Integrating Segmentation and Similarity in Melodic Analysis Weyde: Segmentation & Similarity in Melodic Analysis Presentation by Brian Harlan Integrating Segmentation and Similarity in Melodic Analysis Projects: Medieval Notation, Ear-Training Software Tillman Weyde ISE 599: Spring 2004

Integrated Segmentation and Similarity Model Weyde: Segmentation & Similarity in Melodic Analysis Presentation by Brian Harlan Integrated Segmentation and Similarity Model An analytical model for recognizing melodic structure Integrates knowledge from music theory and empirical studies with system optimization by experimental data Generates all possible structural “interpretations,” and rates them in order to select the most adequate one The interpretations generated can be useful for music retrieval, music tutorials, and interactive music production tools An extension of the system for rhythmic analysis Computes and graphically displays results “Experts” can add to interpretations with a graphical user interface ISE 599: Spring 2004

Integrated Segmentation and Similarity Model The recognition of melodic structure depends on both segmentation and similarity Segmenting the melody into structural units (perceptual groups): Motifs [Motives] Recognizing relations between motifs; determined by similarity Segmentation and Similarity are inter-related, and a coherent computational model of melodic structure must integrate both aspects Segmentation is influenced by the similarity relations of motifs in a melody Similarity relations depend on how a melody is segmented

Weyde: Segmentation & Similarity in Melodic Analysis Presentation by Brian Harlan Motif [Motive] A musical idea either rhythmic, melodic, harmonic, or any combination of these three may be as short as 2 notes, or long enough to consist of smaller units (also motifs, or cells) has a distinct identity A basic structural unit, which can be processed can be sequenced, elaborated, or transformed (figuration) often used in modulating passages to retain the melodic integrity Classical development sections are typically built from motifs introduced earlier in the piece Used to support or contribute to musical narratives (Leitmotif) Motives can even create entire works. ISE 599: Spring 2004

Weyde: Segmentation & Similarity in Melodic Analysis Presentation by Brian Harlan Motif [Motive] 3 motifs from Beethoven’s Pastoral Symphony [no. 6, in F Major, op. 68, 1808] Motives 2 and 3 can be said to be a reversal of rhythmic elements ISE 599: Spring 2004

Interpretation Ratings Weyde: Segmentation & Similarity in Melodic Analysis Presentation by Brian Harlan Interpretation Ratings Interpretation Ratings are essential to the output of ISSM The “quality” of each interpretation is determined by placing values on Segmentation and Similarity features Segmentation features include: number of notes, duration of motifs, and pitch intervals at motif “boundaries” Similarity features include: pitch, tempo, loudness, and contour Segmentation Features correspond to the Gestalt Law of Proximity [events in close proximity are perceived as belonging to a unit] Why is this 2 motives, and not 1? ISE 599: Spring 2004

Interpretation Ratings Weyde: Segmentation & Similarity in Melodic Analysis Presentation by Brian Harlan Interpretation Ratings Segmentation of the melody The ratios of average distance of the inner and outer intervals are calculated for each motif For the outer notes, the minimal distance of interval notes in the circle of fifths is calculated Fig. 3: Inner = 1 semitone average; Outer = 3.5 semitone average ISE 599: Spring 2004

Interpretation Ratings Weyde: Segmentation & Similarity in Melodic Analysis Presentation by Brian Harlan Interpretation Ratings Assignment of related motifs based on Similarity Global deviations and local deviations are rated separately similar to Paradigmatic Analysis (Nattiez): the assignments represent how motifs are interpreted by listeners as being either identical or similar to preceding motifs Interpretation of a simple melody Global and Local pitch differences a motives ‘a’ and ‘b’ Jean-Jaques Nattiez, “Music and Discourse: Toward a Semiology of Music (1990). “All recurrent events belong to a Paradigm. Each unit is a “sign” held in relation to other signs without the connotation of meaning. Semiology: Ferdinand de Saussure’s study of language [sign, signifyer, signified] There is no intrinsic relationship between signifyer (e.g. “chair”) and signified (concept of “chair”) Musical semiotics can either be structuralist (Natteiz) or referential (Leonard Meyer) Nattiez seperates music into 3 domains: Poietic (composer), Neutral (score), and Aesthetic (listener). He focuses on the Neutral. ISE 599: Spring 2004

Interpretation Ratings Weyde: Segmentation & Similarity in Melodic Analysis Presentation by Brian Harlan Interpretation Ratings Rating all possible interpretations is computationally inefficient because the possibilities grow exponentially with melody length, therefore: A limited context of up to 10 notes is used “Perceptually motivated constraints” are used to prevent implausible interpretations (Lerdahl and Jackendoff) Calculation of the overall rating is done by a neural net defined by fuzzy rules [“neuro-fuzzy system”] and extended with a list processing features Each connection of neurons corresponds to a fuzzy rule Allows integration of prior knowledge with learning from data Lerdahl and Jackendoff, “A Generative Theory of Tonal Music”: Theory of tonal music derived from generative linguistics. (Chomsky and Schenker) Surface and deep level structures. “Grouping Structure = basic component of musical “understanding” expressed hierarchically (motive, phrase, section, etc.). This is perceived at a deep level--unlike metrical structure, which is perceived on the surface level. ISE 599: Spring 2004

Learning from Data ISSM learns from interpretation examples and uses these in an interactive training scheme Interpretive training generates relative samples whenever the system chooses an interpretation that differs from one provided by an “expert” The learning process changes the weights in the neural net

Weyde: Segmentation & Similarity in Melodic Analysis Presentation by Brian Harlan ISSM Modules Rates all possible interpretations Filters out according to constraints Calculates the overall rating Matches against adaptive system “Training” generated relative samples ISE 599: Spring 2004