Integrating Segmentation and Similarity in Melodic Analysis Tillman

Integrating Segmentation and Similarity in Melodic Analysis Tillman Weyde

Integrated Segmentation and Similarity Model An analytical model for recognizing melodic structure w Integrates knowledge from music theory and empirical studies with system optimization by experimental data w Generates all possible structural “interpretations, ” and rates them in order to select the most adequate one w The interpretations generated can be useful for music retrieval, music tutorials, and interactive music production tools

Integrated Segmentation and Similarity Model The recognition of melodic structure depends on both segmentation and similarity w Segmenting the melody into structural units (perceptual groups): Motifs [Motives] w 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 w Segmentation is influenced by the similarity relations of motifs in a melody w Similarity relations depend on how a melody is segmented

Motif [Motive] A musical idea w either rhythmic, melodic, harmonic, or any combination of these three w may be as short as 2 notes, or long enough to consist of smaller units (also motifs, or cells) w has a distinct identity A basic structural unit, which can be processed w can be sequenced, elaborated, or transformed (figuration) w often used in modulating passages to retain the melodic integrity w Classical development sections are typically built from motifs introduced earlier in the piece w Used to support or contribute to musical narratives (Leitmotif)

Motif [Motive] 3 motifs from Beethoven’s Pastoral Symphony [no. 6, in F Major, op. 68, 1808]

Interpretation Ratings are essential to the output of ISSM The “quality” of each interpretation is determined by placing values on Segmentation and Similarity features w Segmentation features include: number of notes, duration of motifs, and pitch intervals at motif “boundaries” w Similarity features include: pitch, tempo, loudness, and contour

Interpretation Ratings Segmentation of the melody w The ratios of average distance of the inner and outer intervals are calculated for each motif w For the outer notes, the minimal distance of interval notes in the circle of fifths is calculated

Interpretation Ratings Assignment of related motifs based on Similarity w Global deviations and local deviations are rated separately w similar to Paradigmatic Analysis (Nattiez): the assignments represent how motifs are interpreted by listeners as being either identical or similar to preceding motifs

Interpretation Ratings Rating all possible interpretations is computationally inefficient because the possibilities grow exponentially with melody length, therefore: w A limited context of up to 10 notes is used w “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 w Each connection of neurons corresponds to a fuzzy rule w Allows integration of prior knowledge with learning from data

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

ISSM Modules