^ P ^ s P^ * *tf (S.D.) J J J J J J i J j J J l J j J j J J J j ?F ¥^t%T feb V I . I I V i a . 4^f fj^f ^ ^ , b*i Pf,b>— t frkr, I *tf 3= 3 P F l . O b . jJ,lhJ,Ywi C I . (Bb) F g . ¥ ^ <n si / T, ^ ^ ' i ^ J 4: *PSj * [' CiJ t- " T r p t . ^ r^M 4 if 4 ^ *rLLf"^^ ^ V V I . I V I . I I V i a . ^ "* ^ ^ 2 T b»^» O b . CI . (Bb) F g . Horn(F I I T r p t . i r\ T r b n . V I . I JTH Tf s a M^Pf £^g ^ 104 3 6 i F l . C I . (Bb) F g . Horn(F: T r p t . V I . I V i a . O b . C I . (Bb) F g . Trpt V I . I VI . I I V i a . C I . (Bb) V I . I V I . I I J Cresc V I . I C l . (Bb) 1 2 5 42 felP i ^ ^ is F l . 2 4^  **OT } i.V f a C l . (Bb) F g . Ml # = -ana. T^£ fesi i Hornfr: I I T r p t . T r b n . i Crd. P P 3EEJE ¥ 4-f ii* Z~ 1 Qn3. «f y = ^ t £ i 4= I /ram P VI . I I « « » ^ ^ » . » ^ 2 2T C I . (Bb) 133 44 flJU.Jl ^PF ft S! nLLi » C I . (Bb) F g . ^ I Horn ( F : I I T r p t . m ^ ^ i P # ^ = ^ _k£ i 33 V I . I V I . I I V i a . Q^ =te I t. ' rtfr .J v > 3 ^ ^ p ' ? g ^ g F f # ^ = W = SpsEi bf J » y l ^ " V -^PP e PP C I . (Bb) H o r n l F ! i ^ ^ 1 itCf m M ± h PS ^M i= g^  i fee t*^V T r p t . "I " | | | ^ ^ E 3EEE£ § i£ Up 4-4 f 7 < ^ ^ S 4* £ i-i ? / f T > .JhWt 'i^"V * * KL il ^ *tt F^^ F p* #^M^ ^ ^m_j!-z A ^© ^ ¥£ »i' Y'[' i j ^ i 44-? * CI . (Bb) 142 CI . (Bb) F g . i i H o r n ( F I I T r p t . S. T.Toms M. L. VI . I V i a . ~m m C I . (Bb) I fefc M. # ? s ^ -in ^p O b . C I . (Bb) i ? /' ijTtJ^g fe F g . Horn(F) T r p t . T.Block P e r c . V I . I VI . I I V i a . H so F l . O b . tgl n^ dL^Mj'r C l . (Bb) C I . (Bb) F g . W T=? m m ,mj i (i sfe H o r n l F ! T r p t . f ^ V I . I V I . I I V i a . aroo m ^ ^ s F l . O b . C I . (Bb) F g . V i a . C l . (Bb) F g . Horn (F: Trpt V I . I V I . I I V i a . CI . (Bb) P g . Horn(F: T r p t . V I . I V I . I I C l . (Bb) V I . I V I . I I V i a . 56 P i . O b . C l . (Bb) F g . ALJ f f ij-fJ ^ s SB Horn(F I I T r p t . inm i ^ ? S SjP w tfc_ f tS?: »/ espressivo t =*=*= VI . II Via. HE ^ ^ =1 3 # 57 CI . (Bb) V I . I I V i a . C I . (Bb) F g . Horn (F: T r p t V I . I V I . I I V i a . P I . O b . CI. (Bb) F g . Horn(F I I T r p t . V / V I . I V I . I I V i a . C I . (Bb) O b . CI . (Bb) F g . t \1t * k m ksk 1 J'/fJV ± V? f 1\1 Horn (F I I T r p t . yjw } m£ f^m f i mi Serrpre jjfW i %n k ?=* V t ; ^ A1j Saipre gfe ^z \ t / E / * y K p ^ ^ T r b n . ^ W* /> b . , 1 M^  ^ ^ a / jy/ V I . I I K ^ H V ? ^fe ^ > =fe ^ .'EyV ? 1 \l\jl4 @£ ? f m kt^T'f ^m r fjjhl] Pxzz. arco / ^tjul /n£ Saipre O b . C I . (Bb)| F g . Horn(F I I T r p t . VI . I VI . I I V i a . ? i/ty \t ^m i^ ^ ^ ^ m ^ ^ ^y=r ^ ^ k ^ P§p ^ ^ •f [i / r. * / ^ ^ m £ ^ p ^ / fry m ? f ? ^ all 196 poco r i t . a tempo i =12 J - - 6 4 C l . ( B b ) F g . flfifin ?: = f f i = ? y > ^ ?FFF -rfU -^l- ±=£ $E t 1 * P ^ -#-r - r * -^ espress i £ F ^ * - > - - y ^^r i H o r n t F ! I I T r p t . T r b n . Vibr . P e r c . isl »& <*Z~_ *&: mm Sort. \f t »EJ 1 r ^ ^ ^ £ /»#: 1 I 3 ^ M' ?/• p& <*f£: i«5£--•? j \> \f=$fE \ fr y ^ ^ ^ 4 r > i n ^ 4 ^ 4 — pt u)i sp M^  ^ V I . I 4= e# -£ m&: ^ ^ /•#: ArfC; i t 5 ^ ^ ^ * > U > / V i a . "^T; <»ff: ?> i r, ^ ^ y fr * ? ^ ? Qj f%m m ^m *f^$ ^ S, '~ SIUJL Wf i? ^mm mm ? 1 r> U—4^ ± " V y f. T> y ? f ' r C I . (Bb) F g . ^ ^ K r. y /*| *Jy f, i p\i% r=f: tnff m ^ f ^ HornCF &• d J • "&=- rt-t- fl&: = S = : —*vT /nf-ip ^P ^f' yli ul T r p t . ^ ^ /•#: /Stf= ^ ^ /*£=-*#: S*F ffei i £ i ib ¥ S g ^ V I . I V I . I I " # : / ^ : W- /"j£: W-w u m ^m & m m&: «&l ^ " # ; ^ ^ /*tf/: ^ f \ Y I / IL > ^ 'f r ¥ f /W^ espressi A poco r i t . ^ P^  i /• * / K m £ ££EEEZ PP i# ^ = ^ &F=h ; t>> » p - g Hr—y iH m m ^y=r afe£ C I . (Bb) F g . / J* t J* /= / If / ^ i,i y t t =£ h HornfF! £ m n m£Z: ft&- l«il--T r p t . n. i^A X^Sui,. r < i * T Tam- tam ( L . ) £_ sfsi/fe _2t poco r i t . V I . I V I . I I F l . O b . C I . (Bb) F g . Horn(F T r p t . Trbn . VI . I I V i a . C l . (Bb) F g . Horn(F Trpt 6 9 O b . CI . (Bb) -£-*-/ ? V f • n£ nfiltf mgfg Sempre r["f f g /•if espressivo F g . Horn(F : I I T r p t . I W V I . I VI . I I 3 E /r£ 3ejE i ^ / V Saipre bp * ^ " / / W ^ Saipre O b . C I . (Bb) C I . (Bb) F g . H o r n ( F T r p t . V I . I V I . I I F l . CI . (Bb) F g . J c r e s c . 3J T r p t . ^f'ftr * VV VI . I I w C I . (Bb) F q . TI^J * "Urn ? t ^ / ^ i ¥[? ¥ ~j- l'H t * M H o r n ( F : iui: m$* -yi-S TPjJflTy rl3? « y' I ' Ml •y' y ^ / / | J? / rifei y g j; /- ^ ^ * i 't *f, £ T r p t . F^F 73^$+ \ •j y tF* U p //• >f7i/H V I . I I V I . I CI . (Bb) O b . 77 II. INTRODUCTION The work is cast in a single movement having a duration of approximately 16 minutes. Four groups constitute the orchestra: a woodwind quartet, a brass quartet, a standard small string section (6/6/4/4/2), and a variety of per-cussion instruments. The formal scheme is made up of four sections: A (measures 1-38), B (measures 39-100), C (measures 101-184), and D (measures 185-232). The four sections can be heard by the listener as four separate but interrelated movements. A unifying device, and indeed an important feature of this piece, is the use, from one section to the next, of common materials. In fact, all sections use, to a greater or lesser degree, the same source for melodic materials. In addition, the compositional pro-cesses used in section B relate to those used in section C. The same can be observed in sections A and D; section D subtly delineates a long range textural decrease, which is a retrogression of the formal aspect of section A. Framing the work, sections A and D display the overall shapes of crescendo and diminuendo respectively. Section B is pri-marily concerned with elaborating the thematic material of section A with great variety of harmonies. Section C begins with a rapid progressive inflection of the thematic material used in the previous sections until it disin-78 tegrates following new melodic statements. This process is supported by a short harmonic structure which is continu-ously repeated. The static character of the melody, and the dynamic character of the harmony in section B are exchanged here. Variety among sections is achieved mostly through the use of different compositional processes. For instance, the serial approach in section A is abandoned in section B in favor of an exploitation of the tonal-atonal duality. Consistency is achieved by the use of a rather limited thematic material. Style can be interpreted as a consequence of a method. At a first stage of the precompositional activity, musical ideas come intuitively; at a second stage, each of those ideas is provisionally processed in a strictly rational manner by using a specific suitable technique. I do not impose a priori one single technique to work with throughout the piece. Musical ideas or gestures may be submitted to different techniques, especially in longer pieces where a greater degree of variety may be appropriate. The pre-compositional activity comprises two stages: the first is intuitive, and the second is formal. The synthesis of these two stages is the final compositional activity, where any strict process may be used with flexibility, according to an inner need for a more or less intuitive means of expression. 79 In this piece, I make use of a range from quasi tonal to serial techniques as they are useful to express a par-ticular musical idea. 80 III. SECTION A Form and overall content Section A is textural music in a kinetic form--a crescendo-accelerando, with interacting melodic materials. In the opening section the thematic material is pre-sented either in an improvisatory manner or rather plainly. The theme, or fragments of it, is presented over a fabric of almost independent material composed according to a serial scheme. Notes or intervals of the thematic material are highlighted; at the beginning, certain notes of the thematic material are played successively in the cello, trombone, and bassoon, which are simultaneously stated in the top notes of the previously determined texture. Later in measures 10-14, in the woodwinds, the thematic material, in an improvisatory character, is anticipated and echoed in the serial fabric. Section A conveys a sense of a large structure which shows a drive both from dissonance to consonance and from calm to more active texture. Harmonic organization The thematic material to be heard in section B is used in section A. Example 1 illustrates the principal melodic source partitioned in two tetrachords of the type [0236] and 81 [0148] s u c c e s s i v e l y . Example 1 . tetrachord A tetrachord B I JOL t r r r p-o- t>o - r r o An important structural component in this section is the use of three set-types [012], [016], and [027] as simul-taneities. These trichord-types can appear simultaneously, that is to say, any two of the above trichords can be com-bined in various transpositions resulting in a third so-nority. However, in order to avoid a pervasive cluster sonority, only a limited number of members of a trichord type is used when a larger number of notes is required by the texture scheme. The trichords are treated according to their degree of dissonance. Beginning with the most disso-nant, they are organized in a manner so that the most con-sonant trichord prevails at the close of the section. From a process which I call proliferation, I derive and then employ one or two of the above trichords for each attack given by the serialization of the rhythm and texture. Example 2 shows voice leading in successive trichords which are motivated by a melodic fragment of the melodic material. 82 Example 2 . a) Melodic fragment b) Proliferations i ^o- X E m ^e- X £ 3 X ^ = ^e- XE & 3 E p o t» (016) (012) P-o- 3 E I fc^ o m (027) Proliferation can also be understood as harmonization. However, proliferation is a more adequate term because the idea is simply to generate sound to be attached to a rhyth-mic event, so each attack proliferates 3 notes to create a specific thickness in texture that can be set for various instrumental combinations. Voice leading is always involved with connecting a trichord to one of its own transfor-mations, never to another type of trichord, so there is no harmonic progression in that sense. Only in a large scale structure does harmonic progression take place, as the music gradually goes through the three trichord sonorities, from the most dissonant to the most consonant. Rhythmic structure The overall rhythmic structure creates a single movement from a calm texture to one more active. Example 3 shows the two basic rhythms whose note durations may be 83 divided either into two notes of equal duration or more freely divided when stimulated by the melodic material. For example, in mm.1-2, the oboe states a single note while the clarinet states two notes; the duration of these sounds is established by rhythm a augmented five times. As an example of a freer division, see the response in the first violin, in mm.12-13, to the chromaticism in the flute at m.ll. Melodic references to the melodic source are always on the highest notes, so they can be more easily perceived. Rhythm a is used in the woodwind and brass sections, while rhythm b is used the strings. Example 3. II ft I F? lif, rfrlft 7P7fe»P7 ft P? |t H ii r iMs nfrif; rifrft i^^^ Notice that in rhythm a the rests between attacks progressively become a 16th shorter. In rhythm b, the first attack in each of the first three measures becomes pro-gressively closer to the second sound in that measure, shortening by an 8th note the duration of the event on the downbeat, while the rests have fixed durations. Belonging to a lower structural level, these rhythmic patterns, which bring the sounds progressively closer together, relate to 84 the large structural plan, which shows a drive to a more active texture. Example 4 schematizes the development of texture and sonority; 6a [012] means that rhythm a is augmented 6 times and uses set [012] for proliferation. Example 4. m.l m.7 m.19 m.22 6a[012] 5a [012] 5a [012] 6b [012] 3b[016] 5b[012] 4b[016] 5b[012] / / m.26 m.29 m.30 m.32 m.33 m.34 4a [016] 2a [016] . . . a [027] . . a :2 [027] . . 3a [016] 2a [027] . . . a [027] . . a : 2 [027] . . a [027] . . 2b[027] b [027] . . b : 2 [027] . . 3b [016] b : 2 [ 0 2 7 ] . . 2a [027] a [ 0 2 7 ] . 85 IV.Section B Form and overall content Section B is concerned with elaboration of the thematic material presented in the previous section, using counter-point and a great variety of harmonies and textures. In contrast with the previous section, section B is mostly concerned with exploring tonalities amidst atonality, through a variable "degree" of tonality that oscillates with greater or lesser intensity. Section B presents the tonal-atonal duality through the use of somewhat functional ton-ality, combined with both ambiguous harmonies and atonality. In section B melody is somewhat static because of the almost obstinate recurrence of thematic material. The theme and its variations are worked out in different degrees of tonality and textural situations. Another feature of section B is the dynamic character of harmony. There are some suggestions of tonal centers which do not progress according to standard tonal-harmonic syntax. Harmonic organization In order to create specific atonal sonorities in the beginning of section B, properties of invariance are used. 86 More specifically, example 5 shows how the tritone Ab-D in measures 39-40 is held in common by four transformations of the first tetrachord, A, of the melodic material. Example 5. 39 . -^TIOIA m -o^  XI J,» °fe "K , o J^~ ^ (fadZB. TXY . T6A L —T4IA-The second tetrachord, B, inverted and transposed up a perfect 5th is counterpointed with the material of example 5 so that the chord at measure 41, beat 2, shares two common notes, D and F, between T7IB and T3A. Distinctions between tetrachords A and B at this point are made mainly through vertical and linear positioning and orchestration. Now, the tritone of tetrachord A is no longer Ab-D; it is the low B and the high F, which is also the last note of tetrachord B. Following that chord in measure 41 is a succession of the two tetrachords presented as simultaneities, pitch invariance being a determinant factor in creating a smooth progression. Example 6 shows a reduction of measures 3 9 to 42. Example 6. 87 39 i «s § » f^e f£S-4 5 kJ^f :fcc - •P -9 -3 T3A;B;T4B The following measures continue with a heterophonic process similar to that used in measures 39-40, but intended to release the tension just created at measure 41. The heterophonic "atonality" changes to a pitch process which elaborates pitch-class-invariance in the outer voices with the proliferation method (measures 44-51). This process supplies notes to a local textural plan consisting of an increase from 2 to 6 note-verticalities followed by a gradual return to a vertical dyad. Example 7 illustrates the segmentation of tetrachord A and its subset [014]. In the process of thinning the texture there is a transition towards a more tonal atmosphere. The outer voices of this transition suggest a tonal interpretation because of the implied triadic nature of the intervals--perfect fourth and 88 minor third--that they form. A linear interpretation of measures 46-50 is given in example 8. A somewhat tonally elaborated version of these outer voices begins at measure 51. It is important to bear in mind that the term tonality as I am employing it here is merely a reference to the triadic harmony. Example 7 . 44 m 0-0- &~ °^ lit £ ^ ^ ' ^ • ^ • " ^ . ' ' m ? m (0236) r014) i m !8z5 £z: m _J. F?^ S Pf^f OftfTt > m? (0236) =fef i » - i » -p g g "fcff^ m H $ * J M -(014) .? -#—(•- 1+ ^ » "fry £ ^ ^(014)' (014) S i » — S i * if r i -£ E = $ a ,(014). #^£ 89 Example 8. B minor Following measure 58, the static aspect of the melodic repetition becomes more evident, as does the dynamically oscillating degree of possible tonal implications. The harmonization in measures 58-60 is biased towards tradi-tional chords, avoiding the intervals of minor second, major seventh, and tritone. Subsequently, this rather light sonority gives way to a more dense and atonal sonic quality in measures 64-65. There are two tonal tendencies in measures 66-70, one towards A (from measure 66 to 68), and another toward F (from measure 68 to 70). Following measure 70, there is a reference to the rhythmic material of measures 33-3 7, but it is elaborated by a totally different process. In those measures of section A, the percussion instruments enhanced the rest of the texture, while from measure 70 onward, they are the generators to which the other instruments of the orchestra respond and interact. More specifically, the 90 rhythmic structure is based on the rhythmic pattern pre-sented at measure 70 by the snare drum and tomtoms. This one-measure pattern is systematically ornamented through additional attacks and changes of timbre. Using a style of Klangfarbenmelodie, timbre changes are also applied to the pitch structure, which is, in measures 70-77, a counterpoint of the principal melodic material in the upper voice against its inversion in the lower voice. A free middle voice is added to create triadic sonorities. In measures 78-83, the theme appears in a heterophonic texture in which a monotimbral line, first in the oboe and then in the bassoon, is opposed to a multitimbral line. The mono-timbral and multitimbral components of the heterophony in mm.78-83 are distinguished alternately by legato and non-legato modes of instrumental articulation. Measures 84-87 present a modified repetition of mea-sures 74-77; only percussion is used. Then at measure 88 a crescendo begins which, in a short span of two measures, leads surprisingly to a climax. The most intense part of this abrupt crescendo in the second half of measure 89, consists of an imitative treatment of the thematic line in stretto, with the entries a 16th note apart. Not including the trombone, double bass, and timpani, the vertical result is a strict piling up of fourths symmetrically expanding in tessitura. Example 9 shows the canonic entries and the vertical resultants. Example 9 . 91 89 Canonic entries -&-- o - 3 T H E h&-^ T T X E ^o-3 E - » -XE ^ O -X E ^e- o - P O - T T-H E - © -etc. I Vertical resultants Wrfr -©- PO ten XE >o XE fit o-rje IE -O-f -o- XE ? o tor XE XE ^O- HO- XE p o EZQ: -o- 7C» I m -o-P-o- o- [XC ITT X E The crescendo reaches its peak at measure 90 in a more complex sonority which is derived from the intervallic content of the theme. The climax is characterized by an agitated texture created by the superimposition of previous "phrases". The resumption of previous materials signals the beginning of the end of the section. The portions gathered together in measures 91-94 are from measures 46-50, 51-57, and 58-60. There are some modifications, mainly of rhythmic order, so that they fit together. 92 At measure 91, after the introduction of an accompaniment-like stratum, a two-part counterpoint appears in the flute and the first violin. The brass choir, the percussion, and the double bass add body. As the super-impositions of textural strata end at measure 94, the same type of anacrusis that was used before at measure 91 in the woodwinds is also used to introduce a new texture made of two strata, one of which is derived from the anacrusis itself. The pitch structure of these strata is taken from the first tetrachord of the thematic material. At first, the individual parts of the two strata are distributed in a disorderly manner to the instruments in order to maintain the somewhat complex character of the past superimposition. Then, gradually they go towards instrumental conformity; only at measure 97 do the strata crystalize into two separate choirs, woodwinds and brasses. There is a decrease in tension at this point. The diminuendo at measure 98 acts as a counterpart to the crescendo at measure 89; they frame the climax. A byproduct of the crescendo was an ascending chromatic line in the high notes. Correspondingly, in the diminuendo there is a descending whole-tone line harmonized as to convey a sense of resolution. The harmonies are again taken from the thematic material, namely the set-types [0236] and [0148] . The former resolves its dissonant tritone to a more con-sonant sixth of the latter. Example 10 shows the basic structure of the harmonic progression in measures 97-98 Example 10. 97 * o _Q_ -& & fa tT II I o^°, s^a o o R» i lO ^ " tt- n - O o po ' - - - * » !-> * y $ o4n 1 ° J o i » -»-3 [>o ko * ^ < -©- 3E fc «» «» [ -O-Following the diminuendo there is a rather serene chorale-like texture in the strings that rounds off the section. The theme is presented in the bass. Every chord but the last one has a tritone, so that the passage holds dissonant quality until the more consonant last chord. The tritones are resolved in traditional voice leading. 94 V. SECTION C Harmonic structure Harmony takes precedence in section C, but in spite of its strong tonal connotations, traditionally tonal inter-pretations are ephemeral. Example 11 shows a reduction and analysis of the thematic area in measures 105-109. Example 11. Eb: I IV (bVI) Pass V I E: (VII) I V I Form and overall content The dynamic character of section C parallels that of section B through the use of non-repetition (here with great variety in the melodic lines) and static character (through the use of a fixed harmonic structure continuously 95 repeated, as in a chaconne). Thus there is an exchange of compositional processes in the melodic and harmonic aspects; what is static in section B is dynamic in section C, and vice versa. The transition from section B to section C is rather smooth. The clarinet, acting as a joining force, articu-lates two surrounding phrases in the strings which are of similar character, but which are very different in harmonic content. The clarinet at the beginning of the section uses the melodic theme of section B, then, after the presentation of the harmonic theme, the melodic theme reappears with modifications in the first variation. However, it loses importance due to the appearance of a variety of other melodic interventions. There follows a logically arranged series of 10 variations grouped to create a larger form: variation 1 (measure 110), variation 2 (measure 114), varia-tion 3 (measure 124), variation 4 (measure 130), variation 5 (measure 135), variation 5 (measure 140), variation 7 (measure 149), variation 8 (measure 155), theme (measure 161), variation 9 (measure 165), variation 10 (measure 177). Variation 1 is a natural continuation of the harmonic theme because it contours a sort of consequent answer in the woodwinds. Variation 1 elides into variation 2 which is in a very contrasting mood. Variation 3 is also, in a different way, a continuation 96 of the previous one, functioning rather like a coda to variation 2. The next five variations are paraphrases of portions of previous sections. There are, however, no overt melodic references. These paraphrases use texture as the principal agent for reference to the original passage. A particular textural situation is here molded to fit the harmonic theme. Variations 4 and 5 make general references to section A, while variations 6, 7, and 8 refer to the textures of measures 71-77, 58-61, and 46-57, respectively. After these flashbacks, there is a formal articulation marked by a plainly heard return of the theme. The reprise begins in the brass choir and ends in the flute, bassoon, and first and second horns. The change in instrumental colour half way through the reprise is linked with a change in harmonic direction. There is a modulation to A, a tri-tone away from the Eb of measure 161. An interpretation of this modulation is shown in example 12. Example 12. 161 Eb A: II V I 97 The last two variations (9 and 10) continue in the new key. However, in the very last part of variation 10 there is a return to the home key. Variation 9 is calm, while variation 10 is rather agitated. Their moods recall the beginning of the section, where the theme and variation 1 form a pair with a tranquil atmosphere, while the next pair, variations 2 and 3, have more excited textures. The grouping of the variations by their characters and compositional natures suggests a ternary form. See example 13. Example 13. Original Calm / Active Th. Vr.l / Vr.2 Vr.3 \ A / Flashbacks Generally calm Vrs.4 to 8 \ B / original Calm / Active Th. Vr.9 / Vr.10 \ A' / 98 VI. SECTION D Form and overall content Section B and section C constitute, respectively, a commentary and a digression in relation to section A, as far as melodic material is concerned. Section D is a counter-part of, and a return to, section A. The process of relaxation in section D can be parti-tioned into four stages with individual characteristics. Three of the four stages can be further subdivided, as illustrated in example 14. Example 14. Stage Measures First ... 185-190; 191-196 Second ... 197-204 Third ... 205-213; 214-217; 218-219 Fouth ... 220-227; 227-232 Harmonic organization The first stage is a tutti, the texture setting off the woodwinds from the rest of the orchestra. The woodwind stratum consists of an unfolding of the thematic material. The theme passes from one instrument to another, played forte, and distinguished rhythmically from the accompanying 99 three parts. The agitated accompaniment uses set-type [0236] as its principal pitch source. Another feature of this woodwind stratum is that it is stated in the form of two "phrases"; there is closure both at measures 190 and 196, and the vibraphone helps to distinguish the two phrases by adding distinct features to each of them. The string and brass choirs make up a different texture altogether. The texture is a superimposition of four canonic heterophonies. The instruments are grouped as follows: first violin and trumpet; second violin and first horn; viola and second horn; trombone, cello, and double bass. A very homogeneous texture results from these simultaneous heterophonies. This texture is melodically abstract. Harmonically, it is restricted to only interval-classes 1, 2, and 3, in order to let the harmonically richer music of the woodwinds stand out. The music of the trom-bone, cello, and double bass is a commentary on the melody that passes through the woodwind instruments. Each of the three other "canons" has a distinct twelve-tone row as melodic material. At measure 193, a gradual withdrawal of instruments begins, closing the first stage without trumpet, first horn, second violin, viola, and double bass. The second stage is more integrated than the first. This stage, in comparison with the previous one, has a less 100 agitated quality. There are fewer differences between the woodwinds and the rest of the orchestra. The woodwinds play a texture akin to that of the brasses and strings of the first stage, while a broad melody passes between them. The whole texture is derived from the heterophonic processes. Note that the four woodwind instruments play the same series of notes, and that only subsets of set-type [0236] are allowed vertically. The string and brass choirs continue with a similar texture as a result of the use of a similar compositional process, but now prolonged with soft "resonances". If the mezzoforte attacks only were con-sidered, the vertical results would always be subsets of set-type [0236] . However, the global effect is enriched by the resonances created by the prolonged attacks. At measure 204, after the intervention of the lyrical melody played by the cello, the second stage ends. At measure 2 04 an unexpected fuller texture appears, one that articulates quite pronouncedly the beginning of a new stage. A reduction to four instruments contributes to the overall impression of attenuation. Although the foreground of the passage beginning at measure 205 sounds busy and is in apparent contradiction to the overall shape of the section, there is , nevertheless, a slower tempo. The dynamics are softer, and the few sforzandi only emphasize the recurring melodic line. The notes in piano 101 belong to a "florid counterpoint", embellishing notes of the real melody in sforzando. The sixteenth notes gradually subside. From the second half of measure 210 onwards, long notes prevail. The second part of this stage proceeds naturally from measure 214. This passage uses materials from the previous stage. From this rather calm passage arises a smooth but rapid crescendo in measures 218-219. This fleeting reversal of the overall diminuendo shape articulates the beginning of the last stage. The beginning of the fourth stage reminds us the beginning of the third stage in its florid character, harmonic field, and reduced number of instruments. Here, again, there is a gradual change to a simpler texture. However, this time, it winds up with the final closing passage beginning at measure 227 with the entrance of the sustained notes in the strings and subsequent melodic statements in the woodwinds. 

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