Increasing 
the 
mobility 
of 
Stockhausen’s 
Mobile 
Scores
 Stockhausen
 compositions
 pioneered
 a
 wide
 range
 of
 the
 innovatve
 techniques
 that
 have
 come
 to
 be
 associate
d with
 the
 Avant
 Garde
 Period.
 In
 the
 exploration
 of
 formal
 structure
 and 
the 
means 
of 
presenting 
work 
to 
performers
via 
novel 
media, 
Stockhausen
 was 
one
 of 
the 
key
contributors
 during
 this time.

 These 
innovations 
included:
 • 
The
“mobile”
score
 • 
The
“transformative”
score
 • 
Intuitive
music
 Despite
 the 
fact
 that 
Stockhausen 
lived 
well 
into
 the 
first
decade
 of
 the 
21st
 century,
all
 of
 his 
works 
rely
on 
the
traditional 
notion 
of
 a
 printed 
paper 
score.
 This
 discussion
 explores
 the
 technical
 and
 practical
 possibilities
 of
 adapting
 the
 innovative
 printed
 scores
 by
 Stockhausen
 through
 the
 use
 of
 computer
 technology.
 The
 technological
 recasting
 of
 these
 works
 is
 considered
 in
 light
 of
 Stockhausen’s
 own
 aesthetic 
statements
concerning 
the 
necessity 
to
 comprehend 
the
“uniqueness”
of 
works
 which
were
 born
 to 
a
 particular 
historical 
moment.


1. Increasing the mobility of Stockhausen’s
Mobile Scores
Lindsay Vickery
Lecturer in Music,
WAAPA,
Edith Cowan University 2010

2. Increasing the mobility of Stockhausen’s Mobile Scores
Stockhausen composi0ons pioneered a wide range of the innova0ve techniques that
have come to be associate with the Avant Garde Period. In the explora0on of formal
structure and the means of presen0ng work to performers via novel media, Stockhausen
was one of the key contributors during this 0me.
These innova0ons included:
• The “mobile” score
• The “transforma0ve” score
• Intui0ve music
Despite the fact that Stockhausen lived well into the first decade of the 21st century, all of
his works rely on the tradi0onal no0on of a printed paper score.
This discussion explores the technical and prac0cal possibili0es of adap0ng the
innova0ve printed scores by Stockhausen through the use of computer technology. The
technological recas0ng of these works is considered in light of Stockhausen’s own
aesthe0c statements concerning the necessity to comprehend the “uniqueness” of works
which were born to a par0cular historical moment.

3. The Mobile Score
The Mobile score aimed to
liberate the music score from the
manacles of leL‐right/up‐down
orienta0on. The idea evolved,
both in music and across a range
of art forms in the mid‐twen0eth
century, all sharing a common
impetus to generate the
opportunity for mul0ple readings
defined by the individual.
The element that is mobile in a
mobile score and liberated is the
Performers In the mobile score,
the final ordering and distribu0on
of notated musical events is
deferred by the composer un0l
the performance.

4. The Mobile Score: Precursors
(Henry Cowell’s Mosaic String Quartet 1935) was
an early example of the flexible form. (Rischitelli
2005 p. 102‐3)
The first Mobile score Morton Feldman:
Intermission 6 (1953). (Right)
Stockhausen’s first work in this medium was
Klavierstück XI (1956). He developed these ideas to
encompass two different kinds of Mobile Score. His
term for this structure was “Polyvalent Music”.
(Coenen 1994 p. 218).
Single Page Mobile Score: Notated Elements are
separated by space and distributed across the
page.
MulIple Page Mobile Score: Notated Elements
separated by page and assembled into an order –
usually prior to the concert.

5. Moment Form
Stockhausen proposed a novel formal structure to account for this approach which he
called Moment Form.
A Moment is
a formal unit in a par0cular composi0on that is recognizable by a personal and
unmistakable character. Depending on their characteris0cs, they can be as long or
as short as you like" (Stockhausen 1963 p. 200)
A related technique he developed simultaneously was the “Einschub” (Insert): the
interpola0on of material that has already been heard (memory) or of what will be
heard (premoni0on).
The whole Einschub 'insert' technique is based directly on the overwhelming
experience of inner sound visions which are stronger than your own will... On the
other hand, you are an engineer, you do mental work, and there is some0mes a
conflict between the two: you have overall visions, images which make demands
of a kind you cannot yet realize, and they lead to the inven0on of new technical
processes, but then the technical processes go their own way and become the
star0ng point for other techniques which in turn provoke new inven0ons and you
find yourself bombarded with images again.”
(Stockhausen and Maconie 1988 pp. 135‐6)

6. Stockhausen’s Momente (1962‐69)
Stockhausen expects the performer to vary the order of movements at will, and even
provides for passages from one movement to be inserted into its neighbors. For each
concert the score may be re‐arranged, in accordance with certain instruc0ons; the
extracts or "inserts" may be glued into certain slits in the score, and their dura0on and
volume are varied depending on the context, as indicated by a long list of rules on each
sheet. Then the parts are prepared in whatever order has been selected for the
par0cular concert.
(McElheran 1965 p. 37)

7. The TransformaIve Score
In the transforma0ve score stable materials are “acted upon” by mobile
transforma0ve procedures. Stockhausen referred to this approach as
“Variable” Form. (Coenen 1994 p. 218).
Stockhausen’s first (and only) work
exploring this technique was Refrain
(1959). In the score the staves are laid
out in a circular arrangement and a
transparent plas0c “refrain” ‐ comprising
a range of ornaments and modifica0ons
that “act upon” the materials that they
overlay ‐ is pinned into the centre of the
page allowing it to be swung into
different orienta0ons in rely0on to the
page.

8. The TransformaIve Score
Stockhausen also created transforma0ve scores that are not variable in form‐ the so‐
called “plus‐minus” composi0ons. In these works rather than stable materials that are
acted upon by mobile transforma0on, here its is the transforma0on that is stable and
the materials that are variable – provided either by chance (from a shortwave radio for
example) or impulses that are improvised by the performer.

9. Stockhausen’s Poles (1969)

10. IntuiIve Music
"It is no longer sufficient to expand the musical work - the opus - to a process, to a
growing, self-transforming thing which unfolds at every moment, in the Here and Now;
we have realized instead that the multitude of discoverable processes also leads to yet
more basic, higher powers of formation that are in fact superrational, intuitive in
origin.”
Stockhausen described this approach as:
Opening one's mind in order to receive more vibrations from the universe than one
normally does. (Coenen 1994 pp. 210‐211)
There’s a story of a second violin player who
said, “Herr Stockhausen, how will I know when
I am playing in the rhythm of the universe?”
Stockhausen said, with a smile, “I will tell you.”
(Anthony Pay in Bailey 1992 p. 72)

11. IntuiIve Music
"It is no longer sufficient to expand the musical work - the opus - to a process, to a
growing, self-transforming thing which unfolds at every moment, in the Here and Now;
we have realized instead that the multitude of discoverable processes also leads to
yet more basic, higher powers of formation that are in fact superrational, intuitive in
origin.”
“From the Seven Days” (1969)

12. Stockhausen’s Adieu (1966) was one of the steps on the
path to Intui0ve music. It is unusual in Stockhausen’s
output for several reasons: it contains notated tonal
fragments in a quasi‐”Classical” style, it
juxtaposes these fragments with
text‐based instruc0ons that create
“sound‐mass” style improvisa0ons
from the performers.

13. Mobile Score TransformaIve Scrolling Score Text Score
Polyvalent/Moment Variable Transforma0on Intui0ve
1956 KLAVIERSTÜCK XI
1958 KONTAKTE
1959 ZYKLUS REFRAIN
1962‐4 MOMENTE
1963 PLUS‐MINUS
1964
MIXTUR and
MIKROPHONIE I
1965 MIKROPHONIE II
1965 STOP
1966 SOLO ADIEU
1967 PROZESSION
1968 STIMMUNG SPIRAL
1969 POLE and EXPO

14. Actually Mobile Mobile Scores
The implementation of mobile scores in a computer-based hypertextual
medium may provide a more “natural” vehicle for their performance by:
• creating a more practical, pragmatic medium for presenting
information to the performer;
• preventing performers from preparing a fixed order of the work’s
materials;
• allowing the choice of nonlinear materials based on aleatoric or other
procedures;
• reducing the need for unnecessary cues that create a non-musical
distraction to the performers and/or the performance.

15. Technology and ideology are inextricably intertwined…
what we are dealing with here is yet another example of
the well-known phenomenon of the old artistic forms
pushing against their own boundaries and using
procedures which, at least from our retrospective view,
seem to point towards a new technology that will be able
to serve as a more “natural” and appropriate “objective
correlative” to the life-experience the old forms
endeavoured to render by means of their “excessive”
experiments.
Zizek, S., 2000. The Art of the Ridiculous Sublime.
Seattle: University of Washington Press. p. 39

16. Karlheinz Stockhausen: Klavierstück XI
At the end of the first group, the performer reads the
tempo, dynamic and aoacks indica0ons that follow,
and looks at random to any other group, which he
then plays in accordance with the laoer indica0ons.
As a result the average length
of performances of this work
is normally between 20 and 39
segments. The number of
recordings required to make
computer version of the work
is 192 (361).

17. In the case of a paper score however, involuntary choice is the most pragmatic
solution for achieving an aleatoric order of groups. Stockhausen’s stated
motivation for this instruction is ‘that the performer will never link up expressly
chosen groups or intentionally leave out others. Each group can be joined to any
of the other eighteen’

18. Karlheinz Stockhausen: Klavierstück XI Scoreplayer

19. Stockhausen’s MIXTUR (1964)

21. I II
1 Mixtur 1 or 5 1 High C 1 or 6
2 Percussion 2 2 Pizzicato 2
3 Blocks 3 or 15 3 Layers 3
4 Direction 4 4 Dialogue 4
5 Change 5 , 14/15 5 Steps 5
6 Calmness 6 6 Concert pitch 6, 18 or 1
7 Vertical 7 7 Brass 6, 16
8 Strings 8 8 Tutti 8
9 Points 9 9 Translation 9
10 Wood 10 10 Mirror 10, 5
11 Mirror 11 or 16 11 Wood 11
12 Translation 12 12 Points 12
13 Tutti 13 13 Strings 13
14 Brass 14 or 5 14 Vertical 14
15 Concert pitch 15 , 3 or 20 15 Calmness 15
16 Steps 16 16 Change 16, 7/6
17 Dialogue 17 17 Direction 17
18 Layers 18 18 Blocks 18, 6
19 Pizzicato 19 19 Percussion 19
20 High C 20 or 15 20 Mixtur 10 or 16
I II
1 Mixtur 1 or 5 1 High C 1 or 6
2 Percussion 2 2 Pizzicato 2
3 Blocks 3 or 15 3 Layers 3
4 Direction 4 4 Dialogue 4
5 Change 5 , 14/15 5 Steps 5
6 Calmness 6 6 Concert pitch 6, 18 or 1
7 Vertical 7 7 Brass 6, 16
8 Strings 8 8 Tutti 8
9 Points 9 9 Translation 9
10 Wood 10 10 Mirror 10, 5
11 Mirror 11 or 16 11 Wood 11
12 Translation 12 12 Points 12
13 Tutti 13 13 Strings 13
14 Brass 14 or 5 14 Vertical 14
15 Concert pitch 15 , 3 or 20 15 Calmness 15
16 Steps 16 16 Change 16, 7/6
17 Dialogue 17 17 Direction 17
18 Layers 18 18 Blocks 18, 6
19 Pizzicato 19 19 Percussion 19
20 High C 20 or 15 20 Mixtur 10 or 16

22. PERC. I
CONDUCTOR
PERC. II PERC. IIII
Woodwind Brass Strings Pizz. Str
Screen 1
Screen 2 Screen 3
Screen 4
Screen 7
Screen 6
Screen 5
Performance set‐up for MIXTUR using networked computers to project the
scores synchronously on 6 screens. Such a method could also automate the
electronic component (Ring‐modula0on of the acous0c instruments) and
perhaps also the conductor via click‐tracks.

23. Stockhausen’s Adieu (1966) ProporIons
In many of Stockhausen’s works he employs the Fibonacci series to govern the temporal
propor0ons.
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/!",
! " # $ % !# "! #& $$ %' !&& *#012345#647815
Fibonacci Series Propor0ons in Stockhausen’s Adieu
(Diagram from Kramer 1988 p. 315)
Kramer claims Fibonacci propor0ons to be perceivable and predictable (Kramer 1988 p.
315). In 1990, Clarke and Krumhansl tested this claim and indeed found that “the
listeners were quite veridical in judging the rela0ve dura0ons of the segments” (Clarke, E.
F., Perceiving Musical Time, Music Percep0on, 7:3 p. 236).

24. Stockhausen’s Adieu (1966) ScorePlayer

25. Stockhausen’s Refrain (1959)
The manipula0on of a transforma0ve
overlay is a rela0vely trivial maoer in the
digital domain.

26. Stockhausen’s Refrain (1959)

27. Stockhausen’s Refrain (1959)

28. Stockhausen’s Refrain (1959)

29. Stockhausen’s Refrain (1959)
Even though this opportunity was available
during Stockhausen’s life0me, he did not
take advantage of it himself. In fact, in 2003
he releasde a new version of this piece
with the the overlay fixed in only two
posi0ons.

30. Stockhausen’s Poles (1969)
One of the performa0ve issues with the Plus‐minus composi0ons is the “alien” quality of
their nota0on. The score for Poles requires two pages of explanatory notes and then
refers the performer to a further 11 pages of notes and exemplar realisa0ons of the work
Spiral, in order to understand the nota0on.

32. Stockhausen took the conserva0ve view:
It's extremely important to comprehend works, which were born to a
parGcular historical moment, for their uniqueness… it is my experience of
music that every instrument, every item of equipment, every technique
can produce something unique, which can be achieved in no other way.
Since that is the case, then we can speak of an original technique, and
thus deal with an original instrument.
Simon Emmerson takes a more pragma0c view.
But are we aiming at ‘authenGcity’? Once we embark on such an
enterprise, the regress is infinite. Must we demand original instruments
and original performance pracGce on these instruments? The composer’s
original intenGons may not be inscribed in any single document, in any
medium. The same arguments apply here as in the endless debates on
‘early music interpretaGon’ – except we (may) have the recorded medium
to help us.
The “authen0c instruments” debate in electronic music.

33. Proposed solu0ons to the realisa0on of paper‐based mobile scores:
• Dynamic, mobile, screen‐based nonlinear or scrolling score;
• Use of visual synchroniza0on methods such as on‐screen 0mers or
metronomes;
• Use of computer controlled click‐tracks to synchronise and transmit
formal or other musical parameters;
• The centraliza0on of the score, sound‐file playback, synchroniza0on and
electronic sound processing.
• The bundling of performance materials, score sound‐files, electronics
and means of synchronisa0on into a single unit.

34. Proposed reasons for the realisa0on of paper‐based mobile scores on
computer:
• Convenience and portability
• Beoer realisa0on of the Composer's inten0on
• Real randomness/explora0on of permuta0on
• Performer can't prepare in advance (cheat)
• Representa0on of con0nuous transforma0on
• Coordina0on temporal propor0ons
• Avoidance of fixity and repe00on
• Score and recordings for teaching purposes

35. Technological “upgrades” to mobile form works could be considered in the
following circumstances:
• the work can s0ll be performed according to the composer’s
inten0ons
• the original work would operate more “naturally” within a
contemporary medium that was not available at the 0me of
composi0on.
• the “upgrade” significantly improves the performing situa0on, for
example: facilita0ng more accurate performance or improving the
logis0cal requirements for the work.