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

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

3. 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.

4. 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 p. 297: construction of a germinal motif from an immanent analysis. Example: Kinderszenen, p. 276.

5. 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]

6. 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]

7. 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]

8. 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]

9. 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“)

10. 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)

11. 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

12. 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 notes & span 2 bars -> 237,736 motives
for S take all motives of whole composition plus submotives of notes & span 1 bar -> 711,198 motives

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

14. 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)

15. 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

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

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

18. “... 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

19. “... 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)

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

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

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

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

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

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