experiencing structure in penderecki’s threnody: … · experiencing structure in penderecki’s...

Experiencing Structure in Pendereckirsquos Threnody Analysis Ear-Training and MusicalUnderstanding

mariusz kozak

Elliott Carter once extolled the visceral primitive effect of Pendereckirsquos Threnody on untrained lis-teners In this article I examine how a formalized analytical approach to the central section of thepiece contributes positively to a phenomenological experience of the whole piece Part 1 presents anear-training progression aimed at bringing to attention some important structural relationshipsbetween pitched elements of the passage including pitch-space transformations that act on chordal-density compressions Part 2 initially questions the relevance of transformational analysisndashndashconstrued as an enactment of a particular kind of understandingndashndashto the experience of Threnodyultimately favoring a transformational hearing of the work The conclusion points out how a ratio-nalized ear-training allows a listener to chart an auditory course through the passage and how theresulting experience can illuminate a new way of conceptualizing Pendereckirsquos intricate sonicmaterials

Keywords Penderecki Threnody transformations ear-training

Writing some three years after the premiere ofPendereckirsquos Threnody To the Victims ofHiroshima (1960)ndashndashoriginally titled 8rsquo37rdquondashndashElliott

Carter praised the piecersquos powerfully poignant effect on lis-teners1 What he noted in particular was its ldquoanti-artisticrdquo ex-pression whereby the very severe harsh sonic effects that thecomposer created receive justification from the experientialgoals of the work as a whole For Carter the raw fundamen-tal even ldquoprimitiverdquo sounds that Penderecki elicits from the or-chestra point to the physicality of sound production2 to theacting body that is somehow present both in and behind themusic3 As Carter saw it this ldquocan have a wide appeal on asimple sensuous level and often attracts those not trained to

expect and grasp the higher types of order found in oldermusicrdquo4

Indeed even now the work can lure listeners into its thickweb of historical and cultural associations in which the horrificsounds provide and sustain a breathtaking background for anexcruciatingly emotional release Of course thanks to the so-bering distance of time the work also affords a more re-strained cool-headed response For example RichardTaruskin writes that for him the famous ldquoscreamsrdquondashndashrepresented by the piecersquos opening clustersmdashcan only be iden-tified as screams because they have been marked as such bycritics and by listeners since the workrsquos premiere Meanwhileafter the opening ldquothere is nothing in the piece of a compara-bly pictorial or suggestive characterrdquo5 Considering these op-tions if he were submitting his concert report today Cartermight have drawn on the vast literature emerging from thefield of embodied and enacted cognition to delve deeper intothe workrsquos ldquoappeal on a sensuous levelrdquo and its nonlinearmultifarious relationship to listenersrsquo abilities to ldquograsp thehigher types of orderrdquo6 This juxtaposition of bodily sensationsinduced by the music with a seemingly rational analysis-proneordering of events made possible only with training is particu-larly telling It leads us to invoke the idea of embodied experi-ence in order to consider one way in which analysis and

The author wishes to express his deepest gratitude to Steven RingsRichard Hermann Julian Hook and Joseph Dubiel as well as the anony-mous reviewers and the editorial staff of Music Theory Spectrum for theirinsightful comments and invaluable suggestions on earlier drafts of thisarticle

1 Carter (1963) Penderecki was advised to change the piecersquos title in ad-vance of submitting it to a UNESCO competition in France (Thomas2005 165)

2 It is unclear whether the word ldquoprimitiverdquo is meant to describe Carterrsquosimpression of individual sounds or of their organization (Carter 1963202) In both cases one should take issue with his characterization Withregard to form Pendereckirsquos use of a canon as well as the long-range de-sign shown by both Mirka (2000) and myself below points to a very so-phisticated background of specialized musical knowledge Meanwhilebranding these sounds as ldquoprimitiverdquo belies the highly constructedsociocultural context of string instrument production of performance ofthe relationships between the musicians between them and the conductorand so forth Many thanks to Richard Hermann for pointing this out

3 The relationship between our perception of musical sounds and ourawareness of the human bodies that produce them has been explored withconsiderable interest in the recent years Of the plethora of studies thathave appeared in the last decade some more exemplary ones include Cox

(2011) Godoslashy (2010) and Clarke (2005) For a critical assessment ofsome of the claims made therein see Kozak (2015)

4 Carter points to Stravinskyrsquos Rite of Spring as a precursor to this kind ofaesthetic (1963 202)

5 Taruskin (2005 220)6 Among the plethora of sources on embodiment and enaction we can

point to Varela et al (1991) as the seminal work that attempted to dissolvethe mindbody split in the cognitive sciences For more recent practicaland theoretical developments see Stewart et al (2010)

200

sensation can productively interact with one another contraCarter listening to Threnody is not necessarily a case of ldquoei-therorrdquo

Without reflecting on the implications of such a statementperhaps many readers find themselves asking what kinds of lis-tening attitudes a particular piece of music invites elicits orengenders Indeed as one of the first steps toward understand-ing a musical work this kind of assessment seems well worthit because it positions the listener relative to the piece in a waythat can then serve as a starting point for further analysisSome pieces thus seem to work best with we might call an ldquoin-tellectualrdquo approach or what Theodor Adorno refers to asldquostructural listeningrdquo7 Further elaborating this notion hewrites of letting a composition ldquounfold itself in its own termsrdquoso that it may ldquoassert itselfrdquo and allow one ldquoto enter into itsstructure analyticallyrdquo all of which resonates with the abovenotions of invitation and elicitation that musicians may ascribeto pieces of music8 With such a strategy we might look forways in which the musical surface opens up to reveal an under-lying logic something that we can ldquograsprdquo (in Carterrsquos senseabove) as a rational progression of sounding eventsMeanwhile other works appear to be better experienced emo-tionally viscerallyndashndashwith our bodies rather than with ourbrains9

Of the two attitudes Threnody seems to encourage the lis-tener to become emotionally and somatically absorbed in itssoundsndashndashit seems to facilitate an engagement with the musicrsquosphenomenal experience At least in Carterrsquos view this is thedefault unmediated reception that does not require an intel-lectual engagement with the piece Without doubt there areplenty of musical elements on display here that typecast thework as resistant to rationalization thick microtonal textureslack of articulated and easily identified events and a continu-ously unfolding form that on its surface precludes traditionalnotions of design in favor of an unencumbered process Yetnone of this necessarily disqualifies a structuralist hearing onebased on the development of theoretical and perceptual models

and which allows a listener to approach the piece with an earfor such concepts as structure logic and coherence Quite thecontrary an analytical appraisal of Threnody can enhancerather than impede onersquos embodied sensual experience

One theoretical model for analyzing Pendereckirsquos sonic pal-ette can be found in Danuta Mirkarsquos monograph TheSonoristic Structuralism of Krzysztof Penderecki10 There sheproposes a method based on ideas adapted from Saussurianstructuralism in which her so-called contrary and contradic-tory elements are juxtaposed in a compositional system whoseldquoaxiom is not a concept of a single sound event but of soundmatter taken in its totalitymdashen masse so to sayrdquo11 Contrary el-ements are those that mathematically ldquocan be modeled as arelation between a given set and its complementrdquo while con-tradictory ones are modeled by ldquoa relation of two sets each ofthem belonging to the complement of the otherrdquo12 Less for-mally contradiction describes an opposition between discretestates (eg mobility vs immobility) while contrariety introdu-ces the possibility of a third term in the opposition (eg loudvs soft dynamics where the possibility of a ldquomiddlerdquo dynamicrange also exists) In all cases Mirka illustrates how the rela-tions between various sonic parameters are modeled by fuzzysets with obscured boundaries between limit conditions Setsthat is in which ldquothe transition between membership andnon-membership is gradual rather than abruptrdquo (containingwhat is colloquially referred to as ldquoborderline casesrdquo) such thatmembership is assessed in terms of continuous values between0 and 1 rather than in binary terms familiar from classical settheory13

Mirkarsquos goal is to uncover formalizable relationships in asound world that according to her had previously been de-rided as lacking rational order or logical unfolding Her mostimportant finding is that there are indeed long-range order-ing principles that determine how Penderecki treats the kindsof raw and ldquoprimitiverdquo sounds that so struck Carter but thatdo not operate along the traditional formal paths of linear de-velopment Moreover she demonstrates how elements otherthan pitches and harmoniesndashndashnamely texture density articula-tion loudness and timbrendashndashparticipate in creating structureand cohesion not just in Threnody but also in the composerrsquosother works collectively referred to as ldquosonoristicrdquo14

7 Adorno (2002) For an exposition and critique of structural listening seeSubotnik (1995) For responses to Subotnikrsquos deconstructive reading ofAdorno see essays in DellrsquoAntonio (2004)

8 Adorno (2002 166)9 Of course the dichotomy between the brain and the body is a coarse one

since the former is very much a part of the latter and I am using it here asa heuristic Thus in positing these two attitudes I am not claiming thatthere is a categorical distinction between them or that one necessarily pre-cludes the other Indeed recent embodied extensions to cognitive science(see n 7 above) provide evidence supporting the view that rationalthought is in no way divorced from our bodily states and that our actionsin response to the worldrsquos solicitations are as much a part of our cognitionas abstract reasoning Rather what I am suggesting is that as a way ldquointordquoa piece of music it is possible that some works promote a deliberate sup-pression of explicit bodily exertions in favor of a more detached evenatemporal study of its structural components One of the many ways inwhich composers can achieve this is by eschewing regular pulses therebyattenuating the listenersrsquo abilities to spontaneously entrain to and move insynchrony with the music (see London 2012)

10 Mirka (1997)11 Mirka (2000)12 Ibid13 Dubois and Prade (1980) For an accessible tutorial on fuzzy sets and their

musical application to contour theory see Quinn (1997)14 These include such works as Dimensions of Time and Silence (1960 rev

1961) Polymorhia (1961) Fluorescences (1961ndash2) and Anaklasis (1959ndash60) As Thomas (2005 166) points out with the exception of Threnody

(and even then only after a change) all bear scientific-sounding titles sug-gesting an experimental approach to sound as a matter of objective investi-gation the goal of which was ostensibly to discover its various propertiesFor more on sonorism see Mirka (1997 8) also see a special English-language issue of the Polish musicological journal Muzyka devoted to the

experiencing structure in pendereckirsquos Threnody 201

Despite her comprehensive approach mm 26ndash48 ofThrenody are conspicuously absent from Mirkarsquos large output ofanalyses15 and it is for this section that I have developed a seriesof ear-training exercises that involve contextual transformationsIn this passage Penderecki seems to have abandoned thesound-mass procedures found elsewhere in the piece whichperhaps helps explain why it is not treated in Mirkarsquos accountThe passage stands out as a relatively independent unit itappears in the middle part of the large A (mm 1ndash25) B (mm26ndash61) Arsquo (mm 62ndashend) framework on which Threnody isbased Measures 26ndash48 are audibly distinct from the outer partswhich are less pointillistic and more uniform in terms of sonicprocesses In addition the passage also follows the longest pausein the piece thus far (an interruption of some five seconds dura-tion) The formal technique used here by Penderecki as pointedout by some scholars is a canon16 but this design is thoroughlyobscured by the timbral and temporal characteristics of eachldquovoicerdquo As a result it is difficult to hear each subsequent entryas a reinstatement of the dux (mm 26ndash37) To clarify the audi-tory space and to bring this structure into focus as well as toconstruct a model for a potential hearing of this portion of thework the forgoing commentary will draw the readerrsquos attentionto some of the sonic elements that share common characteristicsand propose possible transformations that relate themAlthough it is likely that such an analysis might unearth thegenerative algorithm that Penderecki used in designing this ex-cerpt the concern here is not in ldquode-compositionrdquo as such17

Instead drawing on Lewinrsquos 1993 essay on StockhausenrsquosKlavierstuck III the goal is to present a listening aid which con-tributes to listenersrsquo active engagement with the piece18

The second section of this article addresses a broader critiqueof applying ldquotransformational ear-trainingrdquo to this particular pieceIt considers the conceptual and experiential underpinnings of theanalysis including the value of the analytical technique presented

in the first section for listening to Threnody Furthermorewhereas Part I is rather narrowly circumscribed within the normsof transformational analysisndashndashfocusing on relationships estab-lished by various complexes of pitched musical elementsndashndashPart IIopens up to a potentially damaging challenge to this method Itis here in fact that I develop a critical dialogue between the aimsof the ear-training model and the role of ldquonon-structuralrdquo eventsin the construction of listenersrsquo experiences of this piece The goalof this seemingly Janus-faced approach is to channel this critiqueinto creating a meaningful encounter with the Threnodyndashndashone ofmany possible encountersndashndashthat subsumes some of the less for-malist epistemological foundations of transformational technology(the ldquotransformational attituderdquo) within a broader field of con-temporary listening strategies19

i

Let us first note that the passage under discussion in whichthe whole ensemble is split into two Orchestras (I and II) dis-plays a wide gamut of varying articulations20 We can arrangethese articulations according to their most general sonic char-acteristics arco (A) and percussive (P) Designation A appliesto all the types of articulation in which any part of the bow(ie hair and stick) is used to produce sustained tones of de-termined duration In contrast elements P are characterizedby an indeterminate duration Example 1 represents this divi-sion Example 2 shows a reduction of the first four measuresof the fragment with annotations illustrating the categoriza-tion of elements into A and P (the former are further subdi-vided into An and Ad as explained below)

Example 3 reproduces the temporal arrangement of Aand P elements in Orchestra I from m 26 to m 48 Measure37 is excluded because in it the previous sonority is sustainedbut without a change in articulation In m 38 Orchestra II re-peats Orchestra Irsquos material in a ldquovisualrdquo inversion of sortsaround the Viola 2Viola 3 axis21 I have separated the exampleat m 38 to illustrate that this and the following measures in

historical genesis and development of the term as a theoretical conceptand an analytical tool (Granat 2008)

15 Here and elsewhere I use the term ldquomeasurerdquo to refer to segments demar-cated by vertical dashes in the score This terminology is used for analyti-cal convenience only and in no way suggests a metric design For more onthe temporal elements in Pendereckirsquos notation see Mirka (1997 Chapter13)

16 Gruhn (1971) Mirka (1997) Taruskin (2005 219ndash20)17 This is to say that I do not intend to ldquocrack the coderdquo of Threnody in a

manner comparable to Lev Koblyakovrsquos (1977) analysis of Boulezrsquos Le

Marteau sans maıtre for example Indeed there is an important differencebetween structure as something that can have significant implications foronersquos auditory experience of a piece of music and as generative algorithmsthat constitute the pre-compositional process With this in mind we canthink of the canon itself as a technique used to saturate the texture withenough voices to create an auditory ldquomassrdquo Meanwhile the kind of struc-ture posited here need not have had tactical significance for the composerbut will nonetheless affect the listenerrsquos experience Of course it is possi-ble that one could learn to hear the canon but I will not pursue this optionherein

18 I also acknowledge that there are a number of other ways to listen to thesemeasures some of which I will point out in the course of the analysis

19 The phrase ldquotransformational attituderdquo which emphasizes process overstate first appears in Lewin (1987 159) Klumpenhouwer (2006) statesthat the attitude in general is essential to Lewinrsquos project which cruciallyrests on its ldquoanti-Cartesianismrdquo even while its use of mathematics to solvemusic-theoretical problems betrays a debt to Descartes However Hook(2007) argues instead that the notion of an attitude forms a surplus intransformational technology beyond mathematical formalism that can besimply referred to as ldquofunctionrdquo and has therefore been overemphasizedin its consequences for the analytical process Perhaps a better word hereis simply ldquotransformational hearingrdquo Whereas ldquoattituderdquo suggests a gen-eral nontemporal comportment or intentionality (Rings 2011b) thischange in nomenclature points to the way in which listeners organize theirexperience in time

20 Although clusters play a role here to a certain extent (for instance in mm35ndash37) I will set aside this particular sonoristic technique for the timebeing

21 It is not a strict inversion in the sense of canonical transformations as willbe seen shortly The reader will also note that mm 43ndash49 in Orchestra Iare a retrograde ldquovisualrdquo inversion of mm 35ndash42

202 music theory spectrum 38 (2016)

Orchestra I (labeled Sec1 for ldquosection 1rdquo) constitute an accom-panimentcountersubject to Orchestra II and is therefore a sepa-rate section from mm 26ndash37 (labeled Sec2) The ldquoreposerdquo inmm 35ndash37 further supports this segmentation which resultsfrom a change in articulation and texture from earlier materialconsisting of instruments playing in two groups with uniformarticulation in each group and together sustaining two micro-tonal clusters The resulting effect is in contrast to previous andfollowing measures where each instrument is treated soloisti-cally with its own articulations The rates of change in both ar-ticulations and registers slow down sharply here perceptuallydemarcating this moment as a separate event

There is a noticeable increase in P elements from Sec1 toSec2 In Sec1 the cardinality of P (P) frac14 12 and the cardinal-ity of A (A) frac14 35 resulting in the ratio AP of 292 In Sec2P frac14 22 and A frac14 30 resulting in the ratio AP of 141 Oneway to conceptualize this is in the relationship of Orchestra Ito Orchestra II in Sec2 Since Orchestra II repeats materialfrom Sec1 where the predominant articulations were arco theincrease in P in Orchestra I allows A elements in Orchestra IIto clearly stand out in the sonic texture In other words ele-ments A and P have such distinct acoustical properties that itis easy to discern between them in listening

Within Pendereckirsquos extended timbral palette each elementin group A can be further subdivided into two categories (1) sus-taining a discrete pitch (labeled Ad) or (2) sustaining a nondis-crete pitch (eg playing between bridge and tailpiece behindthe bridge or on the bridge itself at a right angle at its right sidelabeled An) Example 4 reexamines Sec1 and Sec2 according tothis distinction Notice that Sec1 includes a fragment of a con-tinuous uninterrupted succession of Ad elements In contrastSec2 contains primarily An elements This suggests that Sec1 ofOrchestra I can be perceived by focusing on discrete pitches thecollections they form and the transformations between thesecollections It further indicates that the section played byOrchestra II in mm 38ndash47 (let us call it Sec1rsquo) can also be per-ceived in this manner because Ad elements are fundamental tomodes of hearing taught by Western conservatory ear-trainingprograms and are in general acoustically distinct from An ele-ments Based on these hypotheses let us examine pitch progres-sions in Sec1 and Sec1rsquo first as modeled abstractly in pitch-classspace and later as realized by Penderecki in pitch space

Example 5 shows the important vertical sonorities of Sec1in Orchestra I mm 26ndash35 most of which consist of three voi-ces forming members of set-class 3-1[012] and which areidentified with italicized upper-case letters above and to theleft of each system22 Letters below systems indicate pitch clas-ses The arrangement of set-classes 3-1[012] is more or lessconsistent from beginning to end with a couple of exceptionsFirst the very opening sonority (B C] D labeled A in the ex-ample) forms a member of set-class 3-2[013] instead Themissing pitch class C does indeed sound in close temporalproximity (pizzicato in Viola 1 on the second quarter note inm 26) however to remain consistent with our focus on Adelements I have excluded it from the model The second ex-ception occurs at the very end of the passage mm 33ndash35Here the sounding pitch classes are D and C] (see H in the ex-ample) which are common to sonority A in the beginning Wecould therefore construe of sonority A as made up of two differ-ent sonorities a C] D dyad and a B monad Such an ar-rangement of elements would allow us to consider sonority H asa closure of the progression set in motion by sonority A

An unusual moment occurs in mm 31ndash32 (sonority F)where instead of three five pitch classes are sounding simulta-neously Together they form set-class 5-1[01234] which likeset-class 3-1[012] is characterized by interval-class 1However rather than thinking of this sonority as a five-notesimultaneity which is suggested by the registral proximity ofall pitches we can subdivide it into two sonorities based on ar-ticulations and durations Thus F F] G could constitute onesonority Fb because all three pitches are of the same duration(half-note plus a sixteenth) and are articulated sul ponticelloIn contrast A and A[ are articulated con sordino and arco re-spectively and both last a quarter plus a dotted-eighth Wecan therefore consider this moment in two ways (1) it com-prises two three-note sonorities of set-class 3-1[012] in whichG acts as a common pitch connecting them (in this case ourestablished model of three-note successions remains undis-turbed) (2) A and A[ form a two-note sonority of set-class2-1[01] which is closely related to sonority A (minus the B)and sonority H In this case our model is disturbed but we

example 1 Division of sound events into arco (A) and percussive (P) Abbreviations and symbols in parentheses indicate how these eventsare represented in the score

22 Although the score does specify quarter-tones elsewhere in the piece inthis section only the twelve chromatic pitches are used


have further support of the reading proposed in the paragraphabove However regardless of which reading we do decideupon what remains is that sonority F continues the ic1 rela-tionship between pitch classes that has been established fromthe beginning I opt for the first interpretation below becauseof its analytical elegance but the second alternative couldprove viable as well if one were to pursue it further

Example 6(a) represents Sec1 in pitch-class space as an ab-stract network The nodes contain sonorities labeled with

letters corresponding to the previous example and the arrowsrepresent transformations which in this case are canonicaltranspositions Although initially there may be nothing re-markable about this network one important implication formy ear-training model is immediately made evident Insteadof latching on to seemingly random pitch simultaneities thelistener can now learn to hear the progression using nothingmore than ordinary run-of-the-mill transpositions In factExample 7 shows a realization of this network that can be

example 2 An annotated score of mm 26ndash29 showing elements arco pitched (Ad) arco non-pitched (An) and percussive (P)


example 3 Temporal arrangement of elements A and P in Sec1 and Sec2 (Orchestra I only)

example 4 Temporal arrangement of elements Ad and An in Sec1 and Sec2 (Orchestra I only)


played on the piano and can serve as the first stage in develop-ing ldquoan earrdquo for the passage23 Note that the B in sonority A isin brackets to intimate a ldquofuzzyrdquo transposition in which we fo-cus solely on the C]ndashD similarity between A and H while atthe same time acknowledging its presence in our auditoryexperience

Looking once again at Example 6(a) let us consider sonor-ity E as a medial articulation around which the remaining so-norities are arranged24 An interesting relationship existsbetween progressions A E and E H both end with thesame transposition T3 resulting in a return to C D in

example 5 Vertical sonorities in Sec1 (Orchestra I mm 26ndash35 sounding pitches)

23 This is of course an explicit nod to Lewin (1993)24 This neat arrangement is facilitated by my choice of interpreting sonority

F as two three-note simultaneities as observed above


sonority H that was initiated by sonority A25 Furthermore thetransposition from A to E is T1 whereas the transpositionfrom E to H is T11 which are inversions of one another Inthe model shown in Example 7 one can hear this relationshipby simply playing sonorities A E and H in succession whichmakes it possible to internalize the half-step motion betweenthem Example 6b shows a network of similar half-step rela-tionships that arise from our arrangement of sonorities aroundE Notice for example that G is both a T1 transposition of Cand a T11 transposition of D Once again playing the sonori-ties in Example 7 will help in perceiving the relationships be-tween them Below we will see how Penderecki realizes theserelationships in pitch space

As stated earlier Orchestra II repeats in mm 39ndash47 thematerial stated initially by Orchestra I The reader will recallthat the statement of Orchestra II Sec1rsquo is a ldquovisual inversion

about the viola 2viola 3 axisrdquo of Sec1 This inversion is nothowever executed in its strict canonical sense (something thatcan be seen by comparing Ex 5 with Ex 8) Insteadndashndashandsurprisinglyndashndashthe pitch content of the passagersquos sonorities al-most exactly matches that of Sec1 Therefore the abstract net-work from Examples 6(a) and 6(b) for the most part appliesalso to Sec1 There are however a few interesting exceptionsFirst observe that sonority Arsquo is missing pitch-class B that waspresent in the corresponding sonority A This not only sup-ports our omission of B from the above network but also cre-ates a continuation from sonority H which ends Sec1 Secondsonority Drsquo has an interesting pitch-class structure comparedto its earlier counterpart D as well as within its own contextRather than belonging to set-class 3-1[012] its pitch classesmake up set-class 3-5[016] Despite the fact that this set classintroduces variation into the established model the outer in-terval of a tritone has its own prominent aural properties thatcan help situate the listener within the context of the passageLastly sonority H rsquo is slightly different from sonority H in thatthe former belongs to set-class 3-1[012] and the latter to set-class 2-1[01] even though they both contain three sounds thedoubled D in H now becomes D] While this new sonorityconforms to our model it slightly alters the formal design of

A B C D E Fa Fb G H

A B C D E Fa Fb G H

T1 Te

Te

T1T0

T6 T9 T7 T3 T3T5 T5Tt

T0

T0 T1

(a)

(b)

example 6 A network of (a) adjacent and (b) non-adjacent transpositions in Sec1 (Orchestra I mm 26ndash35)

25 As per Lewinrsquos (1987 3) definitions the operations from E to H andfrom G to H are actually functions (ldquoontordquo but not ldquo1-to-1rdquo) because ofthe different cardinalities of the two sonorities in each pair (numbers 3and 2 respectively) However we can theoretically posit a third pc in so-nority H D] based on the fact that it appears later in the correspondingsonority H rsquo (m 45) in which case the transpositions shown in the net-work in Ex 6(a) materialize


the canon Yet the sonic quality of the sonority is maintainedbecause D] in violin 17 and D in viola 4 overlap only slightlyleaving room for the ic1 between C] and D to remain the lastaurally perceptible sound

The pitch classes that disturb the neatness of our model of-fer an opportunity to consider the role that the scorersquos materi-ality plays in this analysis Namely Pendereckirsquos unusualsymbols required music publishers to create new templateswhich given the visual complexity of the composition couldvery well have resulted in certain notational errors26 In factthe reader can confirm that each pitch that does not fit myanalysis could be ldquofixedrdquo by a simple addition of symbols thatcan be easily overlooked in preparing a music manuscript forprint ledger lines clef changes or accidentals This justifies la-beling the sonorities in Sec1rsquo as ArsquondashHrsquo rather than IndashP in or-der to more clearly demonstrate their correspondence withSec1 Further muddling the matter there exist at least twooriginal manuscripts of Threnody Penderecki completed the

first manuscript in two days in the spring of 1960 and submit-ted it to the Grzegorz Fitelberg Composition Competition(where it received third place) In winter of the same year hewas forced to create a second ldquooriginalrdquo which he sent toPolskie Wydawnictwo Muzyczne for publication This secondmanuscript was created from memory when the composer vis-ited France because the first score was lost in the mail Sixmonths later when the original original was finally recoveredit became clear that customs officials had confiscated it in or-der to decipher its unusual figures thinking that they had en-countered a secret code Although a comparison of the twomanuscripts by the composer at that time revealed ldquono signifi-cant differencesrdquo it is possible that some small changes wentunnoticed27 Still the overall timbral character of the passagefrom m 26 onward remains undisturbed even if not everypitch fits the model outlined above

Until now I have been discussing simultaneities in theirmost abstract form as sets of pitch classes Let us return toExample 5 and examine their realization in pitch spacePenderecki explores the entire pitch range that is made avail-able by the instruments at hand from the lowest E1 in thebass (sonority E) to ldquothe highest note possiblerdquo28 (one ofthe elements in An) The resulting sequences of perceptual

example 7 A piano realization of the pitch transposition network

26 The genesis of Pendereckirsquos notation is an interesting study in itself Onecurious observation (relayed by Erhardt 1975) is that at the time of writ-ing sketches for Threondy the composer lived in a tiny one-bedroomapartment in Warsaw along with his wife (and her grand piano) mother-in-law five-year-old daughter and on top of it all a dog It is not surpris-ing that Penderecki was often seen working at a local coffee shop wheretiny tables forced him to frugally employ a notational shorthand Whilesketching Threnody the composer decided that the unusual shapes moreeffectively represented the essence of his sonic ideas and subsequentlyabandoned regular notation altogether

27 The above incident is recounted in Erhardt (1975 29) The score used inthis analysis was published by Belwin Mills and contains no informationabout which of the two ldquooriginalrdquo manuscripts was used as its source tomy knowledge there exists no critical edition of Threnody

28 As indicated in the score by the composer


discontinuities do not make for the easiest listening experi-ence as onersquos attention has to constantly shift from oneregister to another However since texture is such an im-portant aspect of Threnody we can attempt to train our earsto anticipate various textural transformations in connectionwith the pitch-class transpositions discussed earlier In whatfollows I will borrow Wallace Berryrsquos general concept ofdensity compression which refers to the intervallic content ofa sonority Although Berry quantitatively expresses densitycompression as ldquothe ratio of the number of soundingcomponents to a given total [pitch] spacerdquo I present a

slightly different formalism based on occurrences of pitchinterval 129

Sonority A in Example 5 is realized in pitch space spanningan interval of thirty-five semitones from its lowest pitch D2 toits highest C]5 The sonority contains no literal pitch intervalof one semitone therefore we can say that it is maximally dif-fused (maxdiff) The following sonority B contains two pitchintervals of 1 thus it is minimally diffused (mindiff ) In ourmodel let us position elements maxdiff and mindiff as the

example 8 Vertical sonorities in Sec1rsquo (Orchestra II mm 38ndash47 sounding pitches)

29 Berry (1987 209)


most extreme entities on a density compression scale Let max-diff represent a pitch-space realization in which there are nopitch intervals of 1 consequently let mindiff be a state inwhich all adjacent pitches are interval 1 apart The third ele-ment on the density compression scale will be a pitch-space re-alization in which only two adjacent pitches are one semitoneapart while the other interval is greater than 1 Let us call itmoderately diffused (moddiff) and place it between the two ex-tremities In Example 5 sonorities D and E represent this levelof density compression Further let DFUSE constitute atransformation that acts on the space of diffusion (diff ) statesby increasing (thorn) or decreasing (ndash) the number of occurrencesof interval 130 The textural transformation from sonority A tosonority B is thus DFUSEndash its inverse is DFUSEthorn seen forexample between sonorities C and D If the succession of so-norities results in no change in density compression then letus call it DFUSE0 the identity element An example of thisoccurs between sonorities B and C

The entire textural progression of Sec1 in terms of changesof density compression is represented by the network inExample 9(a) Notice that since we added an intermediary termmoddiff the transformation from A to B has become DFUSEndash2 We intuit this because a transformation from mindiff to max-diff involves two steps in our model At the same time we mustnote that the formalism here is rather loose due to the fact thatDFUSE transformations do not form a group performingDFUSEthorn1 transformations on a maxdiff collection of pitcheswill not yield a new member of the diff set This actually cap-tures my aural intuition because the metaphor of diffusionwhen applied to simultaneities in pitch space seems to work inonly one direction Continual diffusion will not ldquowrap the pitchspace around itself rdquo and result in mindiff rather we would needto apply its opposite (DFUSE1 or DFUSE2) To put it inmusical terms the way in which we typically construe pitchspace is linear extending indefinitely (although eventually lim-ited by our auditory capabilities) in the direction of increasingfrequencies and bounded by some theoretical 0 at its lowest ex-treme While under certain circumstances we can think of oc-tave equivalence as a return to the same ldquoplacerdquondashndashmotivatingperhaps a metaphor of a spiralndashndashsuch a notion does not apply inthe present case A collection of simultaneously soundingpitches in which there are no instances of pitch interval 1 willsimply remain maxdiff regardless of how many times we applythe transformation DFUSEthorn1 No doubt many readers can at-test for themselves that beyond a certain point it becomes diffi-cult to hear the exact compound interval between two pitchesto say nothing of the number of octaves separating them ldquoin anyway more precise than lsquoa lotrsquordquo31

Notably an aurally salient feature of the passage is illus-trated by the density compression network namely that both

outlining sonorities A and H are maxdiff adjacent pairs (BC) and (G Fab) are mindiff finally the middle pair (D E) ismoddiff This is a phenomenon that can establish a distincttransformational pattern for the listener The resulting inter-vals 1 are aurally very prominent and can help tremendously inhearing this passage even when articulations and registerchange dramatically (as between sonorities B and C)

A different story occurs in Sec1rsquo As Example 9(b) showsthe primary mode of pitch space realization is maxdiff thuscreating a kind of ldquofuzzyrdquo inversion of the previous networkHere all but three sonoritiesndashndashArsquo Farsquo and Hrsquondashndashexhibit maxi-mum diffusion resulting in almost no intervals 1 Even of thethree just listed only Hrsquo represents mindiff whereas the othertwo are moddiff Despite a lack of the aurally prominent inter-val 1 the textural transformations in this section create an ele-gant continuity that can establish and confirm listenersrsquoexpectations and can thus aid in hearing the passage as a sys-tematic progression of related events This continuity arisesfrom the fact that almost all textural transpositions areDFUSE0 thus keeping one attuned to the openness of thespace range can become a unifying aspect of this passage Interms of ear-training this aspect can be practiced by first play-ing each section separately as suggested in Example 10 fol-lowed by playing each corresponding pair of sonorities fromSec1 and Sec1rsquo in succession shown in Example 11 In thefirst method which realizes Example 9 in pitch space listenerscan explore different textural transformations separately andcan then use the second method to establish expectations forhearing Sec1rsquo in comparison to Sec1 An advantage to playingthese excerpts on the piano is that one can realize an importantkinesthetic aspect of DFUSE transformations onersquos fingers andhands literally spread from lower to higher density sonoritiesand return together by progressing in reverse32

ii

A serious criticism that could indict the entire enterprise pre-sented in the first part of this article concerns what we mightbroadly describe as the ethics of an ear-training analysis justbecause one can suggest a formalized hearing for the passage inquestion does not necessarily mean one should33 More thanmere handwringing this concern addresses the strain betweenstructure and experience at the forefront of several recent

30 For more on musical spaces see Morris (1995) Hermann (1995) modelsthe ldquospreadingrdquo and ldquocontractingrdquo of pitch space in Luciano BeriorsquosSequenza IV for solo piano using so-called chordal shapes

31 Rings (2011b 54)

32 The above analysis examines the density compression network as a formalrepresentation of temporally unfolding processes where the arrows can beconsidered as analogous to the listenerrsquos perspective (Lewinrsquos ldquofiguralrdquo andJohn Roederrsquos ldquoeventrdquo networks see Rings 2011b 140ndash1) Another wayof looking at the DFUSE transformations between sonorities might be asan out-of-time space of all available diff states akin to spatial networksfound in Rings (ibid) In the interest of space I will not pursue this possi-bility here

33 A similar point of critique is taken up by Quinn (2006) with respect tominimalist music One difference is that I attempt to use formal analysisto shape experience while Quinn is interested in altogether changing thevery objectives of such analysis


discussions where at stake is the accepted notion that analyticendeavors are not just forms of subjective interpretation butalso pleas for certain kinds of understanding34 Indeed ananalysis can be envisaged as a performancendashndashan enactionndashndashofunderstanding which aims to convince readers to participate inthe epistemological and experiential landscapes it reveals Itcan propose a certain kind of hearing thereby effecting a

potential to shape phenomenal experience and alter onersquosperception35 Keeping in mind the consequences of analysis onour hearing we may wonder whether the proposal in Part Indashndash

(a) Sec1 (Orchestra I mm 26ndash35)

(b) Sec1acute (Orchestra II mm 38ndash47)

Amaxdiff

Bmindiff

Cmindiff

Dmoddiff

Emoddiff

Famindiff

Fbmindiff

Hmaxdiff

DFUSE -2 DFUSE +2

DFUSE0

DFUSE0

DFUSE0 DFUSE0

DFUSE +1 DFUSE -1

Bacutemaxdiff

Cacutemaxdiff

Dacutemaxdiff

Eacutemaxdiff

Fbacutemaxdiff

Gacutemaxdiff

Aacutemoddiff

Faacutemoddiff

Hacutemindiff

DFUSE0 DFUSE0 DFUSE0 DFUSE0

DFUSE +1

DFUSE -2

DFUSE +1DFUSE -1

Gmindiff

example 9 Density Compression Networks (a) Sec1 (Orchestra I mm 26ndash35) (b) Sec1rsquo (Orchestra II mm 38ndash47)

34 For particularly engaging and multifaceted discussions of this strain fo-cused around the issues of ldquostructural listeningrdquo see the essays inDellrsquoAntonio (2004) especially Dubielrsquos ldquoUncertainty Disorientation andLoss as Responses to Musical Structurerdquo See also Rings (2011b) for abrief state-of-the-field overview of the emerging friction between analystswho embrace or at least try to account for the experiential implications ofLewinrsquos transformations and those for whom such implications are oflesser concern

35 See especially Agawu (2004) as well as Guck (2006) and Parkhurst(2013) Moreover explicit gestures toward the interrelation between anal-ysis and hearing can be found in numerous passages throughout Lewinrsquoswritings One especially striking example which is subtly revealing as wellas implicitly value-laden occurs in his discussion of the Minuet fromBeethovenrsquos First Symphony (see Lewin 1987 169ff) Here Lewin writesof an ldquoold-fashioned way of hearingrdquo the movementrsquos opening thus expos-ing to interpretation and critique different pronouncements analysts makewith respect to the products of their labor Of course Lewin himself doesnot explicitly pass judgment on which hearing is ldquobetterrdquo quite the con-trary by analogy with the mercurial Mr X he points the reader to con-sider the benefits of a shift in hearing However one could easily imagineconstructing an argument in which a ldquocontemporaryrdquo hearing replaces the


that is to say one that suggests hearing this passage inThrenody with an ear for exact transformations of a handful ofpitch elements embedded in a thick texture of pointillistic tim-bral and percussive effectsndashndashis even appropriate for this piece36

Regardless of onersquos epistemology of analysis the potential fal-lacy of such an enterprise is what Rings (sardonically nodoubt) calls ldquothe most time-honored value of modernist music

theoryrdquo which is ldquothe demonstration of coherence through for-malismrdquo37 We can easily compare this situation to being askedto see regular organization and intelligible patterns in JacksonPollockrsquos drip paintings The problem of course is to insist oncoherence even when such a demonstration takes us far beyondthe limits of perception or when the hard-fought search resultsonly in a Pyrrhic victory over what is purportedly meant to bean irrational visceral experience

This problem is especially germane to transformationalanalysis As posited by Julian Hook compared to an ana-lytic model like Schenkerrsquos for example transformationalanalysis largely depends on the analystrsquos own criteria for

example 10 A piano realization of Sec1 and Sec1rsquo

example 11 A piano realization of pitch mappings between corresponding chords form Sec1 to Sec1rsquo

ldquoold-fashionedrdquo based on any number of methodological and perceptualmerits

36 Indeed such criticism would not be unprecedented with respect to sonor-istic repertoire (see for example Cone [1960] for a rebuttal see Morgan[1977] for recent commentaries on the ldquomythrdquo concerning serialism incomposition and perception see Straus [2008] and Hermann [2011]) 37 Rings (2011a 499)


making almost all decisions even at such a fundamentallevel as determining what sorts of musical elements to con-sider and which relationships between them to foreground38

There is an infelicitous dearth of blueprints or prescriptionsfor this kind of approach the only examples existing in theform of other analyses39 The transformational technology isexceptionally flexible and broad-reaching in that one caneasily adjust it to the particular circumstances of a piece orpassage under consideration but it supplies few rigorousguidelines for the analyst to follow Thus the responsibilityof the latter is to justify her choices in terms that make themost sense musically40

Given that the musical grammar in Threnody is so idiosyn-cratic one may be reasonably suspicious whether my justifica-tions stem from musical intuitionsndashndashthat is whether theypertain to the experience of music I could have easily forgonepositing any relevance that these particular pitch collectionsand the relationships between them might have to listeninginstead simply asserting their presence based on a close read-ing of the score However as I will show below hearing thesecollections in this particular way does have a significant im-pact on how I (at least) experience Threnody41 More thanthat it does so in ways that reveal aspects of the passage thatan ldquoinformalrdquo hearing does not aspects that might influenceour interpretation of the work as a whole Thus I think itmight be productive to frame the question in terms of what isgained and what is lost in various experiential domains whenone engages in a transformational hearing of the middle sec-tion of this piece

We should remind ourselves that to advocate a ldquocoherentrdquoless ldquodisorientingrdquo listeningndashndashalong with the often-handcuffedconcepts of ldquologicrdquo and ldquounityrdquondashndashcarries with it a possible issueof value The relationships between pitches and other sonicelements here represented in the form of transformations areunmistakably there even if ldquothererdquo means simply ldquoin thescorerdquo The concern however is whether the transformationsought to be marked for hearing in such an obvious way Infact one could argue that a kind of incoherent disorientingexperience is exactly what Carter was extolling aboutThrenody a visceral unmediated irrational bodily reaction toprimitive sounds While by itself this does not deny the exis-tence of some sort of a scaffold on which these sounds arebuilt it does call into question an interpretation of this

scaffold as a source of structure and meaning for the listeningexperience42

Carterrsquos praise for Threnody centers on the way in which thepiece can appeal to listeners on a sensuous level This suggeststhat if one favors a more cerebral encounter one loses the im-mediacy of an embodied experience Yet there is nothing nec-essarily standing in the way of structural listening productivelyunderpinning sensation Consider for example how the vari-ous networks offered in Part I crystallize a stable framework ofauditory waypoints which serve as articulations along a contin-uously changing surface of sonic objects While such articula-tions may ldquorationalizerdquo the act of listening they also create theconditions for hearing part B in a particular relationship to itsneighbors Specifically we can characterize the famousldquoscreamsrdquo that open the piece as aggressively exposed andmonolithic their architecture laid bare by way of an audiblytransparent process of change from one state to another In themiddle section by contrast sound events are almost filigreeand the visceral unrest at the surface belies the brittleness oftheir abstract design as if the sonic objects that make them upwere severely underdetermined And in a sense they are ifwe acknowledge that the piecersquos ldquotangiblerdquo musical mate-rials43ndashndashsound masses and sound objectsndashndashexist in a dichoto-mous relationship then all the different sonorities that fill partB straddle the line between them always in danger of spillingover from one category into the other A more holistic hearingthat is attentive for example to the intensity of the passagemight soak up this effect in its totality glossing over the localmicro-scale details

Then again it is precisely these details that really stand outat least in my auditory experience It is the textural change fromslow successions of clusters in part A to a pointillistic canvas ofpercussive effects efflorescent rhythmic figurines and exuberantricochets around the pitch space in part B that draws attentionto these very elements And once attention is focused once theauditory searchlight finds its targets an entirely different paththrough the piece can emerge one that suggests a much morelapidary effort in its design Notice for example how the trans-formational ear-training model addresses the quick successionsof pitches in eminently different ranges Rather than obscuringthis musical featurendashndashsay under the guise of pitch classesndashndashitexplicitly draws attention to it and considers its central role inthe formation of musical perceptions

38 Hook (2007)39 Even Lewinrsquos own analyses offer but snapshots and partial guidelines on

how to construct and more importantly use transformations in analyticalengagements with real pieces of music One exception to this is his ex-tended reading of the second of Arnold Schoenbergrsquos Drei KlavierstuckeOp 11 (1994) however there he limits himself to a specific subset oftransformations Klumpenhouwer Networks More recently Roeder(2009) attempts to rectify this lack of prescription by providing step-by-step instructions on how to choose musical objects and transformations

40 Hook (2007 166)41 This is yet another gloss on Lewinrsquos (1993) essay

42 The question of value in musical structure with respect to experience andmore importantly an understanding of music is perhaps most vehementlyaddressed by Rothgeb (1997) Although dealing with tonal repertoire inthis brief but example-rich essay Rothgeb makes some very strong state-ments about the ethics of listening to that which is beyond salienceWhile his proclamations might sound somewhat misdirected in todayrsquosclimate there is a sense that the work we do leads to a particular kind ofunderstanding of the music we write about It seems justifiable thereforeto examine what kind of understanding onersquos analysis promotes andwhether it does not lead to a misunderstanding

43 Metzer (2009 176)


Turning therefore to a positive perspective of what onemight gain experientially from a transformational ear-trainingapproach I am inclined to follow Judy Lochheadrsquos optimisticassertion that ldquoin principle any piece of music should be apotential subject for analytic understandingrdquo44 The issue inachieving analytic understanding is not one of establishing apriori criteriandashndashof structure unity coherence and so forthndashndashbut one of justifying methodological choices in ways thatmake sense according to whatever framework in which one isoperating and however one defines ldquounderstandingrdquo The goalof such an endeavor would be as Joseph Dubiel has put itldquoto understand how the notes might interact with specificallypromote my awareness of my own involvement in the form-ing of [musical] perceptionsrdquo45 In other words such an ap-proach reinserts the analyst into the analysis as an intentionalagent conscious of the volitional aspect of listening Listeningthus becomes mindfully active which is to say that the ana-lyst is attentive to and cognizant of the very process of thisbecoming this activation As a result structure can retain itsformative function in experience while eschewing both over-arching narratives and ldquoanalyst-as-cryptographer-to-musicrsquos-Enigma-machinerdquo approaches that seek to ldquodecipherrdquo musicalcodes46 Once again this line of inquiry allows us to defer toLewin in particular his suggestion that a more interesting al-ternative to the question ldquoCan you hear thisrdquo is whether ornot following some kind of prescription onersquos hearing issatisfying47

Lewinrsquos proposal bases analytical credibility on experientialimprints made on the listener including the analyst by variousmusical relationships Of course there is no escaping the in-herent subjectivity multivalence and contingency of the con-cept of satisfaction with respect to hearing formally justifiedand prescribed structures and Lewin likely left it as general aspossible in order to allow a wide variety of experiences to un-dergird analytical understanding To productively circumscribethis concept for our discussion we can think of analysis thatprescribes a particular listening strategy as satisfying if it man-ages to somehow extend our hearing in a way that is beneficialand prolific Considered in this light accepting the sonoritiesforegrounded above as structural throws into relief other ele-ments as participating in the creation of a particular musicalexperience and so opens the discussion by showcasing a novelway of perceptually organizing these sounds To illustrate whatI mean let us return to Threnody

An obvious way in which the ear-training model extendsour hearing is by providing points of orientation in the processof sonic unfolding a way of letting the listener hear whethershe is in the middle of a large-scale phrase coming to the endor at the point of initiating a new phrase However this can beaccomplished through means other than transformational

hearing for example by simply reacting to isolated moments inthe sonic flow A nice illustration of such a moment occurs inThrenody at mm 36ndash37 (and then again in mm 48ndash49)where the forward movement is halted and the tremolo sonor-ity is sustained longer than anything that came before Hereone need not have a sense of how this event participates in theoverall designndashndashhow the music arrived here and where it willproceed in the immediate futurendashndashin order to discern that it issome kind of a repose in the middle of an otherwise very activesuccession of sounds

In contrast to such an austere listening in which attentionremains at the phenomenal surface of music my approach issignificantly more complex One challenging aspect ofThrenody is how its two outer parts (A and Arsquo) seem sonicallytechnically and experientially at odds with the middle (B) Toalleviate this concern we could dismiss the entire enterprise asa ldquostudy in sound massesrdquondashndashbefitting its original titlendashndashandconsign its intricate organization to some abstract structurethat was never meant to be heard anyway ostentatious (orworse pretentious) compositional frippery that lacks any audi-ble correlation But I think that instead of supporting such adismissal my transformational ear-training process can actuallyshed some important light on the overall experience of thepiece

Without an awareness of a coherent design events in mm26ndash48 simply go by too quickly for me to grasp their signifi-cance in the flow of sounds However even in Threnody thisdifficulty with actively listening in real time does not by itselfinvalidate a perception of logic and coherence given the rightmusical context For example it is plausible for a listener toperceive the slow and gradual changes between different typesof clusters in mm 1ndash25 as some sort of a lucid whole48 Theconception of this organization can then be stored in long-term memory and in turn help the listener structure otherparts of the piece This seems to be a result of a number of fac-tors In my experiences listening to the piece the overall rateof change here is rather unhurried which allows me to concep-tualize each sound as a clearly defined element and categorizeit according to whatever apperceptions I might have There isalso a progressive directed morphology from one sonic eventto the nextndashndasha ldquogood continuationrdquo of sorts which arises as aresult of transformations between the elements For exampledespite the subito drop in dynamics from fortissimo to forte inm 2 it is possible to hear the opening cluster as smoothlytransformed from stationary to oscillating by the addition ofwide and narrow vibrato Indeed much of the first part ofThrenody (mm 1ndash25 with the possible exception of mm 6ndash9)consists of slow and steady developments of sounds eitherthrough continual modulation of a single sonic parameter orby a gradual imposition of one element on another Thus it isnot difficult to perceive a coherent design in this part thelistener has plenty of time to become familiar with eachsound which makes it possible to predict and to anticipate

44 Lochhead (2006 233)45 Dubiel (2004 196) emphasis added46 For a similar view see Quinn (2006)47 Lewin (1993 44) 48 Such organization is explicated by Mirka (1997)


the next sound by applying some previously encounteredtransformation

In contrast events in mm 26ndash48 succeed one another veryquickly Given the time of fifteen seconds for each section ofthe score and its division into six measures we can calculateMMfrac14 75 for each quarter Some ldquobeatsrdquo are then further sub-divided down to quintuplet and sextuplet sixteenth notesUnder these circumstances changes in pitches and articulationsoccur so rapidly that my ability to process them in real timediminishes dramatically An attempt to pick out every one ofthem and to analyze them in the manner presented in the pre-ceding paragraph requires a very unique specialized type ofhearing However focusing on slower-moving sonic segmentsones that can be easily discerned based on their pitch structureprovides me with a listening model that omits certain soundsthat have entirely different spectral envelopes (in this case ele-ments P and An) in order to follow the passage consistentlyfrom start to finish Furthermore this transformational modelshows a continuity in certain pitches and articulatory elementsthat allows me to pay attention to the progression of the pas-sage The key factor here is that an intuition of transformationsrelating one pitch structure to the next consistently helps meanticipate and act upon (rather than be surprised by and react to)pitch successions Thus it becomes easier for me to hear thismusic without ldquogetting lostrdquo in its complexity

Earlier I made a point that despite forfeiting intensity hav-ing a roadmap through Threnody lets us hear part B as distinctfrom parts A and Arsquo Here I actually want to nuance thisclaim by adding that a transformational hearing of the passagein question stimulates a new way of thinking about the threeparts of Threnody as different perspectives on the same processThis process is readily audible in the outer sections but re-mains obscured in the middle One way to think about it is asif in part B the outside of A and Arsquo becomes the inside butnow only as scaffolding Rather than juxtaposing oppositesthis shift of perspective gives the entire piece a large-scale archform by showcasing different features of the same type of sonicevent Whereas the outer parts exhibit dense chromatic clustersthat are built through expansions and contractions of pitchspace and by gradual additive processes in the dimensions ofpitch timbre dynamics percussive effects and so forth inpart B the sound mass itself becomes the process by manipu-lating the pitch content and diffusion of each trichordPenderecki uses them as sonoristic construction materials intheir own right

The above interpretation postulates a distinct category ofmusical elements situated somewhere between pointillismndashndashexemplified by such works as Stockhausenrsquos Kreuzspiel (1951)and Boulezrsquos Structures (1952)ndashndashand sound masses properWith regard to the former the effect of pointillism in thesepieces is achieved by serial techniques applied to individualpitch-classes In Threnody by contrast we can conceive of en-tire trichords as ldquopointsrdquo that coalesce to make up the whole aprocedure that draws the middle part conceptually closer tothe outer ones By tracking transformations between trichords

and attending to a network that relates all of them in some co-herent manner we can arrive at a different understanding ofthe term ldquosound massrdquo To return to Mirkarsquos exposition ofstructural features in Pendereckirsquos oeuvre in which she con-siders the use of masses as building blocks the trichords herefulfill precisely that role49 When taken as indissoluble butflexible units rather than ad hoc amalgams that merely fall outof a pre-compositional algorithm they behave like registrallyexpanding and contracting pockets that support an effervescentmusical surface

We can thus construe Pendereckirsquos 8rsquo37rdquondashndasha seeminglystraightforward ldquostudy in sound massesrdquondashndashas a very sophisti-cated manipulation of intricate sonic elements While this ap-proach may miss out on the raw physical and emotionalimpact of Threnody lauded by Carter it foregrounds a no lessimportant aspect of the piece an aspect with real consequencesfor the listening experience Namely it directs listenersrsquo atten-tion to the ldquoconstructednessrdquo (to borrow from Dubiel) of thelarge-scale design whereby part B is no longer heard as musi-cally separate from its neighbors50 As in the bookend sectionsit retains chromatic clusters as a structural element and linksexperientially all three sections of the piece The transforma-tional ear-training proposed above also functions in reconfi-guring the visceral embodied reaction of listeners by activelyshaping their affective responses Instead of idly letting themusic direct the intensity of experience they can now partici-pate in what one could call ldquoexperimentalrdquo listening a continu-ous renewal of interpretation though repeated controlledauditory trials

But in a way this is where we have been all along Recall thePollock comparison mentioned earlier which implied that seeingcoherent patterns in his drip paintings might be detrimentalndashndashorat the very least extraneousndashndashto onersquos experience of them Whenwe look at the surface of these paintings we are implored to gazepast and transcend the limits of their physicality their materialityAs viewers our job is to aestheticize the disembodied effects ofreal-world movements and not the movements themselves Butwe must also note that there is a complex relationship betweenPollockrsquos literal strokesndashndashgestures of his arms and handsndashndashandthe painted surface of his artworks The former are limited to theactions that are physically feasible whereas in the latter we recog-nize these limitations in the patterns that we see This may bewhy it is in fact possible to observe intelligible shapes to beginwith a circle reminiscent of a cartoon face here a zigzag sugges-tive of a mountain range there all somehow indexing the bodythat created them Considered in these terms the experiential ef-fect has a striking connection with Carterrsquos assessment ofThrenody Specifically the lack of readily rationalized musicalstructures forces the listener to ldquo[search] into the physical aspectsof musical productionrdquo But even though it may seem like thosevery aspects are raw and unmediated they are both already struc-turedndashndashby the instruments that are played by the performersrsquo

49 Mirka (2000)50 Dubiel (2004)


bodies and their capabilities by Pendereckirsquos directions and soonndashndashand also structuring of experience In consequence there isno escaping the organizing impulse of experience what my analy-sis presents is simply a different way of succumbing to it

works cited

Adorno Theodor W 2002 ldquoOn the Problem of MusicalAnalysis (1969)rdquo Essays on Music Ed Richard Lepperttrans Susan H Gillespie Berkeley University of CaliforniaPress

Agawu V Kofi 2004 ldquoHow We Got Out of Analysis andHow to Get Back Inrdquo Music Analysis 23 (2ndash3) 267ndash86

Berry Wallace 1987 Structural Functions in Music NewYork Dover

Carter Elliott 1963 ldquoLetters from Europerdquo Perspectives ofNew Music 1 (2) 195ndash205

mdashmdashmdash 1995 ldquoISCM Festival Amsterdam (196394)rdquoElliott Carter Collected Essays and Lectures 1937ndash1995 EdJonathan Bernard Rochester NY Rochester UniversityPress

Clarke Eric 2005 Ways of Listening An Ecological Approach tothe Perception of Musical Meaning New York OxfordUniversity Press

Cone Edward T 1960 ldquoAnalysis Todayrdquo Musical Quarterly46 (2) 172ndash88

Cox Arnie 2011 ldquoEmbodying Music Principles of theMimetic Hypothesisrdquo Music Theory Online 17 (2)

DellrsquoAntonio Andrew ed 2004 Beyond Structural ListeningPostmodern Modes of Hearing Berkeley University ofCalifornia Press

Dubiel Joseph 2004 ldquoUncertainty Disorientation and Lossas Responses to Musical Structurerdquo In Beyond StructuralListening Postmodern Modes of Hearing Ed AndrewDellrsquoAntonio 173ndash200 Berkeley University of CaliforniaPress

Dubois Didier and Henri Prade 1980 Fuzzy Sets andSystems New York Academic Press

Erhardt Ludwik 1975 Spotkania z Krzysztofem Pendereckim[Encounters with Krzysztof Penderecki] WarszawaPolskie Wydawnictwo Muzyczne

Godoslashy Rolf Inge 2010 ldquoGestural Affordances of MusicalSoundrdquo In Musical Gestures Sound Movement andMeaning Ed Rolf Inge Godoslashy and Marc Leman 103ndash25New York Routledge

Granat Zbigniew 2008 ldquoEditorialrdquo Muzyka 208 (1) 3ndash6Gruhn Wilfried 1971 ldquoStrukturen und Klangmodelle in

Penderckis Threnosrdquo Melos 10 409ndash11Guck Marion 2006 ldquoAnalysis as Interpretation Interaction

Intentionality Inventionrdquo Music Theory Spectrum 28 (2)191ndash209

Harley Maria Anna 1998 ldquoThe Polish School of Sonorismand Its European Contextrdquo In Crosscurrents andCounterpoints Offerings in Honor of Bengt Hambraeus at 70

Ed F Broman Nora Engebretsen and Bo Alphonce62ndash77 Goteborg University of Gothenburg

Harrison Daniel 2011 ldquoThree Short Essays on Neo-Riemannian Theoryrdquo In The Oxford Handbook ofNeo-Riemannian Theory Ed Edward Gollin and AlexanderRehding 548ndash77 New York Oxford University Press

Hermann Richard 1995 ldquoTheories of Chordal Shape Aspectsof Linguistics and Their Roles in an Analysis of PitchStructure in Beriorsquos Sequenza IV for Pianordquo In Concert MusicRock and Jazz since 1945 Essays and Analytical Studies EdElizabeth West Marvin and Richard Hermann 364ndash98Rochester University of Rochester Press

mdashmdashmdash 2011 ldquoEarly Serialism in the United States Aspectsof Theory History Analysis and Receptionrdquo Theoria 18110ndash37

Hook Julian 2007 ldquoDavid Lewin and the Complexity of theBeautifulrdquo Integral 21 155ndash90

Lochhead Judy 2006 ldquolsquoHow Does It Workrsquo Challenges toAnalytic Explanationrdquo Music Theory Spectrum 28 (2)233ndash54

Klumpenhouwer Henry 2006 ldquoIn Order to Stay Asleep asObservers The Nature and Origins of Anti-Cartesianism inLewinrsquos Generalized Musical Intervals and TransformationsrdquoMusic Theory Spectrum 28 (2) 277ndash89

Koblyakov Lev 1977 ldquoBoulezrsquos Le marteau sans maıtreAnalysis of Pitch Structurerdquo Zeitschrift fur Musiktheorie 8(1) 24ndash39

Kozak Mariusz 2015 ldquoListenersrsquo Bodies in Music AnalysisGestures Motor Intentionality and Modelsrdquo Music TheoryOnline 21 (3)

Lewin David 1986 ldquoMusic Theory Phenomenology andModes of Perceptionrdquo Music Perception 3 (4) 327ndash92

mdashmdashmdash 1987 Generalized Musical Intervals andTransformations New Haven Yale University Press

mdashmdashmdash 1993 Musical Form and Transformation Four AnalyticEssays Hew Haven Yale University Press

mdashmdashmdash 1994 ldquoA Tutorial on Klumpenhouwer NetworksUsing the Chorale in Schoenbergrsquos Op 11 No 2rdquo Journalof Music Theory 38 (1) 79ndash101

London Justin 2012 Hearing in Time Psychological Aspects ofMusical Meter New York Oxford University Press

Metzer David 2009 Musical Modernism at the Turn of theTwenty-First Century Cambridge Cambridge UniversityPress

Mirka Danuta 1997 The Sonoristic Structuralism of KrzysztofPenderecki Katowice Music Academy in Katowice

mdashmdashmdash 2000 ldquoTexture in Pendereckirsquos Sonoristic StylerdquoMusic Theory Online 6 (1)

Morgan Robert 1977 ldquoOn the Analysis of Recent MusicrdquoCritical Inquiry 4 (1) 33ndash53

Morris Robert 1995 ldquoCompositional Spaces and OtherTerritoriesrdquo Perspectives of New Music 33 (1ndash2) 328ndash58

Nattiez Jean-Jacques 1990 Music and Discourse Toward aSemiology of Music Trans Carolyn Abbate PrincetonPrinceton University Press


Parkhurst Bryan 2013 ldquoFraught with Ought An Outline ofan Expressivist Meta-Theoryrdquo Music Theory Online 19 (3)

Quinn Ian 1997 ldquoFuzzy Extensions to the Theory ofContourrdquo Music Theory Spectrum 19 (2) 232ndash63

mdashmdashmdash 2006 ldquoMinimal Changes Process Music and theUses of Formalist Analysisrdquo Contemporary Music Review 25(3) 283ndash94

Rings Steven 2011a ldquoRiemannian Analytical Values Paleo-and Neo-rdquo In Oxford Handbook of Neo-Riemannian TheoryEd Edward Gollin and Alexander Rehding 486ndash511New York Oxford University Press

mdashmdashmdash 2011b Tonality and Transformation New YorkOxford University Press

Roeder John 2009 ldquoConstructing TransformationalSignification Gesture and Agency in Bartokrsquos Scherzo Op14 No 2 measures 1ndash32rdquo Music Theory Online 15 (1)

Rothgeb John 1997 ldquoSalient Featuresrdquo In Music Theory inConcept and Practice Ed James Baker David Beach andJonathan Bernard 181ndash96 Rochester University ofRochester Press

Stewart John Olivier Gapenne and Ezequiel A Di Paoloeds 2010 Enaction Toward a New Paradigm for CognitiveScience Cambridge [MA] MIT Press

Straus Joseph N 2008 ldquoA Revisionist History of Twelve-Tone Serialism in American Musicrdquo Journal of the Societyfor American Music 2 (3) 355ndash95

Subotnik Rose Rosengard 1995 Deconstructive VariationsMusic and Reason in Western Society MinneapolisUniversity of Minnesota Press

Taruskin Richard 2005 Oxford History of Western MusicNew York Oxford University Press

Thomas Adrian 2005 Polish Music Since SzymanowskiCambridge Cambridge University Press

Varela Francisco Evan Thompson and Eleanor Rosch 1991The Embodied Mind Cognitive Science and HumanExperience Cambridge [MA] MIT Press

Zielinski Tadeusz 1968 ldquoTechnika Operowania InstrumentamiSmyczkowymi w Utworach Krysztofa Pendereckiegordquo[Techniques of Employing String Instruments in theWorks of Krzysztof Penderecki] Muzyka 13 (1) 74ndash92

Music Theory Spectrum Vol 38 Issue 2 pp 200ndash17 ISSN 0195-6167electronic ISSN 1533-8339 VC The Author 2017 Published by OxfordUniversity Press on behalf of The Society for Music Theory All rightsreserved For permissions please e-mail journalspermissionsoupcomDOI 101093mtsmtw015


sensation can productively interact with one another contraCarter listening to Threnody is not necessarily a case of ldquoei-therorrdquo

Without reflecting on the implications of such a statementperhaps many readers find themselves asking what kinds of lis-tening attitudes a particular piece of music invites elicits orengenders Indeed as one of the first steps toward understand-ing a musical work this kind of assessment seems well worthit because it positions the listener relative to the piece in a waythat can then serve as a starting point for further analysisSome pieces thus seem to work best with we might call an ldquoin-tellectualrdquo approach or what Theodor Adorno refers to asldquostructural listeningrdquo7 Further elaborating this notion hewrites of letting a composition ldquounfold itself in its own termsrdquoso that it may ldquoassert itselfrdquo and allow one ldquoto enter into itsstructure analyticallyrdquo all of which resonates with the abovenotions of invitation and elicitation that musicians may ascribeto pieces of music8 With such a strategy we might look forways in which the musical surface opens up to reveal an under-lying logic something that we can ldquograsprdquo (in Carterrsquos senseabove) as a rational progression of sounding eventsMeanwhile other works appear to be better experienced emo-tionally viscerallyndashndashwith our bodies rather than with ourbrains9

Of the two attitudes Threnody seems to encourage the lis-tener to become emotionally and somatically absorbed in itssoundsndashndashit seems to facilitate an engagement with the musicrsquosphenomenal experience At least in Carterrsquos view this is thedefault unmediated reception that does not require an intel-lectual engagement with the piece Without doubt there areplenty of musical elements on display here that typecast thework as resistant to rationalization thick microtonal textureslack of articulated and easily identified events and a continu-ously unfolding form that on its surface precludes traditionalnotions of design in favor of an unencumbered process Yetnone of this necessarily disqualifies a structuralist hearing onebased on the development of theoretical and perceptual models

and which allows a listener to approach the piece with an earfor such concepts as structure logic and coherence Quite thecontrary an analytical appraisal of Threnody can enhancerather than impede onersquos embodied sensual experience

One theoretical model for analyzing Pendereckirsquos sonic pal-ette can be found in Danuta Mirkarsquos monograph TheSonoristic Structuralism of Krzysztof Penderecki10 There sheproposes a method based on ideas adapted from Saussurianstructuralism in which her so-called contrary and contradic-tory elements are juxtaposed in a compositional system whoseldquoaxiom is not a concept of a single sound event but of soundmatter taken in its totalitymdashen masse so to sayrdquo11 Contrary el-ements are those that mathematically ldquocan be modeled as arelation between a given set and its complementrdquo while con-tradictory ones are modeled by ldquoa relation of two sets each ofthem belonging to the complement of the otherrdquo12 Less for-mally contradiction describes an opposition between discretestates (eg mobility vs immobility) while contrariety introdu-ces the possibility of a third term in the opposition (eg loudvs soft dynamics where the possibility of a ldquomiddlerdquo dynamicrange also exists) In all cases Mirka illustrates how the rela-tions between various sonic parameters are modeled by fuzzysets with obscured boundaries between limit conditions Setsthat is in which ldquothe transition between membership andnon-membership is gradual rather than abruptrdquo (containingwhat is colloquially referred to as ldquoborderline casesrdquo) such thatmembership is assessed in terms of continuous values between0 and 1 rather than in binary terms familiar from classical settheory13

Mirkarsquos goal is to uncover formalizable relationships in asound world that according to her had previously been de-rided as lacking rational order or logical unfolding Her mostimportant finding is that there are indeed long-range order-ing principles that determine how Penderecki treats the kindsof raw and ldquoprimitiverdquo sounds that so struck Carter but thatdo not operate along the traditional formal paths of linear de-velopment Moreover she demonstrates how elements otherthan pitches and harmoniesndashndashnamely texture density articula-tion loudness and timbrendashndashparticipate in creating structureand cohesion not just in Threnody but also in the composerrsquosother works collectively referred to as ldquosonoristicrdquo14

7 Adorno (2002) For an exposition and critique of structural listening seeSubotnik (1995) For responses to Subotnikrsquos deconstructive reading ofAdorno see essays in DellrsquoAntonio (2004)

8 Adorno (2002 166)9 Of course the dichotomy between the brain and the body is a coarse one

since the former is very much a part of the latter and I am using it here asa heuristic Thus in positing these two attitudes I am not claiming thatthere is a categorical distinction between them or that one necessarily pre-cludes the other Indeed recent embodied extensions to cognitive science(see n 7 above) provide evidence supporting the view that rationalthought is in no way divorced from our bodily states and that our actionsin response to the worldrsquos solicitations are as much a part of our cognitionas abstract reasoning Rather what I am suggesting is that as a way ldquointordquoa piece of music it is possible that some works promote a deliberate sup-pression of explicit bodily exertions in favor of a more detached evenatemporal study of its structural components One of the many ways inwhich composers can achieve this is by eschewing regular pulses therebyattenuating the listenersrsquo abilities to spontaneously entrain to and move insynchrony with the music (see London 2012)

10 Mirka (1997)11 Mirka (2000)12 Ibid13 Dubois and Prade (1980) For an accessible tutorial on fuzzy sets and their

musical application to contour theory see Quinn (1997)14 These include such works as Dimensions of Time and Silence (1960 rev

1961) Polymorhia (1961) Fluorescences (1961ndash2) and Anaklasis (1959ndash60) As Thomas (2005 166) points out with the exception of Threnody

(and even then only after a change) all bear scientific-sounding titles sug-gesting an experimental approach to sound as a matter of objective investi-gation the goal of which was ostensibly to discover its various propertiesFor more on sonorism see Mirka (1997 8) also see a special English-language issue of the Polish musicological journal Muzyka devoted to the






i






































A B C D E Fa Fb G H

A B C D E Fa Fb G H

T1 Te

Te

T1T0


T0

T0 T1

(a)

(b)

















29 Berry (1987 209)







ii



31 Rings (2011b 54)








Amaxdiff

Bmindiff

Cmindiff

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Emoddiff

Famindiff

Fbmindiff

Hmaxdiff

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DFUSE0

DFUSE0 DFUSE0

DFUSE +1 DFUSE -1

Bacutemaxdiff

Cacutemaxdiff

Dacutemaxdiff

Eacutemaxdiff

Fbacutemaxdiff

Gacutemaxdiff

Aacutemoddiff

Faacutemoddiff

Hacutemindiff


DFUSE +1

DFUSE -2

DFUSE +1DFUSE -1

Gmindiff

























43 Metzer (2009 176)

















49 Mirka (2000)50 Dubiel (2004)



works cited



























































i






































A B C D E Fa Fb G H

A B C D E Fa Fb G H

T1 Te

Te

T1T0


T0

T0 T1

(a)

(b)

















29 Berry (1987 209)







ii



31 Rings (2011b 54)








Amaxdiff

Bmindiff

Cmindiff

Dmoddiff

Emoddiff

Famindiff

Fbmindiff

Hmaxdiff

DFUSE -2 DFUSE +2

DFUSE0

DFUSE0

DFUSE0 DFUSE0

DFUSE +1 DFUSE -1

Bacutemaxdiff

Cacutemaxdiff

Dacutemaxdiff

Eacutemaxdiff

Fbacutemaxdiff

Gacutemaxdiff

Aacutemoddiff

Faacutemoddiff

Hacutemindiff


DFUSE +1

DFUSE -2

DFUSE +1DFUSE -1

Gmindiff

























43 Metzer (2009 176)

















49 Mirka (2000)50 Dubiel (2004)



works cited
















































































A B C D E Fa Fb G H

A B C D E Fa Fb G H

T1 Te

Te

T1T0


T0

T0 T1

(a)

(b)

















29 Berry (1987 209)







ii



31 Rings (2011b 54)








Amaxdiff

Bmindiff

Cmindiff

Dmoddiff

Emoddiff

Famindiff

Fbmindiff

Hmaxdiff

DFUSE -2 DFUSE +2

DFUSE0

DFUSE0

DFUSE0 DFUSE0

DFUSE +1 DFUSE -1

Bacutemaxdiff

Cacutemaxdiff

Dacutemaxdiff

Eacutemaxdiff

Fbacutemaxdiff

Gacutemaxdiff

Aacutemoddiff

Faacutemoddiff

Hacutemindiff


DFUSE +1

DFUSE -2

DFUSE +1DFUSE -1

Gmindiff

























43 Metzer (2009 176)

















49 Mirka (2000)50 Dubiel (2004)



works cited




































































29 Berry (1987 209)







ii



31 Rings (2011b 54)








Amaxdiff

Bmindiff

Cmindiff

Dmoddiff

Emoddiff

Famindiff

Fbmindiff

Hmaxdiff

DFUSE -2 DFUSE +2

DFUSE0

DFUSE0

DFUSE0 DFUSE0

DFUSE +1 DFUSE -1

Bacutemaxdiff

Cacutemaxdiff

Dacutemaxdiff

Eacutemaxdiff

Fbacutemaxdiff

Gacutemaxdiff

Aacutemoddiff

Faacutemoddiff

Hacutemindiff


DFUSE +1

DFUSE -2

DFUSE +1DFUSE -1

Gmindiff

























43 Metzer (2009 176)

















49 Mirka (2000)50 Dubiel (2004)



works cited




























































ii



31 Rings (2011b 54)








Amaxdiff

Bmindiff

Cmindiff

Dmoddiff

Emoddiff

Famindiff

Fbmindiff

Hmaxdiff

DFUSE -2 DFUSE +2

DFUSE0

DFUSE0

DFUSE0 DFUSE0

DFUSE +1 DFUSE -1

Bacutemaxdiff

Cacutemaxdiff

Dacutemaxdiff

Eacutemaxdiff

Fbacutemaxdiff

Gacutemaxdiff

Aacutemoddiff

Faacutemoddiff

Hacutemindiff


DFUSE +1

DFUSE -2

DFUSE +1DFUSE -1

Gmindiff

























43 Metzer (2009 176)

















49 Mirka (2000)50 Dubiel (2004)



works cited



























































Amaxdiff

Bmindiff

Cmindiff

Dmoddiff

Emoddiff

Famindiff

Fbmindiff

Hmaxdiff

DFUSE -2 DFUSE +2

DFUSE0

DFUSE0

DFUSE0 DFUSE0

DFUSE +1 DFUSE -1

Bacutemaxdiff

Cacutemaxdiff

Dacutemaxdiff

Eacutemaxdiff

Fbacutemaxdiff

Gacutemaxdiff

Aacutemoddiff

Faacutemoddiff

Hacutemindiff


DFUSE +1

DFUSE -2

DFUSE +1DFUSE -1

Gmindiff

























43 Metzer (2009 176)

















49 Mirka (2000)50 Dubiel (2004)



works cited











































































43 Metzer (2009 176)

















49 Mirka (2000)50 Dubiel (2004)



works cited






































































49 Mirka (2000)50 Dubiel (2004)



works cited
























































works cited























































experiencing structure in penderecki’s threnody: … · experiencing structure in penderecki’s...

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