II CONCEPT SPACES II.3 (Thu Feb 08) Case study II (motifs): Reti

paradigmatic axis syntagmatic axis a b a‘ b‘ Roman Jakobson‘s poetical function: project paradigmatic axis onto syntagmatic axis

Some remarks on neutral analysis: Jean-Jacques Nattiez: Fondements d‘une sémiologie de la musique (Editions 1018, Paris 1975): definition of neutral niveau p. 54 Nicolas Ruwet: Langage, musique, poésie (Seuil, Paris 1972): distinction between synthetical (abstract rules -> concrete message) and analytical models (concrete message -> abstract rules) p. 100/133 What are the abstract rules of syntactial and paradigmatic articulations? Nattiez (loc. cit.): definition of Ruwet‘s paradigmatic theme on p. 264 Les unités paradigmatiquement associées sont équivalentes d’un point de vue donné (le thème paradigmatique), rarement identiques, et reliées entre elles par des transformations qui décrivent les variants par rapport à des invariants. Paradigmatically associated units are equivalent from a given point of view (the paradigmatic theme), rarely identical, and linked together by transformations that describe the variants in relation to invariants.

Reti‘s program of analytical motif theory: Rudolf Reti: The Thematic Process in Music (McMillan, New York 1951, repr. Greenwood, Westport 1978): Program is the analytical construction of a „germinal“ motif of a composition. Michael Kopfermann: Comments on Reti‘s approach. in: Robert Schumann (I,) II (H.-K. Metzger & R. Riehn eds.) edition text+kritik, Munich 1982. p. 297: construction of a germinal motif from an immanent analysis. Example: Kinderszenen, p. 276.

Precise concepts?? In general, the author does not believe in the possibility or even desirability of enforcing strict musical definitions. Musical phenomena come to existence in the constant fluency and motion of compositional creation. Therefore any descriptions of them must finally prove but approximations. It is for this very reason that in the course of this analysis it was considered more useful to cling as far as possible to the familiar expressions, and to apply them even in instances when their accuracy could be debated, rather than to invent new terms. [Reti, p.12]

Germinal motif We call a motif any musical element, be it a melodic phrase or fragment or even only a rhythmical or dynamical feature which, by being constantly repeated and varied throughout a work or a section, assumes a role in the compositional design somewhat similar to that of a motif in the fine arts. [Reti, pp.11-12] Theme A theme, then, could be defined as a fuller (compared to a motif ) group or “period” which acquires a “motivic” function in a composition’s course. [Reti, pp.12]

Shape/abstraction Similar liberties were taken in our analysis on several other occasions...by rearranging the design..., by exchanging the octaves in which some phrases were notated in the score. [Reti, p.243]. He (the classical composer) strives toward homogeneity in the inner essence... toward variety in the outer appearance. Therefore he changes the surface but maintains the substance of his shapes... Tempo, rhythm, melodic detail, in fact the whole character and mood are altered and adjusted to the form in which the composer conceived them fitting to the new movement. [Reti, pp.13-14]

Shape imitations, variations, transformations, indirect affinity imitation, that is literal repetition of shapes, either directly or by inversion, reversion, and so forth; varying, that is, changing of shapes in a slight, well traceable manner; transformation, that is, creating essentially new shapes, though preserving the original substance; indirect affinity, that is, creating an affinity between independent shapes through contributory features. Between imitation and nonrelationship lies a whole complex of features comprising all degrees of structural relationship. Varying, that is, altered repetition, is gradually intensified until it becomes transformation, which forms the central, the most concentrated expression of the thematic phenomenon. [Reti, p.240]

Reti‘s critical identity concept ...his (Beethoven’s) most impressive thematic constructions lie on the border line between being matchless master strokes of transformation or utterances wherein the thematic bond has almost dissolved in that very transformating process by which they were created. [Reti, p.355]. To Reti, the identity of a motif can be brought to a limit by its transformations. But then identity is not a transitive relation („A identical with B“ and „B identical with C“ should imply „A identical with C“)

Make Reti‘s approach precise! (Despite critical comments by Jonathan Dunsby, Geraint A. Wiggins et al. at ISMIR 2002 conference on Music Information Retrieval, IRCAM/Paris)

Submotiv Existence Axiom (SEA) property “... sequence of notes...” A motif is a set of notes having onset and pitch and... (without specifying their order) with different onsets for different notes. Definitions of the motif space MOT(S) in parameter space for composition S. Submotiv Existence Axiom (SEA) property Yes! No! Onset Pitch

Soprano voice in „Träumerei“, selection by Bruno Repp, for S take all 28 Repp motives plus submotives of 2 or more notes -> 1,483 motives for S take all motives plus submotives of 2 - 10 notes & span 2 bars -> 237,736 motives for S take all motives of whole composition plus submotives of 2 - 10 notes & span 1 bar -> 711,198 motives

“... whose shape(s)....” different contours (abstract motives)

COM shape type; Kunst der Fuge, main eight-note theme “... whose shape(s)....” COM shape type; Kunst der Fuge, main eight-note theme Motif1 Motif2 COM(Motif1) COM(Motif2)

India, Dia, and Elast types: “... whose shape(s)....” India, Dia, and Elast types: India = sequence of signs +1,0,-1 for consecutive notes Dia = sequence of pitch differences for consecutive notes Elast = sequence of angles and relative lengths of intervals between consecutive notes: Elast

“... in the sense of imitation....” shift in onset time

COM “... in the sense of imitation....” paradigmatic group -> paradigmatic theme of Nattiez/Ruwet COM

“... in the sense of imitation....” paradigmatic group -> GESTALT = equivalence class under group Number of Motives and Gestalts of Kunst der Fuge‘s 8 Tone Main Theme

“... variation, transformation, or indirect affinity (of the first shape)...” similarity of motives: distance (-2,2,-2,-2) (2,2,-2,-2) (-1,1,-1,-2) (1,-1,1,0) (4,0,0,0)

“... variation, transformation, or indirect affinity (of the first shape)...”

“... variation, transformation, or indirect affinity (of the first shape)...” similarity of motives: similarity between submotives

“... variation, transformation, or indirect affinity (of the first shape)...”

“... is everywhere in the composition...“ presence content weight = presence x content presence content

“... is everywhere in the composition...“

“... is everywhere in the composition...“