Melodic Similarity

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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
• pitch, duration
• Derivable
• intervallic motion, accents
• Non-derivable
• articulation, dynamics

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Conceptual and Representational Issues in Melodic
Comparison

• Pitch Processing
• Different 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

• Multi-dimensional data comparison
• Models
• Kernel-filling model
• 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
• 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
• 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

• 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

• Exact-match algorithms
• 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
  voice-unspecified 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

• (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
• Generalcan be applied to any type of string
  (pitch, rhythm for music)

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Sequence-based melodic comparison a dynamic
programming approach

• 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)
• 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

• 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

• (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

• (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

• (Bainbridge)
• Query by humming
• Four databases North-American/British, German,
  Chinese, Irish folksongs 9400 melodies
• Two alternative algorithms
• 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

• Dynamic Programming Algorithms
• Edit Distance
• Frame-based (pitch contour) matching
• Probabilistic Approach
• Probabilistic Distribution Histogram
• Results
• 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

• (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
• 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

• HTML Bibliography
• http//www.music.mcgill.ca/pkoles
• Questions