Table Of ContentYale University Department of Music
To Cut the Gordian Knot: The Timbre System of Krzysztof Penderecki
Author(s): Danuta Mirka
Source: Journal of Music Theory, Vol. 45, No. 2 (Autumn, 2001), pp. 435-456
Published by: Duke University Press on behalf of the Yale University Department of Music
Stable URL: http://www.jstor.org/stable/3653444
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TO CUT THE GORDIAN KNOT:
THE TIMBRE SYSTEM OF
KRZYSZTOF PENDERECKI'
DanutaM irka
Timbrei s certainlyt he most complex parametero f sound perception.
In contrastt o pitch, loudness, andd uration,e ach of which possesses a sin-
gle equivalenta mong the acoustic parameterso f sound, timbre depends
on the interactiono f several physical aspects of sound. These aspects
include overtones,w ave forms, sound pressure,t ransients,a s well as the
numbera nd frequency of formants.M oreover,a sound's frequency and
intensity-parameters which relateb asicallyt o pitcha ndl oudness-exert
an influence on the resultingt imbre.T he complexity of timbrei s evident
when one attemptst o depicti t within a representationaslp ace:t imbrec an-
not be modeled within one-dimensional space, but only by means of
multi-dimensionals caling techniques (Spender 1980, 401). However, a
set that cannot be projectedo nto a one-dimensionall ine of real numbers
does not constitutea n ordereds et, and its elements are not comparablei n
the mathematicals ense. As a result, no clear relationshipb etween partic-
ulart imbresc an be established,a nd hence no rationalo rganizationo f the
perceptualp arametero f timbreb y means of any rigid system is possible
on the acoustic level. This may be why in the course of music history
timbreh as usually been set aside as a secondaryf actor of musical form.
Even where it achieved a dominantp osition in the styles of individual
composers, as in the case of Debussy or in the Klangfarbenmelodieo f
435
Schoenberg,t imbrew as invariablyo rganizedi n an intuitivem anner.N or
was the problem of timbre solved by serial composers. In spite of the
appearanceso f rationalityt, he serializationo f timbrew as essentially arbi-
trarilyd eterminedW. ho, aftera ll, will withoutq ualificationa greet hatt he
relationb etween the timbreso f violin and contrabassi s the same as, say,
between the violin and oboe or trumpetc on sordino?A ssumptionso f this
sort lie at the base of the timbrer ows used in serial compositions.F or the
young Penderecki, faced with the Gordian knot of timbre, nothing
remainedt o do but to cut it. He did so by transferringw holesale the prob-
lematic issue of timbref rom the hopelessly muddleda coustic level onto
the motoric one: the level of sound generation.
I. Categories
Although the acoustic wave is a highly complex phenomenon, the
process of its generationc an be presented simply as a collision of two
physical bodies, one being a sound source, the other being the body that
vibrates the sound source. It is likely that such a splendidly simplified
image of the sound-producingp rocess was takenu p by Pendereckif rom
the teaching of Mieczyslaw Drobner,t he eminentP olish acousticiana nd
organologist.I n 1958 Drobnerm oved from Lodz to Krakowt o take the
post of lecturer at Panstwowa Wyzsza Szkola Muzyczna, the school
where Pendereckih ad recentlyf inished his study in compositiona nd was
employed as an assistant.T wo years later,i n 1960, the Krak6wp ublish-
ing house Polskie Wydawnictwo Muzyczne (PWM) issued Drobner's
book Instrumentoznawstwoi akustyka,w hich remains the classical Pol-
ish handbooko f both disciplines-organology and acoustics-named in
its title. In this book, Drobnert ermedt he sound source a vibrator,a nd in
his subsequentp ublicationsi ntroducedt he complementaryt erm, inciter,
for the body which agitates the vibrator.A combinationo f vibratora nd
inciter is a sound generator. This formulationp roposed by Drobnerb e-
came an ideal point of departuref or the consistent and rationals ystem of
timbre organizatione laborated by Penderecki in the early 1960s, the
period of his outputl abeled in Polish musicology as sonoristic.2
At that time Pendereckiu nderstoodt imbrep rimarilya s a function of
the materials-in the most common sense of the word-employed in any
individualp rocess of sound generation.T hereforet he timbralc ategories
in Penderecki'ss onorisma re based upon materialsm ost commonly used
in the constructiono f the musical instrumentsa nd accessories of the tra-
ditional symphonico rchestra:m etal, wood, leather,f elt, and hair.3T hese
materialsc an serve as both vibratorsa nd inciters.Y et, while the role of
inciter can be played by any of the listed materials,t he vibratorc an be
only a metal, wooden, or leather body. In fact, almost anything can be
made to vibrate;t hus, it is theoreticallyp ossible for felt and hairt o act as
436
sound sources. But with these materialst he vibrationi s so heavily damp-
ened that it does not persist long enough to be heard.I n practice,t hen, at
least one of the two sound-generatingb odies must be made of metal,
wood, or leather.F or this reason, I will call these threem aterialsp rimary
materials. In other words, metal, wood, and leatherc an interactw ith any
material, including themselves. On the other hand, neither of the two
remaining materials-hair and felt-ever collides either with itself or
with the other within Penderecki'ss ystem, but must always interactw ith
one of the materialst hat constitutes a potential sound source. A simple
matrix, shown in the following table (Figure 1), displays all possible
pairs of interactingm aterials.
Though inspiredb y Drobner'sa coustics, Penderecki'ss ystem never-
theless goes one step furthert han Drobner.I n Penderecki'st imbre sys-
tem, it is of no importancew hether metal, wood, and leather are rep-
resented by a vibratoro r by an inciter, both colliding bodies being of
equal weight as primarym aterials.I n this respect Penderecki-if he had
wanted-might have referredt o the authorityo f the firstf athero f physics,
Sir Isaac Newton: according to Newton's third rule of dynamics, if a
body A acts with some force on body B, body B acts with the same but
reciprocallyd irectedf orce on body A. The same principlea pplies to bod-
ies acting on one anotheri n the process of sound generation.E ven if one
is accustomed to think that hitting a metal cymbal with a wooden stick
results only in the formere mitting a sound, in reality what sounds is not
only the cymbal, but also the beater.O ne may generalize this conclusion
in the following way: if a given body can be a sound source-that is, if it
is made of one of the three materialsc apable of performingt his function
vibrators
m w 1
inciters
m mm wm lm
w mw ww lw
1 ml wl 11
h mh wh lh
f mf wf If
Figure 1. Pairs of materialsr epresentedb y combinations
of vibratorsa nd inciters
437
m
1 . 0* .| *
f* *
h * * *
Figure 2. Pairs of materialsa fter the reduction
(m, w, 1)-then it becomes a sound source regardlesso f whetheri t is hit,
rubbedo r plucked or itself hits, rubs or plucks. It follows that the mater-
ial pairs "mw" and "wm," "ml" and "lm," as well as "wl" and "lw,"
repeatedi n the matrixa bove, may be reducedt o single entries.A s a result
of this reduction,t welve pairs of materialsr emain( Figure2 ). Every such
pair indicates one type of sound generator,a s well as the type of timbre
characteristico f sounds generatedb y it.
As stated earlier,a ll the materialc ategories chosen by Pendereckif or
his timbre system occur among the traditionalm usical instrumentso f a
symphonico rchestra.T his does not by itself mean, however,t hat a sym-
phonic orchestraw ith its traditionals et of instrumentsa utomaticallyr en-
ders the realizationo f that system practicable.O n the contrary,i n order
to use the timbres ystem in concretep ieces, Pendereckih ad to subjectt he
orchestral forces to serious changes. The timbre system presupposed
an equal weighting of the three primary materials-metal, wood and
leather-in performingt he functiono f vibrators,w hereasm etal typically
predominatesi n the symphonic orchestra.O ne merely needs to compare
the numbero f stringedi nstruments( which constitutet he body of the con-
ventionalo rchestra)a ugmentedb y an assortmento f cymbals, gongs, tam
tams, vibraphonesa nd celestas, to the much smaller number of mem-
braneso f drumsa nd timpani,a nd the almost inconspicuousc ollection of
rattlesa nd wood blocks, to convince oneself of this simple fact. Not only
is there a greater diversity of metallic objects that generate sound, but
metallic objects also predominatei n terms of sheer number.T o balance
this unequalp roportion,i t was necessaryt o enlarget he representationo f
the two remainingm aterialc ategories:l eathera nd wood.
Beside addinga whole arsenalo f percussivei nstruments-such as rat-
tles (raganella), claves, guiro, xylorimba,w ood blocks (blocchi di legno),
and drums (casse di legno)-to augment the representationo f wooden
bodies, the composer also employed several elements of stringedi nstru-
ments (sound board, fingerboard,b ridge, tailpiece, bowstick). Further-
more, Pendereckiu sed non-musicale quipmentt hat is usually presento n
438
stage, but that hithertoh ad never been exploited for sound production:
chairsa nd stands,w hich at the beginningo f the 1960s were almost always
made of wood. To play on these new sound sources, the sticks and nuts
of bows were employed. Incidentally,i t is worthn oting thatt he selection
of new wooden accessoriesb etokensa very pragmatica ttitudeo f the com-
poser. Avoiding the cost that would inevitably result from inventing and
producing fanciful percussive tools, he managed to radically increase
the numbero f wooden bodies by using objects near at hand. Moreover,
these objects allowed him to diversify the timbre within the group of
stringed instruments,e nabling him to employ this group separately.I n-
deed, from among the pieces based on the timbre system, as many as
four-Threnody-To the Victims of Hiroshima, String Quartet No. 1,
Polymorphia,a nd Canon-are designed for strings alone.
Leather, as the third of the primary material categories, is supple-
mented first of all by instrumentso f non-Europeano rigin. Congos and
bongos stem from South-American popular music, while tom-toms
reachedP oland along with jazz, about which the young Pendereckiw as
trulye nthusiastic.4O ftentimest he composerb ids instrumentaliststo play
these instrumentsw ith bare hands, which considerablye nlarges the rep-
resentationo f thatm aterialc ategory( skin being understooda s analogous
to leather). Hands and fingers serve also to play stringed instruments:
apartf rom the well-knownp izzicato effect, the composer instructsp lay-
ers to rub, tap, or strikeo n sound boardsa nd strings with the palm of the
hand or the fingertips.5
The invention of new instrumentsa nd accessories does not exhaust
the changes entailed by the timbres ystem. Apartf rom balancingt he pri-
mary materials, it was necessary to obtain the appropriatec ombina-
tions-classes of sound generators-that could embrace all the classes
of timbres determinedb y the pairs of materials.A nd even a rich repre-
sentationo f a given material did not by itself guarantee the existence
of all its possible combinations with other material categories. In this
respect the case of metal is exemplary.W hereas its combinations with
hair (mh) and felt (mf) existed among the traditionalt echniqueso f play-
ing orchestrali nstruments-the formera s the arco playing of strings,t he
lattera s the strikingo f gongs, tam tams, or cymbals by soft, felt sticks-
sound generatorc onsisting of two metal bodies hardly ever occurred.
Theiro nly representativew ithin a symphonico rchestraw as a triangleh it
with a metal rod. The generatorc lass "mm"t hus had to be created by
combining several traditionalm etal accessories to form hitherto non-
existent pairs of vibratorsa nd inciters.A s a result of one such combina-
tion, an astounding sound generator arose: piano strings rubbed by a
cymbal.A nother,n o less surprisingc ombinationo f a metal inciterw ith a
metal vibratorw as achievedb y agitatingp iano stringsw ith a triangler od,
the latter disconnected from its original instrument.A true revolution
439
resulted, however, from the practice-derived from jazz-of playing
with metalb rusheso n suspendedc ymbals.T hese same brushesw ere also
employed by Pendereckit o play gongs, tam tams, and tubularb ells, and
even to play the stringso f harpsa nd pianos.W ith the aim of enlargingt he
numbero f generatorso f the "mm"c lass, Pendereckii ntroduceda type-
writer,c reatinga sensation duringt he first performanceso f the Fluores-
cences. As this quasi-musicalm etal instrumentd emonstrates,m aking up
a representationo f an earliern onexistentc lass of sound generatorsc ould
incidentallyl ead to an expansiono f the set of orchestrali nstrumentsw ith
new accessories. Mostly, such cases issued from practicalc onsiderations,
as when the interactiono f a certainf orm of inciter and a certainf orm of
vibratorc ould have been obtainedo n traditionali nstruments,b ut would
have damagedt hem in the process. In the class of generatorsu nderc on-
sideration,r ubbingt wo metal bodies against one anotherw ould scratch
their surfaces. Therefore,i nstead of costly percussive instruments,P en-
derecki simply used a piece of iron rubbed with a file or sawed with a
hand saw.A saw can also serve to saw wood, in this way creatinga n addi-
tional generatoro f the "mw"c lass, but this entails the use of a disposable
piece of wood.
Although Pendereckit ook into account such practical mattersw hen
inventingh is new sound generators,o rchestralm usicians often disagreed
with the composera s to what was or what was not harmfulf or theiri nstru-
ments. Characteristici s the technique of playing strings that originally
called for the instrumentalistt o tap the sound boardw ith the nut (i)-an
interactiono f two wooden bodies (ww)-which Pendereckid id not intend
to be harmful.H owever,t he performerst houghtt he techniquew ould dam-
age the varnishc overing their instruments( Erhardt1 975, 36). The com-
poser yielded and specified thatt he soundb oardc ould also be tappedw ith
fingertips. Therefore, in the scores of the earliest pieces based on the
timbre system-Threnody (publishedi n 1961), Dimensions of Timea nd
Silence and Fluorescences (printedi n 1962), as well as the String Quar-
tet No. 1 (issued for the first time in 1963)-this effect is described as
"tappingt he body of the instrumentw ith the nut or finger-tips."E vidently,
musiciansp referredt he latterp ossibility,a ndt hus in Polymorphia( issued
at the end of 1963), and Canon (whose score was published as late as
1974), "tappingt he soundb oardw ith fingertips"c onstitutest he sole way
of performingt his effect indicated by the composer.A s a result of this
compromiseb etween the composer and the performers,a generatorw as
included among the class "ww" of sound generatorsw hich in reality did
not at all belong to it.
In light of the above discussion, it is clear that the notion of a musical
instrumenti s useless-not to mention anachronistic-in Penderecki's
pieces based on the timbre system. Because most of the instruments-
except for some simple percussive tools-consist of a number of con-
440
stituent parts, with each part able to interactw ith a numbero f inciters,
every instrumentb ecomes the basis for several different sound genera-
tors, which, in addition, may represent different classes. This has an
obvious effect on the groupingo f instruments,t hat is, on the orchestra-
tion. In contradistinctiont o traditionalo rchestration,i n which every in-
strumenti s ascribed a certain timbral quality, here one and the same
instrumentc an be used in a numbero f differentw ays and cooperatew ith
several different classes of sound generatorsi n different musical con-
texts-depending on which of its elementsi s employeda s a sounds ource.
This issue has in the past been touched upon by musical critics who
applied the term "percussive effects" to some playing techniques on
stringedi nstruments.6B ut this term is unsatisfactoryF. or, if the classifi-
cation of instrumentsd ependso n theirv ibrators-and this is actuallyt he
basic criterionf rom Sachs and Hornbostelu p to Drobner-then a violin
tappedo n with the nut of a bow or with the fingertipsd oes not so much
producea percussivee ffect, butr atheri t becomes a percussivei nstrument:
a wooden idiophone in this instance. Similarly,a wind instrumentt hat is
not blown but tappedw ith stops or pistons is not an aerophoneb ut a metal
idiophone.T his last "percussivee ffect" occurs in Fluorescences as a rep-
resentativeo f class "mm,"a nd it is the only instance of winds in Pen-
derecki'sp ieces based on the timbres ystem. Parentheticallyt,h e absence
of aerophonesf rom other Penderecki scores written in the early 1960s
also results from the system. Since its underlyingm aterialc ategoriesa re
all solid bodies, blown air-the proper vibratoro f wind instruments-
constitutesn o categoryi n the frameworko f this system. Fromh ere it fol-
lows thats oundse mittedb y the traditionallyp layed woodwindsa ndb rass
have-from the viewpoint of Penderecki's timbre system-a neutral,
"transparentv"a lue. That they occur in Fluorescences is most likely due
to the circumstanceso f its commissioning.T he piece was commissioned
by the Sinfonie-Orchesterd es Stidwestfunks,B aden-Baden. If Pende-
recki had used the wind section exclusively for snappings tops and pis-
tons, he would have exposed himself to the commissioner's displeasure
while the musical critics would-in the best case-have suspected him
of a very peculiar sense of humor.
Penderecki's invention of new sound generators-and thereby new
timbres-was thus not a manifestationo f extravaganceb y the composer.
It was not intendedm erely to shock the audience, nor did it spring from
an exuberanti mage of sound. Conversely,t he new timbresw ere not-at
least originally-to serve some vague "new expression."7I f Penderecki
introducedi n his pieces new quasi-musicali nstruments,u nusualc ombi-
nations of traditionalm usical accessories, or any previously unknown
techniqueso f sound articulation,h e did so in terms of his system. With-
out them, the system would remain merely an intellectualc onstructd e-
void of any possible musicalr ealization.S een from this angle, the orches-
441
trations,a nd instrumentalt echniques Pendereckie mployed in the early
1960s departf rom traditionalo nes in the same way as the timbres ystem
based on the materialc ategoriesm etal-wood-leatherd epartsf rom the tra-
ditional partitiono f the orchestrai nto strings, winds and percussion.A t
this point, one must also reject the suggestions formulatedb y some crit-
ics who claimed that, in Penderecki'se arly output,t he "new"e ffects are
opposed to the "old,"t raditionalo nes. Such an oppositionf indsj ustifica-
tion neitheri n the timbralo rganizationo f concretep ieces nor in the com-
ments of the composerh imself. On the contrary,P enderecki'ss tatements
make it clear that the "history"o f a given generatorw as entirelyi nessen-
tial.8I n the frameworko f his timbres ystem, both traditionala nd non-tra-
ditional sound generatorsa re equivalentr epresentativeso f classes fixed
by materialp airs.A s in the case of the periodict able of Mendeleev,w here
classificationa ccordingt o the atomic mass disclosed places for new, not
yet discoverede lements, Penderecki'ss ystem revealedn ew niches which
could be filled with distinctive timbres.T hus, the system helped stimu-
late his discoveries.
II. Morphology
Let us turn from the problems of the practicalr ealizationo f the tim-
bre system to the main subjecto f this article, a reconstructiono f the sys-
tem itself. As explained earlier,t he materialp airs shown in Figure 2 fix
classes of timbres representedb y individual generatorsa nd-what for
Penderecki is one and the same thing-by the individual sounds they
generate.B ut individuals ounds are secondaryi n Penderecki'sm usic. In
his pieces based on the timbre system the elementary unit is a set of
sounds, which I will call a segment. Sound phenomenac ontainedi n one
timbrals egment can be identical or different, in the sense that they are
generatedb y collisions of bodies representingi denticalo r differentp airs
of materials.I f all sounds are producedi n the same way, that is, through
interactionso f the same two materials,t hen the timbreo f a segment will
be covered by only one material pair. Yet such "monochromatic"s eg-
ments occur comparativelyr arely. Much more frequent are segments
whose component sounds belong to several different classes. How can
their overall, resultantt imbresb e determined?
The initial analyticalp rocedurei n such cases is an enumerationo f all
the materialp airs producingt he sounds of these segments. At this stage
of the descriptiono f a single segment, a given materialc an occur several
times as a componento f differentp airs. This is so because bodies repre-
senting one materialc ategoryc an interactw ith bodies made of either the
same or differentm aterials,i n this way producings ound phenomenat hat
differ in timbre.F rom this it follows that differentm aterialsm ay vary as
to the number of occurrences in a segment description. Of course, the
442
...... ..
w .. - W * 91
I-
f
h
Figure 3. Segment with one main material
composite timbre depends most on the materials that occur most fre-
quently. Those exerting a decisive influence on the timbre of a given
segment will be marked as its main materials.T he main timbralr oles,
however, can be played only by primarym aterials-metal, wood, and
leather.F elt and hair can never dominatet he timbreo f a whole segment,
just as they cannot become a source of any one of its components ounds.
The main materialsc an be discernedb y means of a method that I call
a "commond enominators earch."T his searchi s easiest and most obvious
when all pairs belonging to a given segment form differentc onjunctions
with one primarym aterial.T he latter,w hich occurs in all pairs and in this
way forms their "commond enominator,"is the main materialf or the seg-
ment. Such a segment thus has only one main material( Figure 3). If no
single primary material constitutes a common denominatoro f all the
pairs within a segment, one has to search for the common denominator
of the greatestn umbero f pairs within this segment, and then for the com-
mon denominatoro f the remainingp airs. If such a denominatora s a pri-
mary material does exist, the segment has two main materials, and the
search proceduree nds (Figure 4). However, if a common denominator
still cannot be found within the group of remaining pairs, one has to
repeat the procedure:f irst find the common denominatoro f the greatest
numbero f pairs, and then the common denominatoro f the last remaining
group. In such a case, the segment has threem ain materials( metal, wood
443
