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IIII STRUCTURE THEORY STRUCTURE THEORY

II.7 II.7 (Fr Feb 27) (Fr Feb 27) Initial Sets and Performances, Initial Sets and Performances, Performance Cells and HierarchiesPerformance Cells and Hierarchies

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y Performance fields for onset time, pitch, and loudnessPerformance fields for onset time, pitch, and loudness

EE ee

HH

hh

LL ll(E,H,L)(E,H,L) (e,h,l) = (e,h,l) = EH EH LL(E,H,L)(E,H,L)

EH EH LL

diagonal fielddiagonal fieldperformance fieldperformance field

??

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ee00 = e(E = e(E00))

EE00

Reconsider the Reconsider the one-dimensional case, Tempoone-dimensional case, Tempo

linear approximation around E

linear approximation around E 00

T(E) = 1/slopeT(E) = 1/slope

11ee11-- ee00

T(E). (eT(E). (e11-- ee00))

ee11

EE11

[sec.][sec.]

[[qq]]

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XXx x ==(x)(x)

= (1,1,…,1)= (1,1,…,1) = = Const.Const. xx0 0 == II(X(X00))

initial initial performanceperformance

x =x = (X) = x(X) = x00 t. t.

performance field performance field Z, Z, value at X = Z(X)value at X = Z(X)

XX0 0 ∈ ∈ I =I = initial setinitial set

curve curve ∫∫XX00ZZ of flow through of flow through XX00

∫∫XX00Z hits X at „time“ t:Z hits X at „time“ t:

X = X = ∫∫XX00Z(t)Z(t)

XX00 xx00FF

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y A A performance cell performance cell CC is a 5-tuple as follows: is a 5-tuple as follows:

• frame F = cube frame F = cube Parameterspace PParameterspace PEHL...,EHL...,

for set of symbolic parameters E, H, L,...for set of symbolic parameters E, H, L,...• a performance field Z, defined on Fa performance field Z, defined on F

• an an initial initial set I in frame F set I in frame F • a finite set of score events K a finite set of score events K F, le F, le symbolicsymbolic kernel, kernel,

such that each flow curve such that each flow curve ∫∫XXZ through X Z through X ∈ ∈ K meets IK meets I

• an an initial initial performance performance II::I I PPehl...,ehl..., of corresponding physical parametersof corresponding physical parameters

KK

II

FF

II

ZZ

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y Performance as a shifter sign (like Performance as a shifter sign (like II, , herehere, , nownow). ).

It is important to understand the deep meaning of initial It is important to understand the deep meaning of initial performance. We have known performance as a transitional performance. We have known performance as a transitional process from mental to physical reality. This is a transition process from mental to physical reality. This is a transition from the score to the acoustical realization, to be archived on from the score to the acoustical realization, to be archived on sound media such as a CD. Following the valid doctrine—as sound media such as a CD. Following the valid doctrine—as preconized by Paul Valpreconized by Paul Valééry and Theodor W. Adorno—the ry and Theodor W. Adorno—the performance is an integral part of the work of artperformance is an integral part of the work of art, and this , and this means that, in the sense of communication theory of art as means that, in the sense of communication theory of art as described by Jean Molino, performance is part of the semiosis described by Jean Molino, performance is part of the semiosis of the work, its meaning is not complete except when it is of the work, its meaning is not complete except when it is performed. performed.

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y Performance as a shifter sign (like Performance as a shifter sign (like II, , herehere, , nownow). ).

Put it the other way round: The mental score conveys a part Put it the other way round: The mental score conveys a part but not the whole content, and only via performance can we but not the whole content, and only via performance can we complete the work’s semiosis. Performance englobes a kind complete the work’s semiosis. Performance englobes a kind of usage of the mental score sign by a performer. More of usage of the mental score sign by a performer. More specifically, those signs whose content are not only specifically, those signs whose content are not only instantiated but substantially depend on the user are the well-instantiated but substantially depend on the user are the well-known shifters. Performance of a mental score is such a shift known shifters. Performance of a mental score is such a shift from lexicality to full-fledged meaning, since the pure score from lexicality to full-fledged meaning, since the pure score is essentially less than the work of art. In other words, is essentially less than the work of art. In other words, performance is a shifter characteristic of the score semantics. performance is a shifter characteristic of the score semantics.

Production of full-fledged meaning is only possible by means Production of full-fledged meaning is only possible by means of performance, and this adds a semantic aspect to the sign of performance, and this adds a semantic aspect to the sign

which is a non-trivial function of the performer(s).which is a non-trivial function of the performer(s).

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y Sergiu Celibidache

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sourcesource

fundamentfundament

To model To model piano performancepiano performance, one works with , one works with the basis parameters E, H, L, the basis parameters E, H, L, and corresponding fields T(E), S(H), I(L)and corresponding fields T(E), S(H), I(L)duration parameter D (pianola) duration parameter D (pianola)

The The cellular piano hierarchycellular piano hierarchy is the following is the following diagram,diagram,where arrows mean that the target cell is independentwhere arrows mean that the target cell is independentof the other parameters in the start cell, like EH of the other parameters in the start cell, like EH E Efor tempo, etc. for tempo, etc.

TT

SS

III I ×× SS

T T ×× II

T T ×× SS

T T ×× SS

T T ×× II

T T ×× I I ×× SS

TT××II××SS

TT

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y To model To model violin performanceviolin performance, one works with , one works with

the basis parameters E, H,the basis parameters E, H,and corresponding fields T(E), S(H) (and corresponding fields T(E), S(H) (= I(H) here!!)= I(H) here!!)duration parameter D, duration parameter D, glissando parameter G,glissando parameter G,crescendo parameter C crescendo parameter C

CCellular violin hierarchy:ellular violin hierarchy: