AN ANALYSIS OF DU CRISTAL `A LA FUMÉE BY KAIJA SAARIAHO AND AXIOM UNEARTHED, ORIGINAL COMPOSITION. John Clay Allen, B.M.

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1 AN ANALYSIS OF DU CRISTAL `A LA FUMÉE BY KAIA SAARIAHO AND AXIOM UNEARTHED, ORIGINAL COMPOSITION ohn Clay Allen, B.M. Thesis Preared or the Degree o MASTER OF ARTS UNIVERSITY OF NORTH TEXAS May 0 APPROVED: Kirsten Broberg, Major Proessor Andre May, Committee Member Clay Couturiaux, Committee Member oseh Klein, Committee Member and Chair o the Deartment o Comosition Studies Benjamin Brand, Director o Graduate Studies o the College o Music ames Scott, Dean o the College o Music Costas Tsatsoulis, Interim Dean o the Toulouse Graduate School

2 Allen, ohn Clay. An Analysis o Du cristal à la umée by Kaija Saariaho and Axiom Unearthed, Original Comosition. Master o Arts (Comosition), May 0, 9., igure, musical examles, bibliograhy, titles. Beginning in the90s, and aided by the advancement and an increased revalence o comuters, sectral music emerged as an imortant develoment in tentieth century music. Sectral comosers, as exemliied by Gérard Grisey and Tristan Murail, took the harmonic sectra o sounds as the undamental materials o comosition. The resulting music laced an emhasis on texture and gradually evolving orms. The generation o comosers immediately olloing the sectralists assimilated their techniques into distinct and varying styles. Finnish comoser Kaija Saariaho uses sectral techniques to create an aesthetic that generates orm and rogression rom a sound/noise axis. In her iece Du cristal à la umée, a number o endulum and halendulum gestures build u texture and orm. The accomanying original comosition Axiom Unearthed emloys similar endulum gestures and uses sectral techniques to generate melody and harmony in an aesthetic divergent rom traditional sectral ieces.

3 Coyright 0 by ohn Clay Allen ii

4 ACKNOWLEDGMENTS In the rearation o this document and the accomanying comosition, I must acknoledge Dr. Kirsten Broberg or her continuous suort and guidance. Additionally I ould like to acknoledge the suort o my arents ohn and Paula Allen, as ell as Lola Milling, hose suort I could never reay and to hom this document and the accomanying comosition are dedicated. iii

5 TABLE OF CONTENTS Page ACKNOWLEGMENTS... iii LIST OF EXAMPLES... v PART I: CRITICAL PAPER... Introduction... Deinition and History o Sectral Music... Les Esaces Acoustiques (Gérard Grisey), Gondana (Tristan Murail), and Symhony No. (Per Nørgård)... 0 Analysis o Kaija Saariaho s Du cristal à la ume.... Analysis o Du cristal... 9 Analysis o à la umée... Analysis o Axiom Unearthed... 9 Conclusion... Aendix: Sectrograms o Source Materials Used in Axiom Unearthed... Bibliograhy... PART II: AXIOM UNEARTHED... Instrumentation... Perormance Notes... iv

6 LIST OF EXAMPLES Page Examle Messiaen s Chord o Resonance.... Examle Harmonic sectra used in Nørgård s Voyage into the Golden Screen, mvt. I.... Examle Harmonic Sectrum o Prologue and Périodes.... Examle A trombone E Sectrum.... Examle Harmonic sectra used in Grisey s Modulations.... Examle The carrier requencies used by Murail in Gondana.... Examle Summation and dierence tones achieved in Gondana by modulating the irst carrier signal ith the modulating requency.... Examle Symhony No., st mvt., mm. 0.; iano, har, violin.... Examle 9 Subharmonic series used in Symhony No., nd mvt.... Examle 0 The interaction o the ininity series ith the natural overtone series.... Examle Harmonic content at the oening o Du cristal. Black note heads indicate itches added ater the initial chord is sounded Examle Structural Harmonies in Du cristal.... Examle Du cristal, mm., oodinds.... Examle Du cristal, mm., strings.... Examle à la umée, mm. 9 9, solo alto lute and solo cello.... Examle Examle Examle Aroximation o the harmonic sectra o a gong layed iano, mezzo iano, and orte Aroximation o the harmonic sectrum o a susended cymbal scrae Aroximation o the harmonic sectrum o E layed sul onticello on the contrabass.... Examle 9 Axiom Unearthed, measures v

7 Examle 0 Aroximation o the harmonic sectrum o bass izzicato E and its inversion.... Examle Axiom Unearthed, English horn, mm vi

8 PART I CRITICAL ANALYSIS

9 Introduction Since the days o Rameau, the harmonic series as a theoretical rincile has inormed the crat o musical comosition. By the tentieth century, comosers ere using the overtone series to inorm more than harmonic or orchestration choices. The harmonic series and harmonic sectra in general ere elevated to the undamental materials o comosition ith the increased revalence o comuters in the 90s. These comosers blurred the lines beteen harmony, timbre, and texture in an aesthetic distinct rom other tentieth century veins. To describe this shit in aesthetic, l iternéraire member Hughes Duourt coined the term sectral music. With the second generation o sectral comosers, these undamental materials ere emloyed in such a manner that the style as stretched to embody a luralism o aesthetics. Finnish comoser Kaija Saariaho, hile decidedly inluenced by the sectral movement, retains a style that laces texture and melody on equal ooting. Her ditych Du cristal à la umée (99-990) exemliies a comositional aroach marked by axes o dynamics and texture. Each arameter rogresses rom a oint o stasis and stability to extreme tension. Although unmistakably oing much to the sectral school, these to ieces transcend traditional designations and labels. This aer ill oer an analysis o Du cristal...à la umée, exloring the abovementioned sound and texture axes, itch content, and ormal structure. A comarable analysis or my on original comosition, Axiom Unearthed, ill be discussed as a oint o comarison. In order to rovide context, I ill deine sectralism and discuss its Graham Sadler and Thomas Christensen, Ramaeu, ean-phillie, Grove Music Online, Oxord University Press, accessed anuary, 0, htt://.oxordmusiconline.com/subscriber/article/grove/muisc/.

10 history, examining briely to rototyical sectral ieces, Les esaces acoustiques by Gérard Grisey and Gondana by Tristan Murail. Though not considered a traditional sectral comosition, Per Nørgård s Symhony No. ill also be discussed because o its inluence on the accomanying original comosition. Deinition and History o Sectral Music Sectral music can be deined broadly as music that emloys harmonic sectra o sounds as its undamental materials. For examle, the requencies, or artials, that make u a given timbre can be taken as the basis or the itch content o a musical comosition. Comosers then choose to maniulate the requencies in a number o ays by interconnecting the artials to that o other sectra or revealing certain artials over time. Though rimarily concerned ith the harmonic and melodic domain, sectral techniques oten have a signiicant ramiication on orm and time. Whereas in more traditional music the discourse is the result o develoment and rogression, sectral music ossesses a roensity or slo change over time and avors the unolding o rocesses over the traditional sense o develoment. Form, thereore, is more luid ith major sections gradually transorming rom one state to another. The advent o sectral music necessarily coincided ith the rise and increased availability o the comuter. The comuter s rocessing oer made it ossible to quickly record and analyze the harmonic sectra o sounds and reresent them in sonograhic reresentations. Additionally, a number o sectral techniques are transerred directly rom the electroacoustic domain. One such technique takes its ulian Anderson, Sectral Music, Grove Music Online, Oxord Music online. Oxord University Press, accessed anuary, 0, htt://.oxordmusiconline.com/subscriber/article/grove/music/09

11 name ater additive synthesis, a technique in hich a comlex timbre is built u using sine aves. Instrumental synthesis relaces the sine aves ith acoustic instruments resulting in ar more comlex conglomerate timbres. Other techniques, such as requency and ring modulation, lay an imortant role in the music o Tristan Murail. Though sectral music could not roerly exist ithout the assistance o the comuter, the comositional technique has much earlier roots. From the beginning o the tentieth century, comosers have used the harmonic series to generate varied styles o music. Treatises by Harry Parch and Henry Coell laid out harmonic and rhythmic systems based on the overtone series and Partch ent so ar as to invent his on instruments to acilitate the ne systems. Coell s treatise, Ne Musical Resources, discusses a theory o deriving olyrhythms rom the roortions o the harmonic series a technique later dulicated in Stockhausen s Gruen. By the 90s, the inluence o these comosers had reached the minimalist comoser La Monte Young. Young shares ith much early sectral music an interest in sounds o long duration and music hose rate o change is very slo. Together ith all this, La Monte Young has shon close interest in just intonation and the harmonic series. In Euroe, the ork o Paul Hindemith and Olivier Messiaen as strongly inormed by a similar regard or natural acoustic henomena. The harmonic theory laid out in The Crat o Musical Comosition is derived entirely rom acoustic rinciles and Harry Partch, Genesis o a Music: An Account o a Creative Work and its Fulillments (Ne York: Da Cao Press, 99). Henry Coell, Ne Musical Resources (Ne York: Cambridge University Press, 9). ulian Anderson, A Provisional History o Sectral Music, Contemorary Music Revie 9, art (000): 9. Ibid.

12 the treatise is cited by Gérard Grisey as an insiration. In his on treatise, Messiaen cites natural henomena as a basis or his harmonic language. ulian Anderson rites: Messiaen urther emloys the harmonic sectrum to justiy his use o added resonance dissonant uer itches added to a diatonic triad in the middle register; and also to justiy his ondness or inerior resonance dissonant clusters o notes, oten at the bottom o the iano, added to a higher diatonic triad. Messiaen secures his lace as a orerunner o sectralism ith the use o his chord o resonance, containing artials,,,, 9,,, and o the harmonic series (Examle ). 9 Messiaen s enchant or resonance is directly related to his interest in timbre, notating not only the itches o birdcalls, but also a set o corresonding overtones that give each its unique timbre. 0 Examle : Messiaen s Chord o Resonance. Previously, Edgar Varèse exlored the idea o timbre as a undamental comositional element. In orks like Intégrales, instrumentation and orchestration are at least as imortant as itch content, an idea taken even urther by Italian comoser Giacinto Scelsi. [Scelsi s] Four Orchestral Pieces on a Single Note (99) reduced itch content so comletely that the listener is orced to examine otherise unnoticeable Ibid., 0. Ibid. 9 ames Wilson, A Brie Survey o Olivier Messiaen s Harmonic Practise, accessed anuary, 0,.academia.edu/99/A_Brie_Survey_o_Olivier_Messiaen_s_Harmonic_Practise. 0 Ibid.,.

13 minutiae o sound, such as harmonics, beats and dierence tones. Scelsi s emhasis on the acoustic roerties o sound translated directly into the sectral ractice o using harmonic sectra as the basis o a comosition. Scelsi s inluence on the French sectral comosers extended into another acet o the French sectral aesthetic: traces o the slo, gradually evolving rocesses that have become a hallmark o early sectral comositions can be ound in much o Scelsi s ork, most notably his Fourth String Quartet. ulian Anderson, in his article A Provisional History o Sectral Music, cites several comosers active at Darmstadt in the 90s ho exerted an inluence on sectral music. György Ligeti s texture-based music ieces such as Atmoshères (9) and Lontano (9) share ith Scelsi s music (unknon to Ligeti at that time) a reoccuation ith slo rates o change and dense, continuously evolving textures. An emhasis on texture can also be ound in the music o Frederich Cerha, articularly in his orchestral ork Siegel V (9), hich involved slitting the orchestra into eretually luctuating masses o sounds. In the case o both comosers as ell as Scelsi traditional ormal divisions are abandoned in avor o a single, unidirectional rocess. Among the earliest comositions to emloy harmonic sectra as the nucleus o a iece are to by Stockhausen: Stimmung and Mantra. Stimmung (9) or six voices exlores a single B-lat sectrum, iltered by constantly changing honemes. Stockhausen s alication o acoustic research in this iece directly recedes the Ibid.,. Ibid. Ibid. Ibid.

14 techniques undamental to the sectral school. Mantra, ritten to years later and inluenced by La Monte Young, urther uses ring modulation to aect the timbre o the to iano arts, a technique ound in the orks o Tristan Murail and others. Beginning ith Stockhausen and his contemoraries, and continuing through the resent, the advancement o technology has alloed or the ossibility o sectral analysis o the most comlex sounds, in turn alloing or these analyses to become the basis o entire comositions. The same year Stimmung as comleted, Danish comoser Per Nørgård created hat ulian Anderson considers the irst roer iece o sectral music. Indeed Voyage into the Golden Screen oers several recedents or Western music. The second movement incororated Nørgård s irst extended use o his ininity series and irst movement is almost a textbook examle o sectral music. Using to natural overtone sectra G and A-lat loered by a quartertone (Examle ) the movement exloits dierence tones and beating as the to sectra in just intonation unold over an extended eriod o time. Although it is unlikely that Nørgård kne o Scelsi s music, this iece is strikingly similar to that o the Italian comoser. While Nørgård ould never come this close to ure sectralism again, the underlying rocesses and concets o Voyage maniest themselves in much o his outut, including his Third Symhony (see belo). Ibid.,. Ibid.,.

15 Examle : Harmonic sectra used in Nørgård s Voyage into the Golden Screen, mvt. I. Sectralism roer begins ith the generation o comosers immediately olloing those discussed above. To grous in the early 90s are usually associated ith the origins o sectral music: France s groue l Itinéraire and the comosers associated ith Cologne s Feedback Studios. O the Feedback grou are a number o comosers associated ith Stockhausen around 90: ohannes Fritsch, Rol Gelhaar, Clarence Barlo, and Mesias Maiguashca. Canadian comoser Claude Vivier and Hungarian Péter Eötvös have also become associated ith Feedback Studios. Unlike the l Itinéraire comosers, the sectral ieces o the Feedback grou retained a ocus on melody, erhas evidence o Stockhausen s inluence. For examle, in Vivier s music, e ind almost exclusively homohonic textures in hich the melody is harmonized ith a bass and then the to arts are ring modulated against each other to achieve distinct sectra. O the grous, l Itinéraire has erhas become more readily associated ith this style o music. Arguably the most amous members o l Itinéraire are Gérard Grisey and Tristan Murail. Students o Messiaen, the comosers are idely considered athers o French sectral music. The to met in the early 90s and soon ormed l Itinéraire, the Ibid.,.

16 leading ne music ensemble in France at the time. The origins o French sectral music emerged, at least in art, as a reaction to the serial aesthetic that dominated contemorary music rom the mid-tentieth century. The earliest ieces to emerge rom the l Itinéraire comosers include Sables or orchestra and Mémoire/Erosion or horn and ensemble by Murail, and Dérives or to orchestral grous by Grisey. In Sables and Mémoire/Erosion the musical structure is deined by driting beteen moments o ure consonance derived rom the natural overtone series and assages o extreme dissonance analogous to so-called hite noise. Similarly, Dérives ocuses on a recurring consonant E-lat sectrum uon hich transormations occur. Grisey exlores urther the rocesses ound in Dérives in his titanic cycle Les esaces acoustiques. Heavily inluenced by electroacoustic comosition, Murail sent the remainder o the decade exloring the sonic ossibilities o acoustic instruments maniulated by electronics, articularly ring and requency modulation. The culmination o his ork and research during this eriod as the ambitious orchestral ork Gondana. In the case o both comosers, this tye o music has imortant ramiications on orm and time. In addition to these to major grous in France and Germany, there ere arallel develoments in other arts o Euroe. During the same time, Romanian comosers such as Miereanu, Radulescu, Niculescu, Stroe, Dumitrescu, and Loachimescu exlored sectral techniques in a style that combined them ith olk music. In Budaest, the comosers associated ith the Exerimental Grou o Hungarian Radio synthesized many trends rom tentieth century music, emhasizing acoustic ulian Anderson, Grisey, Gérard, Grove Music Online, Oxord Music Online, Oxord University Press, accessed anuary, 0, htt://oxordmusiconline.com/sibscriber/article/grove/music/90.

17 roerties. 9 Other comosers cited as ractitioners o sectralism during this eriod include the English comoser onathan Harvey and the little-knon German comoser Erhard Grossko. By the mid-to-late 90s the sectral movement had begun to inluence a ide range o comosers, resulting in numerous develoments. France has seen the emergence o the nearest thing to a school o comosers exanding and develoing the research o Grisey and Murail. Puils o theirs such as Philie Hurel, Marc-André Dalbavie, ean-luc Hervé, and oshua Fineberg have all exloited the latest technologies. 0 In Finland, the music o Kaija Saariaho and Magnus Lindberg exhibits sectral inluences. In the case o each o these comosers, the aesthetic as assimilated and aroriated into their individual styles. Even the music o Grisey and Murail shited rom the slo, dense textures o the 0s: In their orks o the late 90s and early 90s, [Grisey and Murail] avoided the smooth rocesses characteristic o their earliest mature ork, ocusing instead on discontinuity and unredictable orms, ith a ne emhasis on linear, olyhonic riting. It is erhas no coincidence that both turned during this eriod to riting or the voice. Les esaces acoustiques (Gérard Grisey), Gondana (Tristan Murail), and Symhony No. (Per Nørgård) Beteen 9 and 9 Gérard Grisey created his Les esaces acoustiques, a massive cycle o six ieces exloring sectral techniques and aesthetics. The ork, totaling more than an hour and a hal o music, can be erormed in its entirety or adjacent ieces can be erormed indeendently, ith the excetion o eilogue, hich 9 Anderson, Provisional History,. 0 Ibid., 0. Anderson, Sectral Music. 9

18 may only be erormed hen receded by the entire cycle. As the ork rogresses rom the solo viola that comrises the oening movement, instrumental orces are gradually added hile the harmonic sectrum exands. The entire cycle is based on a attern o inhalation-exhalation-rest. The moments o rest are marked by regular, eriodic atterns and a art o a harmonic sectrum on E. This rise and all o tension maniests itsel most rominently in the transitions rom harmonic and inharmonic sectra, in hich harmonic sectra are those closely resembling the natural overtone series. Each ork is designed to elide naturally into the succeeding movement, alloing seamless transitions throughout the cycle. The only ause beteen movements comes at the end o Partiels hen the ork ades to silence. The six movements are derived or the most art rom various orms o an E sectrum. In the oening Prologue, the solo viola exlores the uer artials o this sectrum, though the undamental is not stated until the olloing movement. As the sectrum transitions sloly rom harmonicity to inharmonicity, the timbre o the viola gradually transorms rom the relatively ure sound o ordinario boing to sul onticello and eventually extreme overressure. The resolution comes ith the return to an area o harmonicity and ure timbre o natural harmonics. As the Prologue dovetails into Périodes, the undamental E is inally stated and it becomes clear that both the material o Périodes and the receding movement are derived rom its sectrum (Examle ). Anderson, Grisey, Gérard. 0

19 Examle : Harmonic Sectrum o Prologue and Périodes. In similar ashion, the transition rom Périodes and Partiels is seamless. Partiels oens ith the very same trombone blasts that close Périodes. The sectrum used in Partiels comes rom the sonogram o a trombone laying E at a orte dynamic. This sectrum is then orchestrated to create the beginning o the movement, a rototyical examle o instrumental synthesis (Examle ). Much like the revious movements, Partiels gradually moves rom the harmonic sectrum o the trombone to an invented inharmonic sectrum. Noise elements are introduced as the ork rogresses and by the end o the movement, the sectrum has deteriorated into hite noise beore ading into silence. Examle : A trombone E Sectrum.

20 Unlike the receding movements, Modulations begins in an area o relative tension and instability. The ork moves rom this dissonant harmonic sectrum to that o relative consonance and back again. A dissonant sectrum can be deined as that hich bears relatively e similarities to the natural overtone series. As the iece traverses a number o sectra, Grisey uses the oortunity to exlore texture. Throughout the movement, e ind examles o static soundmass, imitative olyhony, microolyhony, layered soundmass, and layered microolyhony. One rimary element o transormation Grisey emloys in the iece is iltering. Sectral analysis shos that brass mutes act as ilters, eliminating some artials hile strengthening others. For Modulations, Grisey uses sectra rom harmon mutes, stoed horns, cu mutes, and an imagined mute to generate timbral transormations (Examle ). Kari E Besharse, The Role o Texture in French Sectral Music, (DMA diss., University o Illinois, 009),. François Rose, Introduction to the Pitch Organization o French Sectral Music, Persectives o Ne Music, no. (summer 99): 9.

21 Examle : Harmonic sectra used in Grisey s Modulations. The enultimate iece,transitoires, uses sectral analyses o ive dierent contrabass laying techniques: izzicato, ordinario, near the bridge, almost on the bridge, and sul onticello as its source material. With its enlarged orchestral orces, the iece unctions as the climax o the entire ork and recalls gestural and harmonic materials rom the revious movements. The reerences to the earlier ieces continue in Eilogue, hich, as in Prologue, begins ith solo viola beore being joined by ull orchestra and an additional our solo horns.

22 Tristan Murail s most ambitious iece rom this eriod dras heavily on the ork he reviously did ith electronic music. The bulk o the itch content in Gondana is generated ith requency modulation synthesis. Develoed by ohn Choning, requency modulation involves a carrier requency being altered by a modulating requency, resulting in a sectrum made u o summation and dierence tones. The oening section o Gondana is comrised o a series o sonorities generated by FM synthesis. Examle shos the ive carrier requencies Murail modulates ith the requency 0. Hz (G). Examle shos the requencies achieved rom modulating the irst carrier signal. The comoser then builds the oening harmonies using the summation and dierence tones. Examle : The carrier requencies used by Murail in Gondana. The resulting sectrum is relatively comlex and resembles, to some extent, that o a bell. In his orchestration, Murail emhasizes the bell-like qualities by scoring the lo requencies in the brass and the higher requencies in the oodinds. The attack is emhasized ith a variety o itched ercussion instruments and iano that quickly Ibid., 0

23 dissiate, leaving certain higher requencies. The resulting enveloe is a close aroximation o the enveloe o an actual bell. Examle : Summation and dierence tones achieved in Gondana by modulating the irst carrier signal ith the modulating requency. An imortant iece that uses sectral theoretical systems in an aesthetic ar rom that o the French school can be ound in Per Nørgård s Third Symhony. In this ork, Nørgård links three distinct hierarchical systems reresenting the melodic, harmonic, and rhythmic domains, resectively. The rhythmic system is derived rom the Fibonacci series and the melodic system is Nørgård s hallmark ininity series. The harmonic Ibid., To develo the ininity series, one begins ith to notes, a single interval. This interval contains all necessary inormation to generate the entire series. The interval is marked out rom either initial note, inverted melodically to generate the next to notes. The interval beteen the second and third notes then determines the next to notes and so on. For more inormation on the ininity series see Kullberg, Beyond Ininity: On the Ininity Series the DNA o Hierarchical Music, (99).

24 system comes directly rom the natural overtone series and enables the interaction o the other to systems. In the irst movement, Nørgård chooses to exose the harmonic materials indeendent o the melodic and rhythmic materials. The movement oens ith a strong bass attack that leaves the highest o artials to sell into a quintessential sectral texture. The cascading igures in the high strings and oodinds oint unmistakably to the undamental o G that is later stated during the culmination o the introduction (Examle ). The overtone series is then exlicitly stated in measures through in gloriied ortississimo trombones, so as to make the harmonic materials o this iece exlicit. Examle : Symhony No., st mvt., mm. 0.; iano, har, violin. The second movement oens in a similar ashion ith a statement o the subharmonic series (Examle 9), resulting in a decidedly minor quality throughout the iece. Though more subtle, this statement is no less exlicit than that o the irst movement.

25 Examle 9: Subharmonic series used in Symhony No., nd mvt. In addition to roviding the harmonic underinning or the entire symhony, the overtone series also rovides the means or all three hierarchical systems (melody, harmony, and rhythm) to interact as one comrehensive hierarchical structure. The artials o the harmonic series, understood as ratios, rovide the necessary rameork. I the octave is vieed as a ratio o :, e can easily see ho rhythmic (temo) and melodic relationshis interact (Examle 0). With other artials, the task becomes more comlicated. The relationshi beteen artials to and three can be exressed as a : ratio. In the rhythmic domain this could easily be exressed as a olyrhythm o three against to but the melodic ininity series does not it so nicely. Here the undulating rhythms derived rom the Fibonacci series become necessary to acilitate the linking o the three series. Examle 0 shos the simlest interaction o the harmonic and melodic series as a single hierarchical structure as exressed by the ratio ::. Examle 0: The interaction o the ininity series ith the natural overtone series.

26 Analysis o Kaija Saariaho s Du cristal à la umée O the generation immediately olloing Grisey and Murail, Kaija Saariaho stands out as one major comoser that ully assimilated the sectral techniques o her redecessors hile retaining her on voice and aesthetic. Her earliest orks sho a transition in emhasis rom melody to tone color. By the 90s, timbre and harmony became inextricably linked and unctioned as the rimary elements in her comositions, emloying a noise/sound axis to relace the conventional dissonance/consonance arameters. 9 Saariaho s music is oten inormed by a strong recourse to extra-musical sources including nature, literature, and the visual arts. Her sources o insiration are sharly juxtaosed ith her aroach to comosition, hich is almost alays aided by a comuter and marked by meticulous calculations. Both o these actors igure imortantly into Saariaho s ditych Du cristal à la umée. The title, literally translated as rom crystal into smoke, comes rom the book Entre le cristal et la umée by Henri Atlan. In the comoser s ords, Du Cristal a la umée is one orld ith to aces, both comletely deined, living and indeendent. 0 The to orks may be layed individually or together as a unit. Saariaho s irst ork or large orchestra, Du cristal as commissioned jointly by the Los Angeles Philharmonic Orchestra and the Helsinki Festival, and it as irst erormed by the Finnish Radio Symhony Orchestra. à la umée is essentially a double Kimmo Korhonen and Riso Nieminen, Saariaho, Kaija, Grove Music Online, Oxord Music Online, Oxord University Press, accessed anuary, 0, htt://.oxordmusiconline.com/subscriber/article/grove/music/9. 9 Kaija Saariaho, Timbre and Harmony: Interolations o Timbral Structures, Music and Psychology: A Mutual Regard, secial Issue, Contemorary Music Revie (August 009): 9. 0 ulian Anderson, Programme Note: Du cristal, Kaija Saariaho Personal Website, accessed anuary, 0, htts://saariaho.org/orks/du-cristal. Ibid.

27 concerto or alto lute and cello. It comes as little surrise that the comoser chose these instruments to shocase: they each have received extensive attention in her solo and chamber outut. Like many o Saariaho s orks, Du cristal à la umée makes use o electronics, but to a lesser extent. A rominent synthesizer art is ound in each movement and the soloists in à la umée are amliied. The to ieces, though strikingly dierent on a surace level, are considered by the comoser to acets o the same image; the same materials in diverging directions. The immediately erceivable dierences in the to ieces can be understood as a direct result o their resective titles. Anderson in his rogram note or the ditych rites, Crystal is a classic examle o reeated order, symmetrical, tense, stable mass. Smoke, on the other hand, changes its orm constantly, an unredictable, develoing state. Crystal and smoke, like order and entroy, chaos. The olloing analysis ill exlore the relationshi beteen the to ieces ith regards to symmetry and musical content. For each iece the arameters o timbre, texture, gesture, rhythm, and itch content ill be discussed in order to understand the ays in hich the comoser generates rogression and orm. Analysis o Du cristal The harmonic content o Du cristal is almost entirely derived rom the bell-like chord that oens the iece. During the irst measures o the comosition, the sectrum o the oening sonority is augmented ith the gradual addition o other Ibid. ulian Anderson, Programme Note: à la umée, Kaija Saariaho Personal Website, accessed anuary, 0, htts://saariaho.org/orks/a-la-umee. 9

28 requencies. Examle 0 shos a reduction o the original chord and the sulementary itches. Once these additional itches are added, the oening harmony remains relatively static or the irst 0 measures. An illusion o motion is achieved in the itch domain by the use o microtonal inlections and the movement o instruments rom one itch to another. Glissandi in articular lay an imortant role in the erceived motion o the harmonic material, alloing the string instruments to traverse ide intervals in the chord ithout comromising its overall character. The comoser urther varies the oening harmony by exloring and emhasizing certain itches in the sectrum and constantly shiting the orchestration. Examle : Harmonic content at the oening o Du cristal. Black note heads indicate itches added ater the initial chord is sounded. The stasis o Du cristal s oening is relaced in the middle section ith a relatively quick rate o change. These ne sonorities continuously evolve and change in tandem ith the texture. Several harmonies serve as markers ithin this section because o their location in the structure o the comosition. Measure 09 is the irst signiicant arrival oint o the iece and marks a change o direction that reciitates the climax o the ork, hich arrives at measure. Nearing the end o the ork e ind 0

29 the harmonic material returning to that o the beginning. The original chord, ith slight modiications, is restated tice, the irst being at measure. From this oint, the chord is reduced as itches are gradually eliminated until only the E-lat trill that concludes the movement remains. Examle shos a harmonic reduction o Du cristal. Examle : Structural Harmonies in Du cristal. The concet o melody, as it is traditionally deined, does not aly to Du cristal. There are moments in hich melodic ragments are gradually layered to create distinctive textures. In these instances the ear erceives the ragments as art o larger microolyhonic texture, rather than a broken melody. Examle illustrates such a texture. More oten, hoever, e ind a sense o line created by the intereaving o small gestures by many instruments. In this ay, large sections o the iece are generated rom the most basic o materials. Four indeendent arameters can be delineated as the undamental materials o this iece:. Pitch: trills beteen small intervals or glissandi. Volume: crescendo and diminuendo

30 . Rhythm: change rom short to long durations. Timbre: change beteen bo ressures or beteen itched and non-itched sounds By maniulating these our arameters the comoser generates the orm o the iece and creates a sense o orard motion desite the static nature o the harmony. Examle : Du cristal, mm., oodinds. In the case o each arameter and the ditych at large, a endulum concet is signiicant. Simly ut, a endulum motion involves modiying one arameter and then returning to the original state. We have already seen the endulum motion on a large Martha Brecht, Kaija Saariaho s ditych Du cristal and à la umée: An Analytical Aroach, Toics Texts Tensions: Essays in Music Theory on Paavo Heininen, oonas Kokkonen, Magnus Lindberg, Usko Meriläinen, Einojuhani Rautavaara, Kaija Saariaho Aulis Sallinen (n..,999),.

31 scale in the harmonic construction o the iece, ith a dearture rom and a return to the original chord. Alied globally, a endulum can be observed beteen Du cristal and a la umée, ith the solo cello trill beteen the to movements serving as the center o the endulum. A endulum motion alied to a seciic sound arameter usually lasts beteen and measures. In the dynamic domain, the most tyical maniestation is a crescendo rom niente immediately olloed by a diminuendo. Regarding timbre, changes in bo ressure are most common. A descending glissando is oten balanced by an ascending glissando, and vice versa. The entire orm o Du cristal is built u entirely o these endulum motions. Examle shos a static soundmass texture in the strings constructed ith timbre changes (sul tasto to ordinario) and sells in dynamics. As or the overall orm o Du cristal, I e take the irst measures as introductory material, e can divide the remainder o the iece into three large sections. Measures to are dominated by soundmass textures and occasional microolyhony. Pitched metal ercussion dominates the oreground and the harmonic content is derived rom the oening bell sonority. Measures to are marked by dramatic shits in texture and a aster rate o harmonic change. The harmonic sectrum increases in inharmonicity, groing toard the climax. Rhythm becomes the rimary catalyst or motion in this section, moving gradually rom the irregular rhythms o the timani and rototoms at the beginning to the ounding ostinato o the climax. Hal endulums become rominent in this section. For examle, dissonant sonorities ill be attacked at orte and diminuendo into silence. The inal section, to the end, begins

32 as the ounding ostinato dissolves into sustained textures, signaling a return to the irst section and comleting the endulum motion. Examle : Du cristal, mm., strings.

33 Analysis o à la umée As its name might suggest, à la umée is marked by unredictability and a constant state o change in all the musical arameters. The iece at times even suggests outright chaos. The biggest dierences beteen the to ieces are texture and orm. Whereas Du cristal s texture is dense and changes gradually over time, à la umée is characterized by much sarser textures that change quickly and dramatically. In the case o each, the textures hel delineate the overall orm o the iece. For Du cristal, this results in a endulum motion: a long excursion rom the oening material and back. In à la umée, e get a succession o disarate arts, ith a notable absence o traditional ormal elements. The undamental materials o the to ieces are the same: trills and glissandi, sells in volume, changes rom itched to un-itched sound, and short melodic ragments. Unlike Du cristal here the endulum motion unctions as the building blocks o the comosition, à la umée is almost entirely void o these gestures. Martha Brech, in her analysis, contends that in contrast to Du cristal, à la umée is illed ith hal-endulums. Writing about the rimary gestural materials in this iece Brech rites, it is interesting to note that only the relecting surace is missing to create the characteristic imression o mirroring symmetry ound in Du cristal. These hal endulums are maniested most clearly in the volume domain as shar crescendos rom niente or a diminuendo olloing a shar attack. Examles in other arameters, though less obvious, exist as ell: or instance, glissandi ill reach their terminal oint ithout returning to their itch o origin and boing ill change rom ordinario to sul tasto and Ibid.,.

34 remain there. In each case, these hal endulum gestures unction as contrasting material to the rimary lines usually ound in the solo instruments. Whereas in Du cristal the endulum motions tyically unction as dense textures in the background, the hal-endulums o à la umée usually exist in the oreground. There are three contrasting textures in à la umée rom hich a number o varieties are generated. The irst texture encountered is reerential o Du cristal: static soundmass and microolyhonic textures that are built u rom small endulum gestures. The second is a sarse texture ith energetic lines ound in one or both o the solo instruments. In most instances, the soloists are accomanied only by a thin texture o sustained notes. More rarely hoever, e see individual instruments or amilies o instruments joining the soloists in their material. The treatment o the to soloists is such that hen they lay together, the distinction beteen the to is blurred. The result is a kind o meta-instrument that is heard as one line (Examle ). There are, o course, instances here each soloist lays alone. In such cases, the accomanying textures discussed above aly. The inal texture ound in à la umée is generated hen the soloist s material is built u in the tutti orchestra into microolyhony. Examle : à la umée, mm. 9 9, solo alto lute and solo cello.

35 The most dramatic dierence beteen Du cristal and à la umée is not in the textures emloyed, but rather in the transitions beteen each texture. In the ormer, textures evolve gradually and transitions are seamless; in à la umée, some textures gradually change over time, more oten ne textures are introduced abrutly, requently interruting the revious one. The result is a sometimes jarring scission o lines and materials. It is recisely these vertical breaks in the iece that deine it and distinguish it rom its redecessor. To tyes o vertical divisions in à la umée can be deined: the irst is an abrut shit in the total texture, beginning a ne oint in the structure o the iece; these occur near the beginning and end o the iece. The second tye aects the trajectory o the comosition less; these serve rimarily as interrutions o the solo lines and occasionally act as a trigger or a ne section. In addition to clariying the structure o the iece, these sudden breaks in texture rovide a sense o orard motion in their contrast to the rimary material. In terms o structure, it is diicult to erceive any sort o traditional orm. The iece moves rom its oening transitional material to the rimary section here the soloists interact ith one another and the orchestra. Aside rom several eisodes reminiscent o Du cristal, the section never changes and no real arrival oint is elt. Rather than ending, the iece seems to just sto ith one inal scission. à la umée oens ith the solo cello laying the E-lat trill that ended Du cristal. The remaining celli gradually ade in and out on the same igure as the itch content is built u. Throughout the irst measures the itch content is conservative, building u to a andiatonic set built around E-lat major. Dissonant chords exist in the brass as a means o contrast. The texture remains relatively sarse until measure here the

36 orchestra eruts into a cacohony o microolyhony comrised o igures that oreshado the ucoming material in the soloists a sort o orchestral exosition. The itch sectrum becomes increasingly dense and dissonant throughout this section. Ater measures o this, the texture thins and the energy dissiates. The solo instruments at irst alto lute, then cello are no introduced. The accomaniment is sarse, consisting mostly o sustained lines in the strings. As the section rogresses itched ercussion, olloed by oodinds, join the soloists in their material and build u the meta-instrument hile creating a more active texture. The irst scission occurs at measure in the oodinds and unctions as a simle interrution o the soloists. Several more interrutions occur during the olloing measures, each one becoming louder and more dissonant. The inal vertical break o the section, occurring at measure unctions as a trigger or a ne section, uon hich the orchestra returns to the energetic material earlier in the ork. This latest round o cacohony ends abrutly one o the only occurrences o silence in the entire ditych. The soloists emerge out o the silence. This time each is treated in turn ith dialogue rom the orchestra. The discourse beteen soloist and orchestra continues on or nearly 0 measures until measure, at hich oint the sudden interrutions in the texture return. The breaks are more violent, scored or non-itched ercussion and brass. Unlike the breaks o measure, these strike the listener as being more inal. Each vertical cut leaves the texture thin and inert. On irst listen, one onders i each break ill be the cut to end the iece. Ironically, the scission that does end the iece sounds the least deinitive o all.

37 Measure marks the return o Du cristal material and even includes comlete endulum gestures. In this ay the overarching endulum o the ditych is resolved. The total orm o the ditych can be understood by ay o symmetry ith the trilled E- lat in the cello as the axis. The symmetry comarison is urther suorted by the climax o each iece: Du cristal s occurs about to thirds into the iece, and à la umée mirrors that by climaxing at the beginning o its second third. A more overt unity is established ith the reintroduction o the material rom Du cristal. Analysis o Axiom Unearthed The characteristic techniques and aesthetics o the sectral style served as a oint o dearture or the accomanying original comosition, Axiom Unearthed. The rimary comositional technique or the iece involved sectral analysis and instrumental synthesis. The itch content or the entire iece is derived rom the sectrum o three basic sound sources: a gong layed at multile dynamics, a susended cymbal scrae, and an E layed on the contrabass ith varying bo ressures and attacks. For the gong I created three sonograhic reresentations corresonding to iano, mezzo iano, and orte strikes, resectively. Examle shos the most rominent artials o each notated to the nearest quartertone. For the contrabass, a sectral analysis as made o sul onticello and ordinario boing, as ell as izzicato, all on E. Examles and sho the notation o the susended cymbal scrae and the bass sul onticello sectra, resectively. My notation o the Sonograhic reresentations o the sound sources in Axiom Unearthed ere generated ith the rogram Sonic Visualizer, Nokia Cororation, 0. 9

38 analysis o the cymbal scrae shos the change o requency over the eriod o several seconds. All melodic and harmonic materials are generated rom these sectra. Examle : Aroximation o the harmonic sectra o a gong layed iano, mezzo iano, and orte. Examle : Aroximation o the harmonic sectrum o a susended cymbal scrae. 0

39 Examle : Aroximation o the harmonic sectrum o E layed sul onticello on the contrabass. The orm o the iece is generated rom the rogression o one sectrum to the next (Figure ). The ork oens ith an exloration o the gong sonority, and gradually introduces artials rom the mezzo iano and orte sectra. Three basic materials are imortant in this section: reeated to-note igures, dynamic sells in the brass (not unlike the hal endulums ound in à la umée), and sustained itches. The three igures interact in numerous ays, serving as the building blocks or various textures in the iece and acting as uniying motives throughout. Examle demonstrates the interaction o the three elements. The climax o the oening section coincides ith the most dissonant incarnation layed tutti, immediately dissolving into a more harmonic sectrum.

40 Figure : Formal analysis o Axiom Unearthed The second section, beginning at measure, is characterized by the use o multile sectra, all relatively harmonic. The background material is derived rom the bass ordinario sectrum, resulting in a arm E major sonority, hile the oreground material alternates beteen that o the susended cymbal and the bass izzicato. The bass izzicato sectrum is shon in examle 9 along ith an inversion o the uermost artials in the sectrum. The texture throughout this section is sarse in comarison to the beginning. Solo lines are accomanied by sustained notes in the strings and clarinets. Examle 0 shos the rimary thematic material o this section, derived entirely rom these sectra, as layed by the English horn. The melody is exchanged rom English horn to solo strings beore the maestoso statement in the tutti strings. The material rom the oening briely returns, acting as a transition to the third major section.

41 Examle 9: Axiom Unearthed, measures 0. Examle 0: Aroximation o the harmonic sectrum o bass izzicato E and its inversion.

42 Examle : Axiom Unearthed, English horn, mm. 09. The itch content o the third section comes rom the sul onticello E and its inversion. Foreground in the brass and basses is an outgroth o the reeated-note igure o the oening: as the itch content gradually becomes more dissonant the running igures in the oodinds evolve into a renetic microolyhonic texture. The climax o the ork comes at measure hen the brass in cluster harmonies alternates ith violent outbursts in the oodinds and strings. A ortissimo tam-tam strike marks a sudden return to the gong sectrum that oened the ork. As the texture once again dissolves, only the harmonic artials remain. The coda, measures 0 to, urther modiy the gong sectrum until only the brilliant E major sonority o the last e measures is let. Conclusion Although inluenced by the French sectral comosers and the music o Kaija Saariaho, Axiom Unearthed is dierentiated rom those comosers in the ay it uses its original sound sources and the overall aesthetic o the iece. While the resulting sound orld is strikingly dissimilar to that o traditional sectral ieces, Axiom Unearthed contains a number o imortant similarities. The most imortant relationshi beteen Axiom Unearthed and Du cristal à la umée as ell as other sectral ieces is that itch content is derived rom harmonic sectra. In its use o the instrumental resynthesis o various sounds, Axiom Unearthed

43 emloys erhas the most imortant sectral technique. The dierence beteen Axiom Unearthed and the ieces discussed in this aer is that the ormer relies on sectra only insoar as to generate itch and orm. Whereas in traditional sectral ieces the exloration o harmonic sectra comrises the rimary discourse o the iece, Axiom Unearthed uses sectra as one arameter in service o the greater structure o the iece. In Axiom Unearthed, sectral analyses are used to generate melody and harmony in much the same ay as a tone ro or itch class set; in this ay the iece rogresses more traditionally in terms o themes. The resence o conventional melody in Axiom Unearthed may constitute the rimary dierence beteen it and early sectral ieces. Even Du cristal à la umée is largely void o melody, save or the motivic ideas that generate the rimary material in à la umée. I Axiom Unearthed rimarily uses sectral techniques as a means o generating harmony and melody, Du cristal à la umée emloys the same techniques to achieve color and a conglomerate timbre ithin the orchestra. This dierence accounts or the act that Saariaho reely emloys microtones in her ditych hile Axiom Unearthed uses them only saringly. Desite these dierences, several imortant similarities beteen Axiom and the ditych can be identiied. The various textures throughout Axiom Unearthed are largely inluenced by sectral comosers and Saariaho in articular. Both Du cristal à la umée and Axiom lace emhasis on microolyhonic and soundmass textures. Furthermore, each ork demonstrates a roensity or slo transition over time. The idea o gradual transormation o texture and timbre in Du cristal is one shared by Axiom Unearthed. The hal endulum motives that make u à la umée are nearly

44 ubiquitous in Axiom in the orm o dynamic sells. In regards to harmonic sectra, Du cristal à la umée and Axiom Unearthed each unveil their resective harmonic materials gradually, introducing individual artials over a relatively long eriod o time. Even ith these similarities accounted or, Axiom Unearthed stands out as a unique entry among sectral, ith clear inluences in the domains o itch and texture but ultimately a roduct o many varied inluences. It is a testament to the lexibility o sectral techniques that the aesthetics can vary so greatly rom the earliest sectral comosers o the 90s to the subsequent generation o Kaija Saariaho and beyond. That Axiom Unearthed can emloy some o the undamental tenets o the style at the service o a more traditional idiom is urther conirmation o this act.

45 Aendix Sectrograms o Source Materials in Axiom Unearthed

46 Gong layed iano Gong layed mezzo iano

47 Gong layed orte Susended cymbal scrae 9

48 Bass E layed ordinario Bass E layed izzicato 0

49 Bass E layed sul onticello

50 Bibliograhy Anderson, ulian. A Provisional History o Sectral Music. Contemorary Music Revie 9, Part (000): -.. "Grisey, Gérard." Grove Music Online. Oxord Music Online. Oxord University Press, accessed anuary, 0, htt://.oxordmusiconline.com/subscriber/article/grove/music/9.. "Murail, Tristan." Grove Music Online. Oxord Music Online. Oxord University Press, accessed anuary, 0, htt://.oxordmusiconline.com/subscriber/article/grove/music/90.. Programme Note: Du cristal. Kaija Saariaho Personal Website. Accessed anuary, 0. htts://saariaho.org/orks/du-cristal.. Programme Note: à la umée. Kaija Saariaho Personal Website. Accessed anuary, 0. htts://saariaho.org/orks/a-la-umee.. "Sectral music." Grove Music Online. Oxord Music Online. Oxord University Press, accessed December, 0, htt://.oxordmusiconline.com/subscriber/article/grove/music/09. Besharse, Kari E. The Role o Texture in French Sectral Music. DMA diss., University o Illinois, 009. Brech, Martha. Kaija Saariaho s ditych Du cristal and à la ume: An Analytical Aroach. In Toics Texts Tensions: Essays in Music Theory on Paavo Heininen, oonas Kokkonen, Magnus Lindberg, Usko Meriläinen, Einojuhani Rautavaara, Kaija Saariaho Aulis Sallinen. -0. n..: 999. Cornicello, Anthony. Timbral Organization in Tristan Murial s Désintégrations. PhD diss., Brandeis University, 000. Coell, Henry. Ne Musical Resources. Ne York: Cambridge University Press, 9. Fineberg, oshua. Guide to the Basic Concets and Techniques o Sectral Music. Contemorary Music Revie 9 (000): -. Grisey, Gérard. Did You Say Sectral translated by oshua Fineberg. Contemorary Music Revie 9 (000): - Hasegaa, Robert. Gérard Grisey and the Nature o Harmony. Music Analysis, nos. - (uly-october 009): 9-.

51 Kullberg, Erlig. Beyond Ininity: On the Ininity Series the DNA o Hierarchical Music. In The Music o Per Nørgård: Fourteen Interretative Essays, edited by Anders Beyer, -9. Brookield: Ashgate Publishing Co., 99. Korhonen, Kimmo and Risto Nieminen. "Saariaho, Kaija." Grove Music Online. Oxord Music Online.Oxord University Press, accessed anuary, 0, htt://.oxordmusiconline.com/subscriber/article/grove/music/9. Moscovich, Viviana. French Sectral Music: An Introduction. Temo Ne Series 00 (Aril 99): -. Partch, Harry. Genesis o A Music: An Account o a Creative Work and its Fulillments. Ne York: Da Cao Press, 99. Pressnitzer, Daniel, and Stehen McAdams. Acoustics, Psychoacoustics and Sectral Music. Contemorary Music Revie 9 (000): -9. Rose, François. Introduction to the Pitch Organization o French Sectral Music. Persectives o Ne Music, no. (Summer 99): -9. Saariaho, Kaija. Du Cristal. Helsinki: Edition Wilhelm Hansen, 99.. à la Fumée. Helsinki: Edition Wilhelm Hansen, Timbre and Harmony: Interolations o Timbral Structures. In Music and Psychology: A Mutual Regard. Secial issue, Contemorary Music Revie (August 009): 9-.. Works or Orchestra. Ondine ODE -q, 0, comact disc. Sadler, Graham and Thomas Christensen. "Rameau, ean-philie." Grove Music Online. Oxord Music Online. Oxord University Press, accessed anuary, 0, htt://.oxordmusiconline.com/subscriber/article/grove/music/. Wilson, ames. A Brie Survey o Olivier Messiaen s Harmonic Practise. Accessed anuary, 0,.academia.edu/99/A_Brie_Survey_o_Olivier_Messiaen_s_Harmonic_ Practise.

52 PART II AXIOM UNEARTHED

53 ohn Clay Allen Axiom Unearthed or orchestra FOR REVIEW ONLY

54 Instrumentation Piccolo Flutes Oboes English Horn in F Clarinets in B- lat Bass Clarinet in B- lat Bassoons Contrabassoon Horns in F Trumets in B- lat Trombones Bass Trombone Tuba Timani Percussion (Susended Cymbal, Bell Tree, Tam- tam) Percussion (Bass Drum, Tam- tam) Percussion (Glockensiel, Marimba) Har Strings FOR REVIEW ONLY

55 Perormance Notes Strings Percussion S.P. sul onticello S.T. sul tasto Ord. Ordinario Gradually change rom one laying technique to another. Gradually add bo ressure until tone is relaced ith noise. Susended Cymbal Scrae Boed Tam- tam FOR REVIEW ONLY