structure and numerology in stravinsky's in memoriam dylan thomas

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Structure and Numerology in Stravinsky's In Memoriam Dylan Thomas Author(s): Robert Gauldin and Warren Benson Source: Perspectives of New Music, Vol. 23, No. 2 (Spring - Summer, 1985), pp. 166-185 Published by: Perspectives of New Music Stable URL: http://www.jstor.org/stable/832729 . Accessed: 16/03/2011 00:36 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at . http://www.jstor.org/action/showPublisher?publisherCode=pnm. . Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Perspectives of New Music is collaborating with JSTOR to digitize, preserve and extend access to Perspectives of New Music. http://www.jstor.org

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Page 1: Structure and Numerology in Stravinsky's in Memoriam Dylan Thomas

Structure and Numerology in Stravinsky's In Memoriam Dylan ThomasAuthor(s): Robert Gauldin and Warren BensonSource: Perspectives of New Music, Vol. 23, No. 2 (Spring - Summer, 1985), pp. 166-185Published by: Perspectives of New MusicStable URL: http://www.jstor.org/stable/832729 .Accessed: 16/03/2011 00:36

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and youmay use content in the JSTOR archive only for your personal, non-commercial use.

Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at .http://www.jstor.org/action/showPublisher?publisherCode=pnm. .

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printedpage of such transmission.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

Perspectives of New Music is collaborating with JSTOR to digitize, preserve and extend access to Perspectivesof New Music.

http://www.jstor.org

Page 2: Structure and Numerology in Stravinsky's in Memoriam Dylan Thomas

STRUCTURE AND NUMEROLOGY IN STRAVINSKY'S

INMEMORIAM DYLAN THOMAS

ROBERT GAULDIN AND WARREN BENSON

INCE IT REPRESENTS his initial endeavor in total pitch serialization, Stravinsky's In Memoriam Dylan Thomas has received considerable ana-

lytical attention. In particular, Keller, White, Babbitt, Perle, Ward-Steinman, and Clemmons have contributed to our understanding of this work.' Outside of a few passing comments,2 however, none of the above authors have directly addressed the question of why the composer employed afive-tone set, the fur- ther incorporation of this integer in the structural fabric of the piece, and its possible origin in terms of the poem itself. The intent of this article is a com- prehensive investigation of the above points. It is divided into two parts.

The initial section deals with the derivation and utilization of the number five as a structural determinant in In Memoriam. Obviously, there are inherent dangers in this type of approach, as Charles Warren Fox has pointed out.3 If

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one is intent upon deducing a particular digit, it is only necessary to manipu- late numerical relations until the desired result is achieved. Although many of the statements here may indeed prove coincidental, it does seem possible in this instance to construct a valid case. In order to present an overview of the salient features of the piece, other compositional aspects will be examined. Since certain points already noted by the above authors may be reiterated, an

acknowledgment of their analysis is included in the notes. The second part is more speculative in nature, dealing with the familiar system of number-letter

equivalents, as found in certain Renaissance composers and later in J.S. Bach.4 These latter elements do not perform an actual structural role in the work itself, but may be considered as further extensions of previously established numerical procedures. In this respect they represent "an element of number mysticism, quite Gothic in character"5 with which Stravinsky endowed this

composition.

TEXT ANALYSIS

The composer notes in the Preface to the score that the song setting preceded the instrumental movements. An examination of Dylan Thomas's poem will therefore initiate this investigation, with particular emphasis on those features which may have influenced Stravinsky compositionally. A statement referring to the text of the Cantata (1952) seems particularly appropriate: "I selected verses which attracted me not only for their great beauty and their compelling syllabification, but for their construction, which suggested musical construction. )6

Most scholarly commentary assumed that the poem dealt with his father's

passive attitude toward approaching death.7 Judging from the Preface to the score, Stravinsky favored this interpretation,8 hence his choice of the poem as a fitting memorial on the death of the poet. However, Fitzgibbon has inferred that it actually expresses Thomas's concern over his father's impending blind- ness.9 Key words and phrases develop the contrast of"night" ("close of day, now dark, dying of the light, blind eyes") with "light" ("green bay, sun in

flight, blaze like meteors, burn bright"). There exists an unfinished Elegy which does deal specifically with his father's death.10 Not only are there numerous allusions to blindness, but many of the words and phrases recall the vocabulary of the earlier poem ("night and light, burning, unblessed, prayed, unseeing eyes, crying, frail, tears").

The text is cast in the form of a villanelle, with its customaryfive tercets and a concluding quatrain." The poetic scheme is diagrammed in Figure 1.

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I I I a' b a2 a b a a b a2 a b a a b a2 a b a1 a2

FIGURE 1

The poet set his verses in iambic pentameter of ten syllables per line. The a1 and a2 function as refrain lines, respectively "Do not go gentle into that good night" and "Rage, rage against the dying of the light."12 These refrains are so

arranged thatfive lines occur between repetitions of certain a1 and a2's (refer to

Figure 1). Beginning with the second tercetfive men are mentioned: "wise, good, wild, grave" and finally the "father." These sections develop two rhyme patterns: a = "right, bright, flight, sight, height" while b = "they, bay, way, gay, pray," orfive words in each group. The characteristics enumer- ated in the various "men" are those which Thomas wished for in his father's personality, so that the "father" represents a symbolic unity of the previous sections. Thus the numberfive serves as an underlying structural determinant of the text. As further analysis will reveal, Stravinsky doubtless became aware of this feature during his preliminary perusal of the poem and consequently sought ways of further exploiting the digit in the course of his musical setting.

The text may furnish us with a clue to the origin of the rather peculiar instrumentation. The aI refrain, concluding with the word night, occurs four times, while the corresponding four repetitions of the a2 refrain end with the word lIght. Is it possible to equate these refrains with the orchestral forces: a quartet of trombones (night) opposed to a string quartet (lqght)?'3 Note that these two key words both containfive letters. This number emerges again in the song setting (Quartet + Tenor = 5).

SONG ANALYSIS

The song opens with a short statement for quartet alone, which serves as a recurring ritornello, hereafter referred to as Rx. The use of this principle was certainly not new to Stravinsky during this period, since in the Cantata (1952) the "Lyke-Wake" Dirge functions as a large scale refrain, while in the Ricercar II movement there is a section marked Ritornello.14 In the Passacaglia of the Septet (1953) the first, fourth, and seventh variations (following the opening thematic statement) serve as "varied" refrains, disrupting the otherwise strict serial procedure. SO of the familiar five-tone set is found in Vln. I: 4,3,0,1,2.15 Rx always consists offive set presentations, although only four different trans- formations are actually used (see Figure 2). Each statement of Rx opens and closes with pcs 2,4,11, forming the trichord 025 (or ics 2 + 3 = 5?).16 In the

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initial measures Stravinsky establishes a technique which will reappear in the instrumental movements, that of choosing pairs of transformations which reverse their first and last pcs (see bottom of Figure 2). Rx occurs a total of seven times, not only framing the song in the first and last measures, but also recurring after each tercet.17 The sole exception is found following the fifth tercet ("grave men"), which leads immediately into the final quatrain. In this case the first phrase of the "father" section is itself a setting of Rx with I7/S9 doubled in the Tenor and Cello. Since the recurrence of Rx is somewhat pre- dictable, the composer continually varies its duration. The outer framing statements18 are 7 eighth-notes in length, while the others are 9.5, 6, 4.5, 5, and 6.5 respectively.

Vln. I (S?) 3 0 1 (2

Vln. II (S9) 1 0 9 10 @

Via. (IO) ) 3 6 5 ()

Cello (I7/S9) - 0 3 2 1 0 9 10 II

SO (4 to 2) with I10 (2 to 4); S9 (1 to 11) with I7 (11 to 1)

FIGURE 2

The vocal refrains a1 ("Do not go gentle") and a2 ("Rage, rage") occur four times each. Their original settings may be found in the opening tercet. In contrast to Rx, recurrences of these two refrains basically retain their identical format and length, although some rhythmic modification in the accompani- ment to a1 may be noted. The a1 refrain employs three set forms: I6 overlapped with R? in the tenor, and RI4 in the strings. The a2 refrain makes use again of five set forms: S", IP, R?, RI', and RI7; note the Vln. I/Cello doubling of S1. Particular care is taken with the crucial final word of each refrairi, night and qght. Although both cadence with same pc 4, night is always notated as Fb,

while lIht is set with an Et. The "night" refrain spans an ominous tritone, outlining in the process a diminished triad on Bb (see Figure 3A). The aural effect is not unlike a segment of the composer's beloved octatonic scale. The pcs of the "light" refrain, on the other hand, span a perfect fifth from C to G, with the initial "minor" Eb finding its eventual resolution in the final Et; see Figure 3B. Was Stravinsky perhaps unconsciously influenced by the opening recitative of Haydn's Creation?

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(Do) (night)

A

B

b , 0 b b o M b ^ o b -

(Rage) (light) J,b , M b - W b e -

17' I________________

FIGURE 3

The pcs employed in Rx and the two vocal refrains complete the aggregate, but in an ingenious manner. Seven pcs are held invariant in each (0,1,2,3,4,9,11); note that these include the pcs of SO as well as the framing trichord (2,4,11) ofRx. Other pcs are shared by pairs of refrains: 10 (Rx and al), 8 (a' and a2), and 5,6 (Rx and a2). The remaining pc 7 forms the climactic note of a2.

The a/b lines of the poem deal basically with the five men. Here the unify- ing structural device is canonic imitation. This is not surprising, considering Stravinsky's interest in the procedure as evidenced by those works immedi- ately preceding In Memoriam.19 Instances of canonic technique are illustrated in Figure 4. Rhythmic imitation is fairly strict, although considerable modifi- cation does occur in the second group ("good men"). The distance between entrances decreases proportionally, from essentially four to two eighth-notes. The final "father" section shows no instance of this procedure, unless one considers the unique Tenor/Cello doubling as a "synchronized canon" at the unison, thereby completing the successive stretto effect and achieving a sym- bolic unity in the "father" as regards the previous "men. "

Several aspects serve to distinguish the "father" from the preceding sec- tions. The final a/b lines are divided into two phrases (measures 43-44 and 45-46), each consisting offive set presentations. The first of these, itself a set- ting of the familiar Rx, features the Tenor/Cello doubling noted earlier, the only extended example of vocal doubling in the entire song. The second phrase relates to the a2 refrain in that the same set forms are found (one each of S, I, R, and two of RI), although at different transposition levels. Canonic technique is missing, unless one considers the Tenor/Cello coupling as imitative synchronization. No instances of set overlap occur.

Some observations on overall serial procedure may be briefly summa- rized. The sets are laid out in consistent melodic ordering with no sharing between voices; the single exception occurs in measure 3, where the pizzicato

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"wise men" measures 13-16

Ten: R7 RI2

Cello: R7 R2

Via: R3 RI10

"good men" measures 20-23

"wild men" measures 28-

(4 1 distance)

Vln.I: I'0/R2

Via: I2/R6 (4.5 h distance)

Ten: 17 I8 / I10/ SO

Vln.I: I2 13 /I /S7 (2 } distance)

"grave men" Ten: I6 / 18 measures 36-39

Vln. I: I1 / 3

Cello: I6 /I8 (in aug.)

"father" Ten: I7- S9- measures

Cello: I7- S9-

(2 } distance)

(synchronized?)

FIGURE 4

Bb of the Cello initiates the succeeding RI5 in Vln. I.20 Only three deviations

interrupt the otherwise rigorous serial technique.21 It is tempting to explain the first instance as a printer's error (see the Tenor in measure 17), where the word Do is set with an Ab rather than the more logical Bb.22 The latter would

correspond with the other occurences of the a1 refrain, which always begins with Bb (the initial At is a doubling from the Cello set R7). On the other hand it may be possible to rationalize this deviant as intentional on the composer's part. A glance at the text reveals that the word they, although more properly belonging to the following "Do not go gentle," is retained at the end of the fifth line for purposes of rhyme. This unique instance of overlapping is mir- rored in Stravinsky's setting, where the sets associated with "wild men" are allowed to "spill over" into the a1 refrain. The aberrant Ab in the Tenor is not

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unlike a similar example in the first movement of the Shakespeare Songs (see measures 26-27), where the phrase "do offend mine eare" is accompanied by a momentary breakdown in the serial technique.23 A more obvious nota- tional error may be noted in measure 15, where a natural sign is missing from the Cello's third D (E Eb DO F Gb).24 The other instance is not so easily dis- missed (see the Cello in measures 31-35). The first five pcs of RI4 are stated without regard to order, until the set is completed in measures 34-35. I can give no rational explanation for this passage.

As regards set succession, the composer prefers either disjunct transforma- tions or those which overlap one pc, the significant exception being the tri- chord overlap of the a1 refrain.25 Little or no attempt is made to produce aggregates by employing successive disjunct sets with no invariants.26 In fact, quite the opposite procedure is prevalent. For instance, the four juxtaposed sets of the Tenor in measures 13-16 still lack three pcs to complete the aggre- gate. An overlap of one pc between successive transformations either holds the entire set invariant (S followed by Ror RI), or three pcs invariant with the resultant span of a diminished fifth (S followed by I or S).27 In those passages employing this technique the chromatic turnover is even less. This may be illustrated in measures 29-33, where the Tenor states five sets, the Vln. I four, and the Vla. three. In each case the pc span of the separate parts is only that of a perfect fifth.28

In the "men" sections there appears to be no prevalent scheme as regards either the choice of set transformation or transposition level. One might have conjectured that Stravinsky would have distinguished each category of "men" through contrasting serial procedures, but instead it seems that he was more intent on stressing their common characteristics musically as a pre- lude to the final quatrain of the "father." On the other hand the span of per- fect and diminished fifths produced by overlapping technique does resurface in the relations between the initial pcs of the separate parts in each group of "men," placing an emphasis on ics 5 and 6 (see Figure 5).29

"wise men" "good men" "wild men" "grave men"

5 6

9 11 5 10 4 1 11 6 11 6 5 0 10 5 10 I I I 6I II 1 I I

6 6 5 5 5 5 5

FIGURE 5

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Although such observations are admittedly subjective, the song does not

appear to be a particularly "tonal" piece. It is true that the recurring nature of the Tenor refrains serves to emphasize certain framing pcs: a1 = Bb to Fb, and a2 = El to Et. The Bb and Eb are also reinforced by the same initial pcs in the

accompanying sets.30 The continual rhythmic modification of Rx renders its framing trichord less obvious aurally. The fifth relations between entries of several of the "men" do seem to set up fleeting moments of tonal feeling, although in general there is little sense of cadence in these sections (this lack of cadential definition will be rectified in the instrumental movements). In con- trast to the prevailing "atonal" effect, the musical setting of the a2 refrain

leaps out in a most striking manner. The "voice-leading" diagram of measures 7-10 (see Figure 6) sketches its underlying tertian basis and rising chromatic motion.

u I 1 l 1

(Rage)

\ JrJ "' o

I I

FIGURE 6

The song is 55 measures in length. Important structural points occur in measure 10 (the conclusion of the opening tercet), measure 25, and measure 40 (initiations of the a2 or "Rage" refrain), thus forming recurring segments of 15 measures each (or 5 x 3).

ANALYSIS OF THE PRELUDE AND POSTLUDE

In turning to a consideration of the Dirge-Canons it becomes apparent that Stravinsky both clarified and extended those structural features inherent in the song setting. At least eight specific points may be cited:

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Song Setting

1. Use of instrumental ritornello (Rx) with rhythmic modifications

2. Reversal of framing pcs in Rx

3. Framing trichord (2,4,11) ofRx

4. Canonic technique in "men" sections

5. Use of perfect/diminished fifth in canonic entries of "men"

6. Set succession features mostly juxtaposition or one pc overlap

7. Unification ofpreceding "men" in final "father" section

8. Structural use of numberfive to a limited degree

Dirge-Canons

1. Use ofritornello (see measures 6-8) of Prelude, with exact recurrances)

2. Reversal of framing pcs in both ritomello and 5/4 canons

3. Cadential trichord (0,2,4) of ritornello

4. Use of 4-voice canons in 5/4 sections

5. Use of perfect/diminished fifth in canonic entries of 5/4 sections

6. Set succession features only juxtaposition or one pc overlap

7. Unification of other 5/4 canons in Canon III (measures 16-20), forming the axis of the five canonic sections

8. Extensive exploitation of numberfive as basic structural component

In a broader sense the Dirge-Canons may be considered as a single inter- rupted movement, consisting of five presentations each of alternating (or "antiphonal") canons and ritornello (see Figure 7). It will be noted that cer- tain modifications occur in the pitch field of the 5/4 canons as regards the Pre- lude and Postlude, whereas the ritornello (measures 6-8 of the Prelude) remains constant throughout. In particular the canons of the Postlude are switched and transposed down a step (Canon V = Canon I at T10, and Canon IV = Canon II at T1?), thus creating an arch around the central Canon III.31 This axis canon functions in an analogous fashion to the "father" section of the song setting. The instrumental forces are exchanged in the Postlude for variety of timbre and attack.32

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Prelude i Postlude I ! I

Canon I Rit. Canon II Rit. Canon III Rit. Canon IV Rit. Canon V Rit. Trb. Str. Trb. Str. Trb. Trb. Str. Trb. Str. Trb.

FIGURE 7

Stravinsky's choice of the phrase "antiphonal canons" is somewhat prob- lematic. As the analysis of the song has revealed, there are several instances of strict rhythmic and pitch imitation occurring in the various "men" sections. However, in the recurring 3/2 2/2 3/2 phrase of the instrumental movements (see measures 6-8 of the Prelude) the rhythmic relation between the voices is completely free. Due to the unvaried repetitions of this section, it is more appropriately termed a "ritornello."33 Rhythmic modifications may also be noted in the 5/4 canons as well, even as regards the various imitative entrances. In addition, the relationship of successive set forms is not always kept constant between the separate voices; for instance in Canon II the entries are RI/I, R/RI, I/I (?), and S.34 Most likely Stravinsky equated "canon" with strict serial procedure, since in the Preface he states that the song "is entirely canonic. '

Nevertheless there may be method in this madness. The number of suc- cessive rhythmic durations found in each separate voice of the 5/4 canons is extremely consistent: 16, 12, 11, and 7 (see Figure 8). This is all the more remarkable, considering that frequent rhythmic modifications and note repe- titions take place, thus tending to suggest an intentional procedure on Stravinsky's part.

Canon I Canon II Canon III Canon IV Canon V Trb. 1 7 11 12 Vln. I 11 7

Trb. 2 16 12 16 Vln. II 12 12

Trb. 3 12 (17) (6) Via. 16 16

Trb. 4 11 7 11 Cello 7 11

FIGURE 8

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The difference between 16 and 11 is 5; between 12 and 7 is 5! The number of set forms found in the 16-note groups is 15, while in the 11-note voices it is 10 (15 - 10 = 5). This analogy holds true from the remaining pair: 10 sets in the 12-note voices and 5 in the 7-note groups (10 - 5 = 5). The total number of

separate rhythmic durations in these sections is 230 (2 + 3 = 5)! The pitch interval between imitative entrances is usually a fifth, either per-

fect or diminished. Canon III (measures 16-20 of the Prelude) is somewhat more involved, overlapping both a diminished and perfect fifth. This is not

surprising, since this section forms the central axis of the canons. The 16- and 11-note voices begin on pcs 0, 2, or 4, forming a diatonic complex, while those of the 12- and 7-note voices employ a more chromatic relation (see Figure 9).

Canon I Canon II Canon III Canon IV Canon V

16/11-note 4 2 - 0 0 2 = dia- voices 4 - tonic set

t t t t dim. 5 P5 P5 dim. 5 P5 dim. 5

1 1 1 I 12/7-note 10 9 10- 7 8 = chro- voices - (5) matic

set

FIGURE 9

The ritornello expands the technique noted in Rx of the song, where the

framing pcs between pairs of sets reverse themselves. Here the device is taken one step further, in that now each set begins or ends on one ofthe diatonic pcs ofSO (0, 2, or 4): SO (4 to 2), I'0 (2 to 4), R? (2 to 4), and RI8 (2 to 0).35 The pitch spectrum of the ritornello spans the tritone 0 to 6. Stravinsky is very careful about the resultant "cadential" sonority 0, 2, 4; out of a total of 87 vertical simultaneities (with a cardinality of 3 or more), chords with its interval vector occur only 11 times, and 10 of these are directly associated with the final two sonorities of the ritornello!36

Several characteristics of the ritornello continue to be exploited in the 5/4 canons. The sense of tonal cadence, largely missing in the "men" sections of the song, is intentionally cultivated here, with concluding sonorities on Fb major (measure 5), E minor in first inversion (measure 13), and an incomplete E major seventh chord (measure 21). The Fb notation recalls the same device used on the word night in the song. The set forms leading immediately into the cadential formulas are obviously chosen on the basis of their last pc form- ing part of the final tertian chord. The first two cadences are subsequently

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transposed a step lower to D in the Postlude. The resultant lower level serves to relieve the dissonant tension created by the overlap of the E cadences with the opening D of the ritornello in the Prelude, since in the Postlude the D's of the cadence and ritornello now coincide.37 More significantly, the framing pcs of the sets used in the leading voices of the 5/4 canons (that is, the initial

entry and its octave imitation) consistantly employ the diatonic pcs ofS? (0, 2, 4). (Some of the "cadential sets" noted above may be disregarded.) Thus the "reversal" technique observed in Rx of the song and in the instrumental ritor- nello continues to be emphasized. Those framing pcs employed in the first two canons are either 2 to 4 or 4 to 2, the one exception being the opening voice of Canon II (RI8 or 2 to 0). There are only four sets which satisfy this condition: S?, R0, 10, or RI10. The total pc span of these sets is the tritone 0 to 6. The logical reason for Stravinsky's subsequent transposition of these two canons at T'1 in the Postlude is to retain the framing diatonic pcs ofS? or 0 and 2. Therefore sets S10, 8, and R10 are used, now spanning the tritone 10 up to 4. Observe the RI6 deviant, stemming from the earlier RI8 (see Figure 10). Obviously the emphasis on sets employing framing pcs 0, 2, or 4 hold the pcs

Canon I Trb. I: 4 S 2 2 10 4

Trb. II: 4 S2 2 10 4

pcs 0,1,2,3,4,5,6 CanonII Trb. I: 2 RI8 0 2 I104 2 R4

Trb. III 2 I10 4 ! !

Canon III Trb. I: 0 R 2 T

Trb. IV: 4RI 2 2 I10 4 both

61 CanonIV Vla.: 0 IR610 0 I8 2 R12

. ? I. i .

Vln. I: 0 182 pcs 10,11,0,1,2,3,4

S10 I8

CanonV Via.: 2 0 0 2 ICel: 2 I

Cello: 2 S 1 0 8 2 I _- ,I I

FIGURE 10

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of SO largely invariant. Those sets forming the remaining entries, imitated at the diminished or perfect fifth, tend to complete the aggregate by stressing those pcs absent in the two tritone spans of the leading voices.

Ward-Steinman suggests that the overall tonal movement proceeds from E (Prelude) through D (Postlude) to the final ritornello cadence on C.38 How- ever, this cadence recurs throughout the instrumental movements. The appar- ent rationale for the subsequent transposition is to complete the scheme of diatonic framing pcs. As Perle and Clemmons point out, it would seem more

logical to consider D as the tonal axis (4 to 2 of the Prelude and 2 to 0 of the Postlude).39 Both authors note the spatial placement of the D in the ritornello cadence, being equidistant from the upper E and lower C; D always initiates the ritornello.40

Canonic entries are five beats apart, although in order to alleviate the resultant periodicity, slight modifications of one beat are introduced in three of the five sections. The 5/4 meter of the canons is related to those of the ritornello: (3 + 2 - ) . The succession of meter signatures 5/4 3/2 2/2 3/2 5/4 suggests the arch structure of the five canons.41 The number of set forms in the canonic sections is 40, while those in the ritornello

equal 20, making a total of 60; 60:40 = 3:2 or 3 + 2 = 5. There are 32 sets

employed in the Prelude (3 + 2 = 5), and 28 sets in the Postlude (2 + 8 = 10 or 5 x 2). Of the total of 60 sets in both movements 46 begin on pcs of SO (4 + 6 = 10 or 5 x 2). There are 32 quarter-note beats in the string ritornello of the Prelude (3 + 2 = 5); in the corresponding sections of the Postlude there are 50 beats.

Several further occurrences of the number five may be noted. The abbrevi- ated title used by the composer to denote the song ("Do not go gentle.... ") containsfive syllables, as do the phrases In Memoriam, Prelude Dirge Canons, and Postlude Dirge Canons. The note E, the initial pc of the SO set which

opens the work, is thefifth letter of the alphabet! As mentioned previously, the second part of this paper is more speculative

in nature. Although it is possible to dismiss each of the following statements as examples of mere coincidence, the cumulative effect of the evidence is hard to

ignore. Perhaps only a detailed study of the sketches for this elegy will even- tually shed the proper light on this area of investigation.42

Stravinsky was in the habit of indicating the duration of compositions writ- ten during this period.43 In Memoriam is no exception: the Preface states six minutes. Assuming a tempo of = 101 M.M.,44 the timings for the Prelude and Postlude would be 1'04" and 58" respectively. The marking of = 60 M.M. for the song yields 3 '40". Allowing for the fermata in the song and for pauses between movements, the total of 5'42" closely approximates Stravinsky's given duration. However, the composer has also denoted a sepa- rate timing at the conclusion of each movement which is precise to the sec- ond. This procedure is unique among compositions of this period. As Figure 11 illustrates, not only are these at considerable variance with the above, but

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the total figure is well over a minute off. On the basis of this remarkable dis-

crepancy, considering the meticulous nature of his scores, one is compelled to delve further into this paradox for a plausible explanation.

Real Time Stravinsky's Timings Prelude (at = 101 M.M.) 1'04" 1'27"

Song (at = 60 M.M.) 3'40" 4'30"

Postlude (at = 101 M.M.) 58" 1'23"

5'42" 6'00" 7'20" (?)

FIGURE 11

Suspecting the possible employment of ludus ingenii ("intellectual games"), let us begii by applying the system of letter-number equivalents, as

practiced by some Renaissance composers. Using the standard code of A = 1, B = 2, etc. (I and J = 9, while U and V = 20), the last pair of digits which

represent the second timing in the outer movements yields the initials of

Stravinsky and Thomas: (1'): 27" = I.S. and (1'): 23" = D.T. The number of seconds in the song (4'30" or270") again equals I.S. The sum of27 and 23 = 50, in which the magic 5 resurfaces. Combining the separate digits of each (2 + 7 = 9; 2 + 3 = 5) produces 95, which is the total number of measures in the composition. 9 + 5 = 14 (or 1 + 4 = 5), suggesting the performance forces of the song (Tenor + Quartet), as well as the poet's birthyear 1914; In Memoriam was written in 1954! Stravinsky's total timing of 7'20" = THOMAS. Note the relationship between Dirge Canons and Dylan Thomas, in that both contain the same number of letters and identical framing D and S.

Finally the five syllables of NMEMORIAM = 104! The several occurrences of digits 1 and 4 suggest another hypothetical ave-

nue of speculation. J.S. Bach's numerical signature (using the above code) of 14 (BACH) and its reverse 41 (JSBACH) is well known.45 In a lecture deliv- ered in 1955 entitled "Symbolism in the Music of Bach," Karl Geiringer men- tioned a passage in the St. John Passion where the Jews reply to Pilate that "It is unlawful for us to put any man to death." Quoting Geiringer, "Bach's theme has here five weird chromatically ascending notes on the word 't6ten' (kill), thus referring to the fifth commandment the Jews have just mentioned. This theme is repeated ten times so as to make it quite clear that the composer actu- ally refers to one of the ten commandments. "46 It is really impossible to ascer- tain whether Stravinsky may have been aware of this specific example through some previous contact with the musicologist.47 Nevertheless, a number of striking "coincidences" follow.48 The pc content ofBach's "toten" motive is

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identical to Sttavinsky's SO set (see Figure 12 quoted from Geiringer). If one can assume that the composer interpreted Thomas's poem as a commentary on his father's passive attitude toward his approaching death (he states in the Preface that the poem was written "to the memory of his father"), then this relation is reflected in the actions of Jesus before Pilate in light of his impend- ing crucifixion.

ff:w irr r t6- ten

FIGURE 12

Due to his background in the Eastern Orthodox faith, Stravinsky was obviously aware of the significant role of the Pentateuch in that church's ritual and theology. Even the cathedrals themselves visually celebrate thefive books of the Law in their architecture.49 The Hebraic commandments were doubt- less inscribed on two tablets, the first five laws pertaining to man's relation to Jehovah God and the final five pertaining to man's relation to his fellow man.50 This framing arrangement of 5 + 5 may be observed in several aspects of In Memoriam:

1. the number of measures in the song: 55

2. the five sections each of the Prelude and Postlude, forming a kind of Triptych around the central song

3. In the Prelude of 5/4 canons, with their five measure points of imita- tion, frame the string ritornello:

5/4 (5 meas.) 3/2 2/2 3/2 5/4 (5 meas.)

In addition, the number 10 recurs in various guises:

1. the number of syllables in each line of the poem 2. the difference between the number of beats in the Prelude and

Postlude: 107 and 97

3. using the previous code: SONG = 42 DIRGE = 52 CANONS = 62 or differences of 10

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The skeptic may raise the question: Is this intellectual process a natural one? The answer is affirmative. When we communicate, we employ this proc- ess continually. In meaningful communication, you must concentrate on the subject at hand. The greater this concentrated focus, the more insight you gain, since you are further immersed in your idea or feeling. The more you care, the more careful you are, the more precise, the more ritualistic, the more

symbolic to endow your care with universal indentifiers-symbols-mean- ings. Your expression becomes fundamentally more universal because it is more personal in this deepened, elaborated, enriched sense. Thus the philoso- pher Leibniz's definition of music seems a fitting conclusion: "Music is a secret exercise in arithmetic of the soul, unaware of its acts of counting."

NOTES

1. Hans Keller, "In Memoriam Dylan Thomas: Stravinsky's Schoenbergian Technique," Tempo, 35 (Spring 1955): 13-20; Eric Walter White, Stravinsky: The Composer and His Works (London: Faber and Faber, 1966): 479-80; Milton Babbitt, "Remarks on the Recent Stravinsky," Perspec- tives of New Music, 2/2 (Spring-Summer 1964): 39; George Perle, Serial Composition and Atonality, 3rd edition (Berkeley: University of California Press, 1972): 58-59; David Ward-Steinman, Serial Techniques in the Recent Music ofStravinsky (Ann Arbor: University Microfilms, 1972): 37-48; W. Ronald Clemmons, "The Coordination of Motivic and Harmonic Ele- ments in the Dirge Canons of Stravinsky's In Memoriam Dylan Thomas," In Theory Only, 3/1 (April 1970): 8-21.

2. Richard F. Goldman, "Current Chronicles," MusicalQaterly, XLII/2 (April 1956): 237; Charles Burkhart, Antholo,gyfor Musical Analysis, 2nd edition (New York: Holt, Rinehart, and Winston, 1972): 490; Ward- Steinman, Serial Techniques, 46.

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3. Charles Warren Fox, review of J. A. Huisman's Neue Wege zur dichterischen und musikalischen Technik Walters von der Vogelweide in Journal ofAmerican Musicological Society, IV/3 (Fall 1951): 255-61. Since this study will concentrate on the digitfive, it is useful to ascertain how often this number (or those whose sum equals five) occurs in purely random sampling. In paramutual terms, using single integers the odds are 9 to 1. With double digits the odds of 23, 32, 14, 41, 50, or 55 occurring are roughly 15 to 1.

4. In this system A = 1, B = 2, etc. In this regard see Marianne Henze, Studien zu dem Messenkompositionen Johannes Ockeghems (Berlin: Verlag Merseberger, 1968): 199-201 concerning Ockeghem changing the spell- ing of his name (from Okeghem) in order to produce a symmetrical numericalpattern:O+ C = 17;K + E = 15;G + H = 15;E + M = 17, or 32 + 32 = 64 (8 x 8). His first name equals 81 (9 x 9). Bach's use of his numerical signature will be discussed later.

5. A phrase used by Goldman ("Current Chronicles," 237) in referring to the relation between the five-note cell and the meter signatures of 5/4 and 3/2 + 2/2.

6. Igor Stravinsky, Program Notes for the premiere of the Cantata(Los Angeles, November 11, 1952). Quoted in White, Stravinsky, 429.

7. For example, see Derek Stanford, Dylan Thomas (London: Neville Spear- man, 1954): 117-18; William Moynihan, The Craft and Art of Dylan Thomas (Ithaca: Cornell University Press, 1966): 186-87; David Holbrook, Dylan Thomas and Poetic Dissociation (Carbondale: Southern Illinois University Press, 1964): 52-53 (note the reference to Stravinsky's setting). White also assumes this interpretation (see his Stravinsky, 479).

8. He states that the poem was composed "to the memory of his father."

9. Constantine Fitzgibbon, The Life of Dylan Thomas (London: J. M. Dent and Sons Ltd., 1975): 332.

10. A reconstruction of this poem by Vernon Watkins appears on pages 200-01 of The Collected Poems of Dylan Thomas (New York: New Direc- tions, 1957).

11. Although White mentions the villanelle (see Stravinsky, 479), Ward-Stein- man seems unaware of this poetic form, judging from his curious analysis of the structure of the song (Serial Techniques, 42).

12. The complete text may be found on page 128 of The Collected Poems.

13. The only information regarding the orchestration is supplied by Craft. "... Stravinsky requested a list of instruments expected to take part in the

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concert which would sponsor its first performance. When he knew for cer- tain that four trombones would play in Schuetz's Fili Mi Absalom, a cor- tege of mourning canons was added to the Thomas setting." Robert Craft, "A Concert for St. Mark," Score, 18 (December 1956): 47.

14. A number of similarities suggest that the Cantata may have served as a kind of model for In Memoriam. In addition to the above mentioned Ritor- nello, the terms Dirge and Canon appear in the score. The central Ricercar II, employing a tenor and quartet of instruments, is framed by the Dirge and remaining movements.

15. The "Theme" of SO and its subsequent forms are bracketed and labelled in the Prelude. This was an admitted oversight on the composer's part while correcting the final proofs (see Keller, "In Memoriam," 15). The chromatic filling in of the M3rd is noted by White in several other works of this period: the four-note set of the first movement of the Shakespeare Songs (11,7,9,10) and later in A Sermon, A Narrative, and A Prayer (3,4,0,2,1,10,11,6,7,9,8,5). See White, Stravinsky, 479 and 511. The same tendency may also be found in the opening tetrachords of Agon (3,2,4,5) and later in its Adagio (5,6,9,8,7,10,11,2,1,4,3,0). Note the reversal of pentachords in the last two works.

16. Perle, Serial Composition, 58.

17. Ward-Steinman, Serial Techniques, 39.

18. Ward-Steinman notes the instrumental switching of sets S? and I10 in the last statement ofRx (Serial Techniques, 40).

19. The designated Canons in Ricercar II of the Cantata (1952) are only strict as regards pitch material. Also see the short canonic passages beginning in measure 2 of the second movement of the Shakespeare songs (1953). The final two movements of the Septet (1953) feature numerous imitative sec- tions which are in strict canonic relation.

20. An occasional doubling of isolated pcs between instruments or voice may be encountered (see measure 5).

21. Goldman quotes a friend who assures him that "every note except one is accounted for" ("Current Chronicles," 238). Ward-Steinman, on the other hand, observes that "Every note can be serially accounted for" (Serial Techniques, 46).

22. Keller's ingenious analysis of this passage ("In Memoriam," 14 and 17) accounts for the Ab through a complex series of set sharing between differ- ent voices, although this method seems unduly forced in light of the pre- vailing straightforward serial procedures. The note in question is retained

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on the recording presumably done under the composer's supervision (Stravinsky's Chamber Works 1911-1954, Columbia recording ML-5107).

23. See Craft's comment on this passage in the notes to the above recording.

24. This error is corrected in the recording.

25. Babbitt's paragraph on this work admirably summarizes the inherent the- oretical properties of the set, noting in particular the possibility ofemploy- ing all four transforms while holding the pc collection invariant ("Remarks," 39).

26. In this regard see the remarks of Goldman ("Current Chronicles," 236-37), and Clemmons' hypothetical set overlap producing an aggregate ("Coordination," 10-11).

27. This procedure will continue to play a significant role in the instrumental movements.

28. This passage is particularly interesting. Each span of a perfect fifth overlaps the succeeding ones by a whole step: Via.: Cf - GO, Vln. I: FO - CO, Tenor: B - F.

29. These perfect-diminished fifth relations recur in the pitch entries of the 5/4 canons of the Dirge-Canons.

30. Babbitt makes the observation that the pc Bb in the Tenor is always set

against a corresponding Bb in the accompanying parts. It is true that

Stravinsky does seem to reserve the pc for the initial note ofphrases. How- ever, Babbitt's statement is slightly misleading, since of a total of six occur- rences in the Tenor voice, only one is actually sounded directly against another Bb; in the "father" section the coupled Bb's are the result of the Tenor/Cello doubling. Babbitt also mentions that the D's in the Tenor are accompanied by every other pc of the aggregate; however, the same could also be said for the Tenor Db's as well.

31. Most of the authors mention this transposition.

32. White, Stravinsky, 480.

33. Both Perle (Serial Composition, 58) and White (Stravinsky, 480) employ this same term.

34. This problem is also discussed in Goldman ("Chronicles," 237-38) and Clemmons ("Coordination," 11-12).

35. Perle, Serial Composition, 59.

36. See the vector chart given in Hanson symbols in Clemmons ("Coordina- tion," 12).

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37. Perle, Serial Composition, 59.

38. Ward-Steinman, Serial Techniques, 44-45.

39. Perle, Serial Composition, 59, and Clemmons, "Coordination," 16-17.

40. Perle, Serial Composition, 49, and Clemmons, "Coordination," 17.

41. Ward-Steinman, Serial Techniques, 46.

42. Craft's catalogue of Stravinsky manuscripts concludes with the year 1952 (see White, Stravinsky, 599-618). Presumably the sketches for In Memo- riam are in his widow's possession.

43. This includes the Mass (1948), Cantata (1952), Canticum Sacrum (1956), Agon (1957), and Threni (1958).

44. The metronomic marking is J = 100 - 102 M.M.

45. See Friedrich Smend, Johann Sebastian Bach bei seinem Namengerufen (Kassel, 1950).

46. Karl Geiringer, "Symbolism in the Music of Bach" in Lectures on the His- tory and Art ofMusic (New York: Da Capo Press, 1968), 121-38.

47. Geiringer at the time was on the faculty of Boston University. However, the example cited had appeared earlier in an article by Martin Jansen, "Bachs Zahlensymbolik, an seinen Passionen untersucht," Bach-Jahrbuch 1937, 99.

48. Bach became the cantor at St. Thomas, Leipzig, in 1723. Bach's blindness

preceding his death parallels that of the poet's father.

49. See White, 482-83 concerning the "analogy between the five movements of the Canticum Sacrum and the five domes of St. Mark's."

50. Deuteronomy 5:22, Exodus 20:2-12 and 13-17 (appropriately the final footnote).

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