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Melodic Similarity

MUMT 611, March 2005Assignment 4Paul 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 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

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

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