1 Melodic Similarity MUMT 611, March 2005 Assignment 4 Paul Kolesnik

2 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

3 Conceptual and Representational Issues in Melodic Comparison Components of Melodic Representation  Representative pitch, duration  Derivable intervallic motion, accents  Non-derivable articulation, dynamics

4 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)

5 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

6 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)

7 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

8 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

9 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

10 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

11 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)

12 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.

13 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

14 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

15 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

16 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

17 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 1 st degree, intermediate phrase beginning that did not start on the 1 st degree.

18 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

19 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

20 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

21 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

22 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

23 Melodic Similarity - Providing a Cognitive Groundwork (Hoffman-Engl, ) 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

24 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

25 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

26 Conclusion HTML Bibliography Questions