Transcript Integrating Segmentation and Similarity in Melodic Analysis Tillman Weyde

Integrating Segmentation and
Similarity in Melodic Analysis
Tillman Weyde
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
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
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)
Motif [Motive]
3 motifs from Beethoven’s Pastoral Symphony
[no. 6, in F Major, op. 68, 1808]
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
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
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 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
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
ISSM Modules