1. V THREE COLLABORATIVE PILLARS
V.4 (We Apr 3) Gesture Theory (4)

2. g X body skeleton pitch Γ time position
Hugues de Saint-Victor (French theologist XIIth Century):
Gestus est motus et figuratio membrorum corporis, ad omnem agendi et habendi modum.
Gesture is the movement and figuration of the body‘s limbs proper to the achievement of all action and attitude.
body
skeleton
position
pitch
time X g Γ

3. Γ @X = topological space of gestures of directed graph Γ
= topological space of gestures of directed graph Γ in a topological space X 
Hypergestures!
„loop of loops “
knot
circle

5. Proposition (Escher Theorem)
Given a topological space X, a sequence of gesture skeleta
1 ,  2, ...  n
and a permutation  of 1, 2,... n.
Then there is a topological isomorphism
 ...    ... 
„The skeleta of hypergestures can be exchanged“ 
„a loop of lines = a line of loops“ 

6. convex concave

7. belvedere

8. cycle

9. Look differnetly at spaces
Look differnetly at spaces! Take points as being affine homomorphisms from the zero space A=0. Here is the generic notation and visualization: Apoint is an A-parametrized set of points in F.

10. Look at LvB/op. 106/Allegro Fanfare to Understand Rhythm Here!
1/8

11. repetition of halting gesture
halting of repetition gesture
halting gesture
repetition gesture

12. David Lewin’s characteristic gesture
Turn this Abstract Logic into a Gestural Movement
Solution: Complexification + Deformation
David Lewin’s characteristic gesture “ i—  
Complexification exchanges duration/onset ~ repetition/halting!

13. h g k
Comprendre est
attraper le geste et
pouvoir continuer.

14. gesture morphisms: throwing gestures around y z x X g v u w Y  f

15.  y z x X g
Generating musical time s r t Z Σ g  v u w Y f

16. Heinz Spoerli‘s Zurich Opera Ballet 2006
Guerino Mazzola and
Heinz Spoerli‘s Zurich Opera Ballet 2006
Rebecca Lazier
VANISH 2002
More precisely, performance is a transformation P from the symbolic reality of the score to the physical reality of sounds (a quarter note is not determined in its physical duration, only the metronome yields the relation between symbolic reality and physical reality).
The mathematical analysis of tempo and pitch transformations shows that the performance transformation P can be described by a performance vector field, as shown to the left in the symbolic parameter space.
Essentially, performance is calculated via integration of such performance vector fields, much as the time is calculated via integration of the tempo curve.
In this language, performance operators are built in order to produce new performance fields from the old ones inherited from the relative mothers.

17. Rebecca Lazier: Vanish choreography (7 dancers) New York City 2002
for Arnold Schönberg‘s String Trio op. 45 (1946 after heart attack)
Paper: Making Schoenberg Dance
In: Sound Moves Proceedings of the Int. Conf. on Music and Dance, Roehampton Univ.

18. Lazier refers to Michael Cherlin‘s paper
Memory and Rhetorical Trope in Schoenberg‘s String Trio (J. Amer. Musicol. Soc. 1998, vol. 51, no. 3)
Schoenberg explained the many juxtapositions of unlike material within the Trio as reflections of the delirium which the composer suffered during parts of his illness. Thus, the seemingly fragmentary nature of the Trio‘s material represents the experience of time and events as perceived from a semiconscious or highly sedated state. These unusal juxtapositions also represent ... the alternate phases of „pain and suffering“ and „peace and repose“ that Schoenberg experienced.
(Schoenberg shared his illness experience with friends and students.)
distraction/imperfection

19. Cherlin‘s three levels of memory are hypergestural networks
musical world
memory ~ gestural movement
work
extramusical world
work
work

20. Teil 2 doze off
Episode 2 awaking

21. Parts
Duration in DVD
Bars in Score
Bars in Score for specific structures
choreographic structures
Teil 1
1:54
17:19-19:13
1-51
7 dancers‘ 12-tone rows for word sequence
near-death/transience/flight/hover/shiver/slide/ propel/crash/soar/fling/tender/explode
Episode 1
5:38
19:13-24:51
52-132
82-101
rhythmic structure solos
choreographer‘s phrase
Teil 2
3:27
24:51-28:18
catching phrase/partnering version
catching phrase/iuxtaposition against 12-tone phrases
catching phrase/idea structure
Episode 2
2:32
28:18-30:50
Ode to Lucinda, structure based on physical limitation
Teil 3
5:25
30:50-36:15
shortend form of m..51-> 24 (retrograde)
reprise Episode 1
catching phrase (Teil 2)
catching phrase deconstruction