Identifying Successful Melodic Similarity Algorithms for use in Music

Identifying Successful Melodic Similarity Algorithms for use in Music Retrieval Margaret Cahill Donncha Ó Maidín University of Limerick, Ireland. [email_address]

Introduction
MIR - Music Information Retrieval
Field of research concerned with searching digitized collections of music
Various formats:
raw and compressed audio
scores
MIDI

Musical Scores
This research is concerned with music in score format
Collections of scores online e.g.
KernScores http://kern.humdrum.org/
MuseData http://www.musedata.org/
Music notation editors and scanning software allow saving/exporting in score format

Melodic Similarity
The ability to detect similar melodies allows:
searching for query melodies
analysis of compositional style
analysis of musical form/structure
identification of recurring themes and motifs

Current Approaches
Many current algorithms are based on string-matching techniques from the IR world
e.g. edit-distance algorithm
calculates the cost of turning one string into another using delete, replace, and insert actions
Operations suited to text are not always suited to melody

Features of a score
A wide range of features are available from a melodic score:
Which features
are important?
How should they
be combined?
Which algorithms
are suitable?
Table 1: Some of the musical features available from a score implicit pattern of strong and weak stresses – metrical stress beaming ties tempo directions note duration phrasing accidentals ornamentation note pitch dynamics instrumentation articulation key signature rest time signature barlines clef

Our Approach
Use music perception research as a guide to choosing suitable features
Use a test-bed of melodies for which we already know the degree of similarity
Identify potential algorithms
Test use of features, method of combining features, values of internal weights and parameters
Tweak algorithms to improve performance

The Listening Experiment
Variations on Twinkle, Twinkle, Little Star for recorder by Duschenes.
Theme and Variations provides a natural range of similar melodies.
Provides a context for the listener – all melodies are related to the Theme.
The Theme is 8 bars long.
9 variations.
Good examples of some musical issues melodic similarity algorithms face:
different time signatures
different keys
augmentation of theme (1 bar stretched to 2 bars)
triplets
single notes replaced by repeated rhythmic repetitions
ornate elaborations of the theme using both stepwise movements and arpeggic leaps

Theme Figure 1: The first 2 bars of the Theme and Variations

Listening Experiment
The Theme and each variation easily segments into 4-bar phrases.
Two 4-bar segments were extracted to form Part A and Part B of the experiment.
Pairs of melodies
played
Similarity was rated
on a 7-point scale.
Questionnaire and
comment sheet
Time = 24-30 minutes.
34 subjects participated.
Table 2: Structure of the listening experiment

Consistency of Results
Spearman’s correlation coefficient (correlation on the ranks) used to measure the consistency of subjects.
used the similarity rating given by subjects for the sequential and random (repeat) playing of melodies.
Only retained data from highly-correlated subjects:
>.789, significant at the .01 level
Part A: 26 subjects.
Part B: 16 subjects.
Ratings for random (repeat) playing discarded following the consistency check.

Consistency of Results
Inter-subject correlation used as
a rough measure of the overall
reliability of the data.
calculated from the correlation
matrices of each section
how each subject correlated
with every other subject
Median ratings used for
comparison with algorithmic
measures of similarity.
Table 3: Inter-subject correlation Table 4: Results of listening experiment – median ratings.

The Algorithms where: k = the time windows of the score p 1 , p 2 = pitch values of the first and second melodies in a window w k = the weight associated with that time window totaldur = the duration processed Figure 2: Algorithm - Ó Maidín 1998

The Algorithms
processes the score in time windows
the duration of the shortest full note at that particular point in the score.
sum of the absolute pitch differences in each window multiplied by a corresponding weight for that window
weights can be duration, metrical accents,or combinations of these and other weighting factors
currently exploring variations of this algorithm using different combinations of musical features
transposition identified using the median value of the pitch differences with the associated weight value (similar to using frequency in statistics)
edit distance algorithm to be explored next

Comparing the Algorithmic and Human Measures of Similarity
Two main approaches taken
Correlation
gives an overall measure of performance across all variations rather than individual variations
Normalize data, then apply metric
z-scores or min-max normalization
can compare the algorithm performance for
individual variations
metric used to measure performance across
all variations
Figure 3: Possible metrics for use with normalized data

Current Work
Have identified the use of duration and metrical stress weights for melodies by comparing algorithmic and human measure of similarity
Investigating the use of duration and metrical stress weights for melodies by comparing the algorithmic and human measures of similarity
Analyzing results through correlation and other metrics to determine which features are most successful for use in melodic similarity algorithms

Identifying Successful Melodic Similarity Algorithms for use in Music

by inscit2006 on Jan 02, 2007

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Identifying Successful Melodic Similarity Algorithms for use in Music — Presentation Transcript