translation of rhythm into pitch in stockhausen klavierstück xi

The Translation of Rhythm into Pitch in Stockhausen's Klavierstck XIAuthor(s): Stephen TrueloveSource: Perspectives of New Music, Vol. 36, No. 1 (Winter, 1998), pp. 189-220Published by: Perspectives of New MusicStable URL: http://www.jstor.org/stable/833580Accessed: 26/07/2010 21:55

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THE TRANSLATION OF RHYTHM INTO PITCH

IN STOCKHAUSEN'S KLAVIERSTUCK XI

STEPHEN TRUELOVE

KARLHEINZ STOCKHAUSEN'S Klavierstiick XI has the unique distinc- tion of being one of the most often discussed yet least-well-

understood compositions of the twentieth century. It is celebrated for its "open form," in which the nineteen component fragments may occur and recur in any order. In Jonathan Cott's Stockhausen: Conversations with the Composer, Stockhausen spells out the relationship between "noisy" timbres and "aleatoric" formal processes, specifically with refer- ence to Klavierstiick XI: "Piano Piece XI is nothing but a sound in which certain partials, components, are behaving statistically.... As soon as I compose a noise, for example-a single sound which is nonperiodic, within certain limits-then the wave structure of this sound is aleatoric. If I make a whole piece similar to the ways in which this sound is organized,

Perspectives of New Music

then naturally the individual components of this piece could also be exchanged, permutated, without changing its basic quality" (Cott 1973, 70). This concerns the large-scale formal concept, which is the well- known aspect of the piece, but tells us nothing about the two most sig- nificant aspects of its actual composition: rhythm and pitch. The rhythms for the entire piece were composed first, and only then were they translated into pitch.

Of the various studies touching on Klavierstiick XI (Boehmer 1967; Decarsin 1991; Harvey 1975; Helffer 1993; Maconie 1990; Pflugradt 1972; Volans 1971), only Konrad Boehmer's monograph, Zur Theorie der offenen Form in der Neuen Musik, throws any real light on the compositional makeup of this extraordinary piece. While his insights go some way toward explaining durational and contour relationships, he makes no attempt to explain pitch derivation or any relationships that might exist between pitch and duration (i.e., rhythm).

Stockhausen's unpublished sketches for Klavierstuck XIreveal the processes he used to organize the work's rhythmic structure-which was created first, in its entirety. Stockhausen then derived the pitch content of the piece from the already-composed rhythms. For this reason it will be necessary first to illustrate the construction methods used for the rhythms. In November of 1980 I researched Klavierstiick XI in Stockhausen's personal archive at Kurten, Germany. Later at his home Stockhausen removed the folder for Klavierstiick XI from his vault, which contains original manuscripts and the sketches for his compositions. As source material for this study, Stockhausen then allowed me to photocopy the original manuscript of Klavierstiick XI and twenty-six additional pages of notes and sketches.

The nineteen music fragments that constitute Klavierstick XI were composed by a matrix system of serial polyphony in which rhythm matrices, often serially reordered by number matrices, were combined together to form the separate columns of a Final Rhythm Matrix consist- ing of six columns and six rows. Stockhausen then chose nineteen of the thirty-six rhythmic blocks this 6 x 6 structure generated, to use for the pitch realization of Klavierstiick XI.

In composing the rhythmic structure for Klavierstick XI, eight number matrices (Example 1) were employed by Stockhausen in reordering the contents of associated rhythm matrices. The rhythm matrices from Stockhausen's sketches, upon which the number matrices operate, are shown in Example 2, and the end product, which I shall call the Final Rhythm Matrix, is shown in Example 3. The rhythm matrices, with their columns of varying sizes, amount to sets of two-dimensional "scales" upon which serial ordering operations may be performed. Beginning

190

Stockhausen's Klavierstuck XI

1. 6 1 4 3 7 5 2 1365274 4621537 3517426 7254 163 573264 1

2. 5 3 4 1 6 2 312546 156324 42 36 5 1 64 52 13 2 6 14 35

3. 4 5 2 1 3 14 532 312 54 25 14 3 42 3 15 5342 1

4. 3 4 2 1 5. 3 4 2 1 4132 4132 1243 2314 2314 1423 3241 3241 4132 4312

6. 4 1 3 2 1243 3421 2314 3241 4312

7. 2 3 1 31 2 123 13 2 23 1 32 1

8. 2 3 4 5 6 7 4 6 8 10 12 14 6 9 12 15 18 21 8 12 16 20 25 28 10 15 20 25 30 35 12 18 24 30 36 42

EXAMPLE 1: NUMBER MATRICES 1-8

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194 Perspectives of New Music

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with rhythm matrix 1 and proceeding through 11, this "scale" can be observed (a "scale of scales," so to speak) having six basic values, with duplications of values 4 and 2: 7, 6, 5, 4, 4 (retrograde columns, shuffled subdivisions), 4 (reordered columns), 3, 2, 2, 2, and 2 columns. Yet all rhythm matrices have 6 rows, each a more complex subdividing of the basic value than the one above it.

An examination of the interior blocks of the Final Rhythm Matrix reveals rhythmic sophistications of the original reordered rhythm matrices, as well as additional elements such as trills, pauses, and so forth. Both rhythmic sophistications and additional elements were introduced by processes whose discussion is not within the scope of this article. For example, a series of element matrices containing trills, pauses, and so on, were combined to form a Composite Element Matrix. The original rhythm matrices and Composite Element Matrix were then added together to form the Final Rhythm Matrix.

The first page of Stockhausen's sketches contains rhythm matrix 1, which was used in constructing the sixth column of the Final Rhythm Matrix (Example 4). (In all matrices, both of numbers and of rhythms, the term "row" will designate a horizontal succession, and the term "column" will designate a vertical succession. The top row of a matrix will be designated "row 1," and the column at the left side of the matrix will be designated "column 1.") A succession of rhythm matrices, each one unit smaller than the previous matrix, was employed in constructing columns 5 to 1 of the Final Rhythm Matrix: Rhythm matrix 2 and number matrix 2 produced column 5 of the Final Rhythm Matrix, rhythm matrix 3 and number matrix 3 produced column 4 of the Final Rhythm Matrix, and so forth.

The rhythmic cells in each column of the Final Rhythm Matrix correspond in number to the total number of columns in the rhythm matrix from which the rhythmic cells are derived. This is because an entire rhythm matrix is transferred to a single column within the Final Rhythm Matrix. Each successive rhythm matrix Stockhausen used in constructing the Final Rhythm Matrix has one less column. Therefore, column 6 of the Final Rhythm Matrix has seven rhythmic cells inside each block, column 5 has six rhythmic cells, and so on.

Number matrix 1 was employed in reordering the blocks within rhythm matrix 1 in the following manner: The rhythmic blocks in the successive rows of rhythm matrix 1 were matched with numbers occupy- ing the same positions in the corresponding rows of number matrix 1. When Stockhausen transferred rhythm matrix 1 to a single column of the Final Rhythm Matrix, the numerical sequence of the rhythmic blocks in each row was reordered by the matching numbers from the number

202

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EXAMPLE 4: RHYTHM MATRIX 1 AND NUMBER MATRIX 1

1

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203


matrix in the following way: The rhythmic block which matched up with the number 1 from the number matrix was placed first, the rhythmic block that matched up with the number 2 from the number matrix was placed second, and so forth.

The result of this reordering process, along with further sophistications of most blocks when transferred, is column 6 of the Final Rhythm Matrix (Example 5).

EXAMPLE 5: COLUMN 6 OF THE FINAL RHYTHM MATRIX

If one observes the successive durations in row 1 in the above example, it becomes easily apparent they correspond to durations in row 1 of rhythm matrix 1, which have been reordered in the following sequence: 6 1 4 3 7 5 2. This corresponds to the number series from row 1 of number matrix 1. A comparison of rows 2-6 of both rhythm matrix 1 and number matrix 1 will reveal the same reordering process.

Column 1 of the Final Rhythm Matrix has no associated number matrix. Since the rhythm matrices that produced this column had only 2 rhythmic cells per block, each pair of rhythmic cells being located in a single column, Stockhausen obviously felt no need to reorder them with

204

Stockhausen's KlavierstOck XI

a number matrix before transferring them to the Final Rhythm Matrix. (Rhythm matrix 11 is also found in this group of matrices, but no rhythmic cells from this matrix were used.)

Column 2 of the Final Rhythm Matrix also has no associated number matrix. However, Stockhausen accomplished a reordering of rhythm matrix 7 by using a three-unit duration scheme shown in Example 6a. The number matrix, Example 6b, is not found in Stockhausen's sketches, but has been added to express the numerical reordering of the duration scheme.

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EXAMPLE 6: RHYTHM MATRIX 7 AND NUMBER MATRIX 7

The matrix in Example 7, not found in Stockhausen's sketches, illustrates blocks in the Final Rhythm Matrix used as rhythmic sources for the nineteen published fragments of Klavierstuck XI.

205


EXAMPLE 7: SELECTION OF NINETEEN FRAGMENTS FROM THE FINAL RHYTHM MATRIX

Fragment 6 of Klavierstiick XI is thus found to originate in row 2, column 2 of the Final Rhythm Matrix. The rhythm of fragment 6 resulted from the reordering process occurring in row 2 of Example 6. The duration scheme of a dotted quarter note, followed by an eighth note and a quarter note, creates a reordering scheme expressed by the number series (3 1 2).

The top portion of Example 8 illustrates the rhythm of fragment 6 as it appears in Stockhausen's sketches before he composed its pitch realization, and below that is fragment 6 as it appears in the score. In this example one also observes the fact that Stockhausen doubled all duration values from the Final Rhythm Matrix when composing the pitch realizations of each fragment.

The added grace notes and fermatas in this fragment come from the Composite Element Matrix (Example 9), the construction of which is found beginning on page 88 of my D.M.A. Document (Truelove 1984). The Composite Element Matrix, having the same dimensions as the Final Rhythm Matrix, was then combined with it when Stockhausen wrote out the rhythms which he used to realize the pitch content of the piece. For

206

Stockhausen's Klavierstbck XI

example, the various elements in row 2, column 2 of the Composite Ele- ment Matrix would be matched with the durations found in row 2, column 2 of the Final Rhythm Matrix, and so on.

'4k V y J V

EXAMPLE 8: FRAGMENT 6

The fact that one of the grace notes in Example 9 is slurred to another note, while the second grace note in this fragment has no slur and occu- pies a more remote register than the note that follows it, was not determined by instructions within the Composite Element Matrix, which only indicated the presence of two grace notes. It was Stockhausen's choice to contrast the two grace notes in this manner in his sketches when he was writing out rhythmic fragments in numerical order while consulting the Composite Element Matrix and Final Rhythm Matrix. This contrast between the two grace notes reflects Stockhausen's constant quest for variety and sophistication, rather than simple repetition, in all parameters under consideration during the process of composition.

The pitch structure of Klavierstick XI was composed by a method which reflects, but does not always exactly equal, the harmonic relationships of overtones to one another within the natural harmonic series. This was achieved by translating duration proportions between adjacent durations, occurring within the rhythmic structures derived from the Final Rhythm Matrix, into pitch fluctuations. The pitch fluctuations thus correspond to identical proportions within the overtone series: If the fundamental tone, or partial, is given the numerical value of 1, and

II 1

f 7 1 ^1^ -^

207


= three large clusters (I etc.) tied through a certain region. Not tied 3 to one another.

= four grace-note attacks placed at different points, having 8, 6, 7, and 5 pitches respectively. = tied elements (single pitches, chords, trills, or tremolos) which are placed at the end of a fragment and linked ("binden") to the following fragment that is subsequently played. = trill.

N = neutral. = three grace notes, each having 1 pitch, placed at different points in the fragment.

, = tied chords or single pitches which are silently depressed.

o mrr = grace-note groups of single pitches per attack: 10 attacks begin the fragment, and groups of 3 and 6 attacks occur within the fragment. = fermata(s) to be inserted within note groups. = an echo effect.

Y = a group of 28 single grace-note attacks to be written with connected nr stems above and below the note heads in order to divide notes between

hands. r- = a group of 15 grace-note attacks which fluctuate between single

pitches, clusters, and chords. 4--.m. = tremolo. At1sv = a chord tied over at the end of the fragment.

EXAMPLE 9: COMPOSITE ELEMENT MATRIX

208

Stockhausen's Klavierstbck XI

successive ascending partials are numbered from 2 to 12, the resulting numbers approximate the vibration proportions of the partials to both the fundamental and to one another. The proportion between the second and third partials is that of 2:3. The proportion becomes 3:2 if the third partial is considered first. The interval between the second and third partials is a perfect fifth. When Stockhausen encountered a duration proportion of 2:3 or 3:2 between any two durations in the rhythmic structures, he used this proportion to generate an interval of a perfect fifth, with a possible "adjustment" of the interval to that of a diminished or aug- mented fifth. Similarly, the 2:1 duration proportion either yielded an octave or an "adjustment" resulting in a major seventh or minor ninth. The "adjustments," one half step above or below the pitch implied by the duration proportion, were made in order to maintain atonality by avoid- ing octaves or triadic harmony whenever Stockhausen considered it appropriate. A possible genesis for Stockhausen's practice of allowing a duration proportion to imply more than one possible pitch is to be found in the following quotation from Stockhausen's "...How Time Passes . ..":

Such an abrupt shift from "pointillist" to "statistical" temporal perception has now become a further motivation for statistical field composition. This means, however: the elements themselves are no longer conceived as discrete values of some scale or other (be it now as discrete pitches or durations, that is, as a measured duration and number of the microtemporal phases: phase duration = 1/440 sec. and number of phases = 220, produces an A4 with a duration of half a second). On the contrary, a field magnitude replaces each discrete value in the sense described above (field duration from 1/440 sec. to 1/550 sec.-thus a possible pitch between A4 and C5, and a fundamental duration between 1/2 sec. and 1 sec., etc.). Such field magnitudes are now the "elements", and so composition is brought into the statistical character of mass structure within the elements.

(Stockhausen 1963 (Texte 1), 129) The field-size of possible pitch fluctuations resulting from duration

proportions is three chromatic pitches. The central pitch in this "statistical field" expresses the interval resulting from harmonic-relationship duration proportions. The other two pitches are chromatic adjustments of this interval a half step in either direction.

Stockhausen also used the proportions of harmonic relationships between nonadjacent partials for determining pitch fluctuations. For example, the intervallic relationship of the fifth partial to the first partial

209


is a major seventeenth. The second and third pitches (D# and G#) of fragment 6, shown in Example 8, have a 5:1 duration proportion, which generates the interval of a major seventeenth. If Eb is considered as the enharmonic spelling of the D#, the interval between the two pitches can be understood as being originally a major seventeenth which, during composition, was adjusted upwards one half step from the G to G#. The registral disposition of these two pitches also illustrates another aspect of Stockhausen's use of rhythmic duration proportions in relation to the natural harmonic series: notes with longer values have lower registers than adjacent notes with shorter values. This reflects the fact that lower partials generally sound both louder and last longer than the higher partials in most ordinary sounds. Exceptions can occur from octave displace- ments of the pitch implied by the duration proportion, or by simply calculating the interval in the opposite direction from that indicated by the longer of the two note values within the duration proportion.

After its completion, Stockhausen retained identical note values from the Final Rhythm Matrix when he composed the pitch realizations for fragments 1-16 and 18-19 without grace note groups. He then doubled the note values for the nineteen fragments when writing their pitch realizations with grace note groups included. He then cut the completed ver- sions out separately in order to disperse them throughout the original manuscript of Klavierstiick XI. Although the arrangement of fragments according to relative sizes is similar to the published score of Klavierstuck XI, some individual fragments occupied different positions relative to one another in the original manuscript (Example 10). The interested reader may compare this example with the published score of Klavier- stuck XI to determine the alternative spatial disposition Stockhausen later chose.

Since the pitches of Klavierstiick XI were derived from duration proportions, and not twelve-tone sets, a discussion of the relationship of the duration proportions of the original rhythmic scheme to the pitches of the separate voices within fragment 1 will be helpful in understanding Stockhausen's pitch realization procedure. To observe the gradual forma- tion of this fragment, see row 3 of rhythm matrix 8, row 3, column 1 of the Final Rhythm Matrix, and row 3, column 1 of the Composite Ele- ment Matrix (Example 11).

The grace note, fermata, and diamond-shaped notes (which are silently depressed) in this fragment originate in the Composite Element Matrix. Grace notes occur both singly and in groups in the various nineteen fragments of Klavierstuck XI. Since the pitches for these grace notes were not determined by a sequence of varying proportions, they were freely "improvised" by the composer. Free pitch improvisation is also logical in

210


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this context because the proportion 1:1 also yields a "free" change of pitch between the duration proportions originating in the Final Rhythm Matrix. This is identical to the duration proportion between successive grace notes in a common group.

The duration proportion between the D and C# in the upper voice is 2:1. This generates an ascending octave, which Stockhausen adjusted downwards a half step. The relationship of the C# to the following B is more complex, being that of an eighth-note triplet to a quarter-note quintuplet. Multiplying 3 x 5 results in a common counting unit of a 15- uplet. The C# (1/3 of 15 in the triplet group) gets 5 duration proportion units, and the quarter note (2/5 of 15 in the quintuplet group) gets 6. This results in a duration proportion of 5:6 between the two pitches. The interval for this duration proportion is a descending minor third. With a starting point of an imaginary A# a minor third below the C# in the example, the following B can now be seen as resulting from both an "adjustment" of one half step upwards from the A#, and then an octave displacement one octave downwards. The duration proportion between the B and the following D# is 2:3, which generates a descending perfect fifth. Thus the D# can be seen as being "adjusted" downwards a half step beyond a perfect fifth below the B in the fragment.

The duration proportion between two chords in the lower voice (omitting the silently depressed chord) reflects Stockhausen's practice of changing some rhythms when he transferred them to the Final Rhythm Matrix. In this instance, the rhythm in the lower voice of row 3 in rhythm matrix 8 is simplified somewhat by changing the dotted sixteenth note tied to a double-dotted eighth note to a dotted eighth note, and quadrupling the value of the following thirty-second note into a resulting eighth note. This changes the duration proportion from 9:1 to 3:2. When the composed pitches are observed in Example 11, there is no 3:2 (perfect fifth) duration proportion exhibited between any of the four pitches of the two chords. However, the original 9:1 duration proportion, with an octave displacement downward by two octaves and a pitch "adjustment" downwards by a half step, exists between the F in the first chord and the F# in the second. The 9:1 duration proportion also exists between the F in the first chord and the G in the second. There is no pitch "adjustment" involved in this pairing of notes, the G being simply displaced an octave downwards.

An additional consideration is needed for the calculation of certain pitch realizations in the composition of Klavierstiick XI: attack-point duration calculations. This is necessary because Stockhausen further sophisticated many rhythms originating in the rhythm matrices by placing rests within their interiors when transferring them to the Final

212

Stockhausen's Klovierstuck XI

Rhythm Matrix. He did this by decreasing the value of single durations and placing the rests after the new duration value generated. A quarter note thus shrunk to a dotted eighth note would be followed by an eighth-note rest. In calculating such a duration proportion the attack- point of the first duration will be the eighth note, and the new space between the two durations created by the rest must be compensated for by including the value of the intervening rest with the value of the first duration. An inserted rest can be observed when comparing the top voice of row 5 in rhythm matrix 9 with the top voice of row 5, column 1 of the Final Rhythm Matrix.

Fragments 17 and 11 are exceptional among the nineteen fragments of Klavierstuck XI. Each exhibits compositional procedures not present in the other seventeen fragments. The procedures involved in constructing fragment 17 (Example 12) are extensive, and a thorough discussion is not within the scope of this article. The block at row 1, column 6 of the Final Rhythm Matrix was employed in creating fragment 17. The varying durations in this block were used in a manner similar to the way Stock- hausen composed Klavierstiick X(see Henck 1980): In addition to being translated into seven different pitches, the size of these durations also determined regions into which groups of notes with much smaller time values were composed. Stockhausen's compositional method for fragment 17 can thus be viewed as a conceptual link with the piano piece that numerically precedes it.

The durations in fragment 17 which originate in the Final Rhythm Matrix can be observed in the lower voices of both the rhythmic scheme and the pitch realization of this fragment. They are found in sections 2, 4, 6, 8, 10, and 13.

Fragment 11 (Example 13) is perhaps the most mysterious in mood of all the fragments of Klavierstiick XI.1 Not only does it sound mysterious, there is also a mystery associated with the pitches of the upper staff, and two pitches in the lower. With the exception of the F, the seventh duration in the upper staff, the pitches in this staff do not originate in the Final Rhythm Matrix. This is also true of the third and fourth durations in the lower staff. One may thus conclude that these additional pitches were "improvised" around the other durations coming from the Final Rhythm Matrix. The intervals of the improvised pitches also do not con- form to the duration proportions implied by their respective durations. Although the interval between the improvised pitches in the bottom staff is a minor third (pitches: D and F), a general chromatic tendency can be observed in the pitches of the improvised durations in the upper staff. The G#-A-A#-B constitute the first four improvised durations. The following chromatic pitches C and C# are present in the next duration. The

213


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F, being the seventh duration in the upper staff, originated in the Final Rhythm Matrix. The eighth duration contains further pitches which con- tinue to fill out the chromatic space from the point left off at the sixth duration: D-Eb-E-F#-G-G#-A-A#. The absence of an F within the eighth duration is accounted for by observing this pitch as the preceding duration, hence the avoidance of the repetition of pitches. If one considers the mysterious mood of this entire fragment, as well as the final tremolo with which it ends, what a mysterious ending for a performance of Klavierstuck XIwere this fragment to be the final fragment played in a particular performance!

The unifying force of Stockhausen's kernel serial idea, which applies to rhythm and pitch in like fashion through a system which derives the pitch succession from the previously composed rhythmic structure of each fragment, is given great expression by the extreme sensitivity to nuance and detail brought to bear upon the polyphonic and, simultaneously, the harmonic fabric of the music that resulted when composing the pitches from the rhythms. After having become familiar with many aspects of the basic procedures Stockhausen employed in creating both the rhythmic and pitch structure of Klavierstiick XI, I should hope that the reader's experience of this fascinating and seminal twentieth-century piano piece will now be enhanced by an examination of the score with "new eyes," as

217


well as from repeated listening to both performances and recordings of this work with "new ears."

The author wishes to acknowledge Karlheinz Stockhausen's generosity in providing the original manuscript and sketches for Klavierstiick XI, access to his personal archive, and use of the photocopy machine in his home. Study and travel with Stockhausen, at his personal invitation, during the 1980 European tour with the Ensemble InterContemporain was extremely beneficial; further study at his home after the tour and a con- tinuing correspondence have provided additional insights and inspira- tion.

NOTES

1. The many different tempi, dynamics, articulations, registers and orders in which the various fragments can be played either during a single performance or from one performance to the next, causes them to be perceived in ever-changing perspectives. This highly sig- nificant formal aspect of Klavierstuck XI also gives it the potential to generate different subjective experiences for both performers and lis- teners. For example, in my subjective experience listening to recordings and performances of Klavierstuck XI, and also practicing the work myself, fragment 11 always strikes me as being very "mysterious" in character at slower tempi, and seems to move into a more "impatient" or "hurried" mode at the faster tempi.

218


REFERENCES

Andree, R. V. 1971. Selections in Modern Abstract Algebra. New York: Holt, Rinehart, and Winston.

Boehmer, Konrad. 1967. Zur Theorie der offenen Form in der Neuen Musik. Darmstadt: Edition Tonos.

Cott, Jonathan. 1973. Stockhausen: Conversations with the Composer. New York: Simon and Schuster.

Decarsin, Francois. 1991. "Le Klavierstuck XI de Stockhausen." Les Cahiers du C.I.R.E.M. nos. 18-19 (March): 101-109.

Harvey, Jonathan. 1975. The Music of Stockhausen. Berkeley: University of California Press.

Helffer, Claude. 1993. "La Klavierstuck XI de Karlheinz Stockhausen." Analyse Musicale 30 (Feb.): 52-55.

Henck, Herbert. 1980. Karlheinz Stockhausen's Klavierstuck X: A Contri- bution toward Understanding Serial Technique: History, Theory, Analy- sis, Practice, Documentation. 2d ed., revised and expanded. Trans. Deborah Richards. Cologne: Neuland Musikverlag Herbert Henck.

Karkoschka, Erhardt. 1965. "Stockhausens Theorien." Melos 32:5-13.

Kurtz, Michael. 1992. Stockhausen: A Biography. Trans. Richard Toop. London: Faber and Faber.

Maconie, Robin. 1990. The Works of Karlheinz Stockhausen. 2d ed. Lon- don: Oxford University Press.

Pflugradt, William Charles. 1972. "Continuity and Discontinuity in the Piano Music of Karlheinz Stockhausen." M.M. thesis, Indiana Univer- sity, Bloomington.

Stockhausen, Karlheinz. 1963, 1964, 1971, 1978, 1989a, 1989b. Texte. Vols. 1-6. Cologne: DuMont.

Truelove, Nathan M. Stephen. 1984. "Karlheinz Stockhausen's Klavier- stuck XI: An Analysis of Its Composition via a Matrix System of Serial Polyphony and the Translation of Rhythm into Pitch." D.M.A. disser- tation, University of Oklahoma, Norman.

Volans, Kevin. 1971. "The Klaviersticke-Stockhausen's Microcosm." Bachelor's thesis, University of Witwatersrand, Johannesburg.

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Worner, Karl Heinrich. 1973. Stockhausen: Life and Work. 2d ed. Trans. and ed. Bill Hopkins. Berkeley and Los Angeles: University of Califor- nia Press.

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Issue Table of ContentsPerspectives of New Music, Vol. 36, No. 1 (Winter, 1998), pp. 1-270Front Matter [pp. 1 - 4]Sofia Gubaidulina: "My Desire Is Always to Rebel, to Swim against the Stream!" [pp. 5 - 41]Transmission, Interpretation, Collaboration-A Performer's Perspective on the Language of Contemporary Music: An Interview with Sophie Cherrier [pp. 43 - 58]A Seventieth-Birthday Festschrift for Karlheinz Stockhausen (Part One)Guest Editor's Introduction [pp. 59 - 64]Orientation to Hermann Hesse [pp. 65 - 96]Through the Sensory Looking-Glass: The Aesthetic and Serial Foundations of Gesang der Jnglinge [pp. 97 - 142]On the Serial Shaping of Stockhausen's Gruppen fr drei Orchester [pp. 143 - 187]The Translation of Rhythm into Pitch in Stockhausen's Klavierstck XI [pp. 189 - 220]Extending Contacts: The Concept of Unity in Computer Music [pp. 221 - 246]Karlheinz in California: A Personal Reminiscence [pp. 247 - 261]

Editorial Notes [pp. 262 - 264]Back Matter [pp. 265 - 270]

translation of rhythm into pitch in stockhausen klavierstück xi

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