A Theory for the Analysis of Spatial Music Derived from Stockhausen’s Lichter-Wasser.pdf
Transcript of A Theory for the Analysis of Spatial Music Derived from Stockhausen’s Lichter-Wasser.pdf
A Theory for the Analysis of Spatial MusicDerived from Stockhausen’s Lichter-Wasser ()
Proposal for (Los Angeles)
by Paul Miller Prince St., No. Rochester,
[email protected]( ) -
Graduate Student and Instructor of Music Theory,Eastman School of Music (University of Rochester)
A Theory for the Analysis of Spatial MusicDerived from Stockhausen’s Lichter-Wasser ()
Proposal for (Los Angeles)
Equipment required:Overhead Projector
A Theory for the Analysis of Spatial MusicDerived from Stockhausen’s Lichter-Wasser ()
Proposal for (Los Angeles)
Abstract. This paper proposes a new technique for the analysis of spatialized music by
using a recent work by Stockhausen, Lichter-Wasser, as a test bed. A tool called the motion
profile segment (MPSeg) is advanced to aid in the detection of spatial motives throughout the
work. Then, by generalizing the mathematical group properties of transformations in two
dimensions, we can relate spatial motives. These techniques can further our understanding of
the composer’s compositional strategies in the spatial domain, and may also be useful for other
spatialized works, especially those of Xenakis.
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A Theory for the Analysis of Spatial MusicDerived from Stockhausen’s Lichter-Wasser ()
Proposal for (Los Angeles)
Published analyses of Stockhausen’s music often focus on issues of formal design and
pitch. Analysts such as David Lewin, Jerome Kohl, Hermann Conen, Richard Toop, Imke
Misch, and the composer himself have all offered detailed analyses of Stockhausen’s methods
of compositional design and coherence. While these contributions offer compelling views of
Stockhausen’s compositional craft, only rarely do they expound upon the spatial aspects of the
music – and even then, not in a way that sheds much light on their internal structure. Yet,
since his early electronic works of the s, Stockhausen has consistently devoted a significant
amount of attention in his compositional process to spatialization.
On the other hand, Maria Harley’s extensive work suggests many fruitful ways of
analyzing spatialized music; but despite her valuable observations, she does not offer any
techniques for analysis. This investigation will demonstrate that transformation theory and
statistical methods can be used to analyze the spatial movements in a recent work by
Stockhausen, Lichter-Wasser (). These methods can be generalized so that they can apply
to other spatialized music.
Envisioned as the first part in the Sunday opera from the gigantic Licht cycle, Lichter-
Wasser employs a core ensemble of musicians. The musicians are divided into two
orchestras based on register, and are arranged in a geometric pattern throughout the audience
(Example 1). Over the course of the -minute work, two melodic lines (one assigned to each
orchestra) weave their way through the performance hall. Each musician plays a note or a
group of notes before handing their melody off to the next player. There are nearly ,
such movements in Lichter-Wasser.
We can analyze the spatial motion in Lichter-Wasser by detecting spatial motives, or
sequences of movements that recur (Examples 2a and 2b). These motives are related by
various transformations within the physical space that the piece occupies. For example, some
cardinality 3 motives that recur within orchestra 1 and orchestra 2 are related by rotation,
retrograde, transposition and flip operations (Examples 2c-2e). While the two counterpointed
melodies that wind through the piece exhibit individualized spatial motion (due to the different
spatial configuration of each orchestra), the methodology I employ finds motivic releationships
across orchestras as well (Example 2f). In my presentation I will show how the operations of
transposition, rotation, flip, and multiplication operate in a two-dimensional space, and how
motives related by these operations create spatial coherence in Lichter-Wasser.
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How can we decide which spatial motives are important, even when there are many
good candidates to choose from? By analyzing the speed of motion in Lichter-Wasser, we
can discern motivic activity by detecting a recurring contour in the rate of change of motion
that I call an “MPSeg” (motion profile segment). The speed of motion in meters per second
can be calculated throughout most of the work’s twelve main sections, since the positions
of the players in the hall are known, and Stockhausen’s painstaking method of notating
rhythmic durations allows us to determine the timing of each note with the utmost precision.
In Examples 3a and 3b, the rate of motion is charted for sections 1 and 11. (In the score,
Stockhausen refers to these sections as “waves”.) If we calculate the distance that the two
melodies traverse in the first section, we find that each moves about one kilometer in roughly
. minutes, for an average speed of . m/sec and . m/sec, respectively. While the motion
profile (MP) of the first section is highly irregular, the slow rate of motion allows us more easily
to perceive motives that do not recur frequently.
The eleventh section (lasting only about seconds,) moves far more distance in much
less time; its average rate of motion is approximately m/sec and m/sec for each orchestra
respectively (Example 3c). Although a higher rate of motion should make it more difficult
to discern motivic activity, an MPSeg in the graph of the eleventh section recurs throughout
(indicated by horizontal brackets in Example 3b). While the eleventh section exhibits a far
higher density of spatial motives than the earlier section (Examples 4a, 4b), our hearing can
be guided by motives that create recurring MPSegs. Thus, even though the rate of motion
in the eleventh section is roughly eight times faster than the first section and there is greater
motivic saturation, there is still spatial coherence. Using this method to explore the other
sections of Lichter-Wasser will allow us to see how various sections of the work employ different
compositional strategies in the spatial domain.
These techniques of analyzing Lichter-Wasser suggest broader application to works that
are spatialized in different ways, especially Xenakis’s Terretektorh and Nomos Gamma. The
paper proposed herein will use these methods to investigate the spatial design of Lichter-Wasser
more completely. Then I will set the stage for looking at other kinds of spatialized music
in a more analytically fruitful way by generalizing the mathematical group properties of the
four basic operations of transposition, rotation, flip and multiplication in a two-dimensional
space.
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References
Brant, Henry (). “Space as an Essential Aspect of Musical Composition.” In Contemporary Composers on Contemporary Music, ed. Elliott Schwartz, Barney Childs. New York: Da Capo Press.
Coenen, Alcedo (). “Stockhausen’s Paradigm: A Survey of His Theories.” Perspectives of New Music ⁄: -.
Conen, Hermann (). Formel-Komposition: Zu Karlheinz Stockhausens Musik der siebziger Jahre. Mainz: Schott.
Harley, Maria Anna (). Space and Spatialization in Contemporary Music History and Analysis, Ideas and Implementations. Ph. D. Dissertation, McGill University.
---------- (). “Musique, Espace et Spatialisation: Entretien de Iannis Xenakis avec Maria Harley.” Circuit. Revue Nord-Americaine de Musique du XXe Siecle ⁄: -.
Kohl, Jerome (). “Into the Middleground: Formal Syntax in Stockhausen’s Licht.” Perspectives of New Music ⁄: -.
Lewin, David (). “Making and Using a Pcset Network for Stockhausen’s Klavierstück III .” In Musical Form and Transformation: Four Analytic Essays. New Haven: Yale University Press.
---------- (). Generalized Musical Intervals and Transformations. New Haven: Yale University Press.
Misch, Imke (). “On the Serial Shaping of Stockhausen’s Gruppen für drei Orchester.” Perspectives of New Music ⁄: -.
Stockhausen, Karlheinz (). Composition Course on Lichter-Wasser. Kürten: Stockhausen Verlag.
---------- (). “Music in Space.” Trans. Ruth Koenig, in Die Reihe vol. . Pennsylvania: Presser.
Toop, Richard (). Six Lectures from the Stockhausen Courses Kürten . Kürten: Stockhausen Verlag.
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
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1
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V5 F2 P1 V3 Fa1
B Sax
Va5 Eh F1
T1 Va1
K Va3 Fa2 Va2 P2
H1
T V1
V2 T2
Va4 Eu
Ob V4 H2 Kb Tu
30 m
eter
s
27 meters
(1, 4) (26, 4)(7.25, 4) (13.5, 4) (19.75, 4)
(1, 29)(7.25, 29) (13.5, 29) (19.75, 29)
(26, 29)
(1, 10.25)
(1, 16.5)
(1, 22.75) (26, 22.75)
(26, 16.5)
(26, 10.25)(13.5, 10.25)
(13.5, 16.5)
(13.5, 22.75)
(7.25, 16.5) (19.75, 16.5)
(radius = 12.5 m
)
(9.08, 20.92) (17.92, 20.92)
(17.92, 12.08)(9.08, 12.08)
(4.66, 25.34)
(22.34, 25.34)
(22.34, 7.66)(4.66, 7.66)
conductormixing console synth.
V5F2P1V3Fa4BSaxVa5EhF1T1Va1KVa3Fa2Va2P2ThV1H1V2T2Va4EuObV4H2KbTu
1.00 29.007.25 29.00
13.50 29.0019.75 29.0026.00 29.00
4.66 25.3422.34 25.34
1.00 22.7513.50 22.7526.00 22.75
9.08 20.9217.92 20.92
1.00 16.507.25 16.50
13.50 16.5016.5016.50
19.7526.00
9.08 12.0817.92 12.08
1.00 10.2513.50 10.2526.00 10.25
4.66 7.6622.34 7.66
1.00 4.004.004.004.004.00
7.2513.5019.7526.00
Key
Coordinates of eachinstrument
violin 5flute 2
trombone 1violin 3
bassoon 4bass clarinet
saxophoneviola 5
english hornflute 1
trumpet 1viola 1
clarinetviola 3
bassoon 2viola 2
trombone 2tenor horn
violin 1horn 1
violin 2trumpet 2
viola 4euphonium
oboeviolin 4horn 2
e-flat clarinettuba
Example 1. Spatial Layout of Lichter-Wasser *
instrument abbreviation x-coord.
y-coord.
= instrument in orchestra 2
= instrument in orchestra 1
(radius = 6.25 m)
= location of a loudspeaker
* The hall in which the premiere took place measured 27 × 30 meters.
V5 P1 V3 Fa1
B Sax
Va5 Eh F1
T1 Va1
K Va3 Fa2 Va2 P2
H1
T V1
V2 T2
Va4 Eu
Ob V4 H2 Kb Tu
F2 V5 P1 V3 Fa1
B Sax
Va5 Eh F1
T1 Va1
K Va3 Fa2 Va2 P2
H1
T V1
V2 T2
Va4 Eu
Ob V4 H2 Kb Tu
F2
Example 2. Motivic Design of the 1st Section (”Wave”) in Lichter-Wasser
Example 2a. Motives that occur in Orchestra 1 Example 2b. Motives that occur in Orchestra 2
c
d
c
d
Example 2c. Relationship of motives a and b
Example 2d. Relationship of motives c and d
Example 2e.Relationship of motives e and f
Example 2f.Relationship of motives a and c
c
[transpose(6.25,-6.25)][rot(180)]a = b [retrograde]c = d or [flip(vertical)]c = d
or
[flip(horizontal)][rot(180)]c = d
[transpose(0, -12.5)][retrograde][flip(horizontal)]e = f
[mult(2)][rot(315)][transpose(4.4, 8.1)]a = c(The order of operations is always from right
to left.)
a
b
e
f
a
b
e
f
a
Example 3a. Rate of Motion or Motion Profile in the 1st Section (”Wave”) of Lichter-Wasser
0 50 100 150 200
0
5
10
15
20
25
30
35
25 75 125 175 213
rate
of m
otio
n (m
eter
s per
seco
nd)
elapsed time (seconds)
Orchestra 1
Orchestra 2
Total Distance Traversed
Number of Movements
Average Speed
Orchestra 1 Orchestra 2
801 m
105
3.8 m/sec
1061 m
100
5.0 m/sec
Example 3b. Rate of Motion or Motion Profile in the 11th Section (”Wave”) of Lichter-Wasser *
0 10 20 30 40 50
0
50
100
150
200
rate
of m
otio
n (m
eter
s per
seco
nd)
elapsed time (seconds)
5 15 25 35 45
Orchestra 1 Orchestra 2
1794 m
210
37 m/sec
1687 m
165
34 m/sec
Key
Example 3c. Comparisonof the Rate of Motionin Sections 1 and 11of Lichter-Wasser
Section 1 (213 seconds) Section 11 (49 seconds)
*brackets indicate a recurring motion profile segment
Approx. Rate of Movement .5 moves/sec .5 moves/sec 4 moves/sec 3 moves/sec
Example 4a. Frequency of Cardinality 3 Motives in the 1st Section (”Wave”) of Lichter-Wasser
Example 4b. Frequency of Cardinality 3 Motives in the 11th Section (”Wave”) of Lichter-Wasser
Orchestra 1 Orchestra 2
eh à t1 à va3v2 à v1 à va2
f1 à v2 à kv3 à eh à t1va5 à k à va3t1 à va3 à thk à va3 à bk à ob à v4va3 à th à v2va2 à va1 à ehth à v2 à v1v1 à va2 à va1t2 à f1 à v3ob à v4 à kbv4 à kb à t2kb à t2 à f1
33
22222222222222
p1 à sax à fa1fa1 à p2 à tub à p1 à saxb à va5 à h1sax à p1 à bsax à fa1 à p2p2 à th à eueu à fa2 à btu à eu à fa2
p1 à b à va5fa1 à sax à p1va5 à h1 à va4va3 à th à va4fa2 à b à va5h1 à va4 à h2va4 à h2 à fa2eu à tu à p2h2 à fa2 à eutu à p2 à eu
333333333
2222222222
Orchestra 1
v1 à va2 à va1
v3 à f2 à v5f1 à v3 à f2va3 à v2 à kbva2 à va1 à ehv2 à kb à t2t2 à f1 à v3v4 à v1 à va2kb à t2 à f1
v5 à k à obf2 à v5 à kk à ob à v4ob à v4 à v1
eh à t1 à va3t1 à va3 à v2va1 à eh à t1
eh à va3 à v2va1 à eh à va3
14
1313131313131313
12121212
111111
22
eu à h2 à p1h2 à p1 à btu à eu à h2
fa1 à p2 à tusax à fa1 à p2va5 à h1 à va4fa2 à sax à fa1p2 à tu à euth à fa2 à saxh1 à va4 à thva4 à th à fa2
p1 à b à va5b à va5 à h1
p1 à b à v5b à v5 à va5
v5 à va5 à h1fa1 à th à tuva5 à h1 à fa1th à tu à euh1 à fa1 à th
131313
1111111111111111
1010
33
22222
Orchestra 2
frequency motive frequency motive
frequency motive frequency motive