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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
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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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Stravinsky's In Memoriam Dylan Thomas
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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Stravinsky's In Memoriam Dylan Thomas 169
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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170 Perspectives of New Music
(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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Stravinsky's In Memoriam Dylan Thomas
"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
171
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Perspectives of New Music
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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Stravinsky's In Memoriam Dylan Thomas 173
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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Perspectives of New Music
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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Stravinsky's In Memoriam Dylan Thomas
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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Perspectives of New Music
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
176
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Stravinsky's In Memoriam Dylan Thomas
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
178
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Stravinsky's In Memoniam Dylan Thomas
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
179
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Perspectives of New Music
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
180
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Stravinsky's In Memoriam Dylan Thomas
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.
181
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Perspectives of New Music
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
182
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Stravinsky's In Memoriam Dylan Thomas
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
183
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Perspectives of New Music
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).
184
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Stravinsky's In Memoriam Dylan Thomas
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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Issue Table of ContentsPerspectives of New Music, Vol. 23, No. 2
(Spring - Summer, 1985), pp. 1-332Front Matter [pp. 1 -
111][Illustration]: Stephen Swaney: Untitled, 1983, Collage, 8 by 8
Inches [p. 11]Six Tanglewood Talks (1, 2, 3) [pp. 12 -
22][Illustration]: Mojuana Tolon: #50, 1980, Oil on Canvas, 54 by
42 Inches [p. 23]Stockhausen on Opera [pp. 24 - 39]Electronic Music
for Kathinka's Chant as Lucifer's Requiem [pp. 40 -
60][Illustration]: Francis Celentano: Alternate Curve of Isis in
Black and Orange, 1984, Acrylic on Plastic, 9 by 593/4 Inches [p.
61]Forum: Improvisation[Introduction] [p. 63]Language, Thought, and
the Talents of Species [pp. 64 - 70]
[Illustration]: Mojuana Tolon: Stairs #4, 1982, Graphite on
Paper, 19 by 12 Inches [p. 71]Forum: ImprovisationAre You Serious?
[pp. 72 - 88]
[Illustration]: Stephen Swaney: Untitled, 1983, Print, 8 by 8
Inches [p. 89]Forum: ImprovisationInterface Part I: Commentary: The
Barrytown Orchestra on Hunger Day November 15, 1984 [pp. 90 -
94]
[Illustration]: Lee Mueller: Ron Hook at Our Own Damn Gallery,
1981, India Ink Drawing, 9 by 6 Inches [p. 95]Forum:
ImprovisationImprovisatory Word Piece on a Tape by Ben Boretz &
J. K. Randall [pp. 96 - 100]
[Illustration]: Lee Mueller: Jazz Piano, 1983, India Ink
Drawing, 6 by 8 Inches [p. 101]Forum: ImprovisationThree
Texts[Untitled] [pp. 102 - 103]What [pp. 104 - 105]Sight, Sound and
Vision: Reflections on a Multimedia Experience [pp. 107 - 109]
In Memoriam Roger Sessions (1896-1985)I Remember Roger [pp. 112
- 116]Roger Sessions: A Reminiscence [pp. 117 - 118]Anton Webern in
a Dream [p. 119]Roger Sessions Admired [pp. 120 - 122]In Memoriam
R. H. S. [p. 123]Another Page from a Diary [pp. 124 - 130]Roger
Sessions at Berkeley: A Personal Reminiscence [pp. 131 - 138]Roger
Sessions Remembered [pp. 139 - 140]In Memoriam-Roger Sessions [p.
141][Untitled] [pp. 142 - 143]Momenti, for Piano Solo (1978) [pp.
144 - 146][Untitled] [p. 147]Remembering Roger [pp. 148 -
151]Studying with Roger [pp. 152 - 154]Roger Sessions Remembered
[pp. 155 - 158]Praeludium [p. 159]The Trial of Lucullus or A
Session with Sessions [pp. 160 - 161]Roger Sessions: In Memoriam
[pp. 162 - 164]Portrait of Roger Sessions [p. 165]
Structure and Numerology in Stravinsky's In Memoriam Dylan
Thomas [pp. 166 - 185]A Proliferation of Canons: Luigi
Dallapiccola's "Goethe Lieder No. 2" [pp. 186 - 195]Automated
Composition: An Installation at the 1985 International Exposition
in Tsukuba, Japan [pp. 196 - 215]Colloquy and ReviewRoger Sessions
and His Music: A Book Review [pp. 216 - 219]Musical Grammars and
Computer Analysis: A Review [pp. 220 - 234]
[Illustration]: Stephen Swaney: Untitled, 1983, Collage, 8 by 8
Inches [p. 235]Colloquy and Review1984 International Computer Music
Conference 19-23 October, Paris France [pp. 236 - 250]
[Illustration]: Stephen Swaney: Untitled, 1983, Collage, 8 by 8
Inches [p. 251]Colloquy and ReviewReport from Vancouver: 1985
International Computer Music Conference [pp. 252 - 265]Digicon 85
[pp. 266 - 272]
[Illustration]: Mojuana Tolon: #32, 1979, Oil on Canvas, 40 by
30 Inches [p. 273]Colloquy and ReviewDarmstadt 1984 [pp. 274 -
291]By the Time We Got to Phoenix: Report on the 1985 A. S. U. C.
National Conference [pp. 292 - 303]Letter to Michael Kowalski [pp.
304 - 309]Michael Kowalski Responds [p. 310]
[Illustration]: Mojuana Tolon: #72, 1982, Graphite on Paper, 21
by 12 Inches [p. 311]Editorial Notes [pp. 312 - 313]Correspondence
[p. 314]Back Matter [pp. 315 - 332]