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Melodic Similarity
MUMT 611, March 2005
Assignment 4
Paul Kolesnik
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Conceptual and Representational
Issues in Melodic Comparison

(Selfridge-Field)
 Melody
 Melodic material can be:
 Compound, self-accompanying, submerged, roving,
distributed
 Theme
 A shorter sample from longer melodic materials that can be isolated
and classified
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Conceptual and Representational
Issues in Melodic Comparison

Components of Melodic Representation
 Representative
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pitch, duration
 Derivable
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intervallic motion, accents
 Non-derivable

articulation, dynamics
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Conceptual and Representational
Issues in Melodic Comparison
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Pitch Processing
 Different
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ways of pitch labeling
Base 7, base 12, base 21, base 40
 Approaches
to melodic pitch representation
profiles of pitch direction (up-down-repeat)
 pitch contours, melodic contours (sonographic data,
shapes of melodies)
 pitch-event strings (employ base-system representation)
 intervallic contours (intervallic profiles)
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Conceptual and Representational
Issues in Melodic Comparison
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Multi-dimensional data comparison
 Models:
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Kernel-filling model
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melody seems to evolve from a kernel consisting of outer note of a
phrase
uses both pitch and metrical data
Accented-Note Models
Coupling Procedures
Synthetic Data Models
Parallel processing models
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A geometrical algorithm for
melodic difference (Maidin)
 identifies similar
1, 8-bar segments in irish folk-dance
music
 based on:
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juxtapositioning of notes in two melodic segments
pitch differences (using base-12 or base-7)
note durations
metrical stress
transpositions (trying different transpositions and taking the
minimum differenc value)
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String-matching techniques for
musical similarity and melodic
recognition


(Crawford, Iliopoulos, Raman)
Describes string-pattern matching algorithms
 approaches
with known solutions
 approaches with unknown solutions

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Notion of themes, motifs
Notion of characteristic signature
Motifs have melodic similarity if they have matching
signatures
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String-matching techniques for
musical similarity and melodic
recognition

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String: sequence of symbols drawn from alphabet
Uses two-dimensional mode: pitch, duration
Pattern matches:
 exact
(pitch info is matched)
 transposed (intervallic info is matched

special case of transposed: octave-displaced match
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String-matching techniques for
musical similarity and melodic
recognition
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Exact-match algorithms
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Exact matching
Matching with deletions (no duration patterns preserved)
Repetition identification (non-overlapping patterns in different
voices/same voice)
Overlapping repetition identification
Transformed matching (retrograde, inversion)
Distributed matching (across voices)
Chord recognition
Approximate matching (Hamming distance)
Evolution detection
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String-matching techniques for
musical similarity and melodic
recognition

Inexact-match:
Unstructured exact matching (find a pattern in voiceunspecified mixture of notes)
 Unstructured repetitions (identified repeating patterns
that may/may not overlap)
 Unstructured approximate matching
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Sequence-based melodic comparison:
a dynamic programming approach
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(Smith, McNab, Witten)
Describes dynamic programming (string matching)
algorithm
Used on database of 9400 folk songs
Based on edit distance (cost of changing string a into
string b) using edit operators: replacement, insertion
and deletion
General:can be applied to any type of string (pitch,
rhythm for music)
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Sequence-based melodic comparison:
a dynamic programming approach

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Cost/weight assigned to each operation, based on the
input string components
Uses local score matrix (scores for each element of
the two strings), global score matrix (score of a
complete match between two strings)
Techniques of fragmentation/consolidation
 Eg.
four notes can match one longer note and vice versa.
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Signatures and Earmarks: Computer
recognition of patterns in music

(Cope)
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Creating new scores based on originals using
‘Experiments in Musical Intelligence’ (EMI) system
Musical signature

a
motif common to two or more works of a given
composer, 2-5 beats in length and composites of melodic,
rhythmic, harmonic components

Uses base-12 system, a number of controllers
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Signatures and Earmarks: Computer
recognition of patterns in music
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Earmarks
 More
generalized than signatures, refer to identifying
specific locations in the structure of a musical score (what
movement of a work we are hearing)
 Eg. trill followed by a scale, upward second followed by a
downward third
 Distinguishing quality: location
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A Multi-scale Neural-Network Model
for Learning and Reproducing Chorale
Variations
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(Hornel)
 Style
is learned from musical pieces of baroque
composers (Bach, Pachelbel), new pieces are
produced
 System able to learn and reproduce higher-order
elements of harmonic, motivic and phrase structure
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A Multi-scale Neural-Network Model
for Learning and Reproducing Chorale
Variations
 Learning
is done using two mutually interacting NN,
operating on different time scales, unsupervised learning
algorithm to classify and recognize structural elements
 Complementary intervallic encoding
 Given a chorale melody, a chorale harmonization of the
melody is invented, and one of the voices of harmonization
is selected and provided with melodic variations
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Judgments of Human and Machine
Authorship in Real and Artificial
Folksongs
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(Dahlig, Schaffrath)
 Listeners presented
with series of original and artificially
created folksongs
 Perception of the nature of composition varied with
perception of the music itself
 Associations with original: rhythmic similarity of phrases,
final cadence on the 1st degree, intermediate phrase
beginning that did not start on the 1st degree.
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MELDEX: A Web-based Melodic
Locator Service
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(Bainbridge)
 Query by humming
 Four databases: North-American/British, German, Chinese,
Irish folksongs; 9400 melodies
 Two alternative algorithms:

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simple, fast, state matching algorithm
slower, sophisticated dynamic programming algorithm
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Themefinder: A Web-based Melodic
Search Tool

(Kornstadt)
 Database of 2000 monophonic theme representations for
instrumental works from 18th-19th centuries

Search parameters
 pitch
direction (gross contour or refined contour)
 letter name of pitch
 pitch class
 intervallic name
 intervallic size
 scale degree
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A Probabilistic Model of Melodic
Similarity
 Hu,
Dannenberg, Lewis (2002)
Compares dynamic programming to probabilistic
approach in sequence matching
 Used query by humming as input
 Collected and processed 598 popular song files
 Processing done using MUSART thematic
extractor (10 themes per song), 5980 entries with
average 22 notes per song
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A Probabilistic Model of Melodic
Similarity
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Dynamic Programming Algorithms
Edit Distance
 Frame-based (pitch contour) matching
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Probabilistic Approach
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Probabilistic Distribution Histogram
Results
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Probabilistic model outperformed dynamic programming
algorithms by a narrow margin
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Name That Tune: A Pilot Study
in Finding a Melody From a
Sung Query
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(Pardo, Shifrin, Birmingham)
A query by humming system
Two-dimensional: pitch and rhythm
Comparison between string-alignment (edit cost) dynamic
programming and HMM algorithms (each theme represented
as a model)
Also compared to human performance
Results
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String-alignment algorithms slightly outperform HMM
Human performance is superior to both HMM and string
algorithms
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Melodic Similarity - Providing a
Cognitive Groundwork

(Hoffman-Engl, 1998-2004)
Original algorithms: string comparison-based
 New: geometric measure, transportation distances,
musical artist similarity, probabillistic similarity,
statistical similarity measures, transformational models,
transition matrices.
 Comparison problem: validity of results
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Melodic Similarity - Providing a
Cognitive Groundwork
 Dynamic
values as a separate dimension
 Similarity must not be based on physical but on
psychological dimensions
 Meloton, Chronoton, Dynamon
 Generalizations
 Larger the transposition interval, smaller similarity
 Larger tempo difference, smaller similarity
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Melodic Similarity - Providing a
Cognitive Groundwork
 Factors contributing to melodic similarity
 Melotonic distance (pitch value difference)
 Melotonic interval distance (distance between pitch intervals)
 Chrontonic distance (difference between durations)
 Tempo distance
 Dynamic distance (difference between dynamic values)
 Dynamic interval distance (between relative dynamic values)
 A cognitive model
based on those factors is presented
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Conclusion
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HTML Bibliography
http://www.music.mcgill.ca/~pkoles
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Questions
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