tree structured representation of music for polyphonic music information retrieval

Tree structured representation of Tree structured representation of music for polyphonic music music for polyphonic music

information retrievalinformation retrieval

David Rizo

Departament of Software and Computing Systems

University of Alicante

Funciona muy bien

Muchas gracias por vuestra antención

Tree construction process Tree construction process (Rizo et al. ’03)(Rizo et al. ’03)

Based on the logarithmic nature of music notation Each tree level is a subdivision of the upper level

whole 4 beats

half 2+2

quarter 4×1

8×½eighth

Leaf labels can be any pitch magnitude Rests are coded the same way as notes Duration is implicitly coded in the tree structure

. . . . . . . . . . . . . . . . . . . . . . . . .

F

C

E G

1 4/4 bar

Initial time

Duration

Tree representation for monodiesTree representation for monodies

The complete melody is a forest Bars can be grouped sequentially or hierarchically

F

C

E G

Inner nodes need to be labelled

Rules for label propagation and for pruning less relevant branches

Tree construction processTree construction process

A B

C G

Sequential grouping:

C E G F A B C G


The distance is computed as the cost of the operations to transform one tree into the other.

TREE EDIT DISTANCETREE EDIT DISTANCE (Zhang & Shasha, 1989)

C

G

C

A

A

C

C

C

G

C A

C

C

A

A

t1 t2d(t1,t2)

Weighted operations of

insertiondeletion

replacement

Melodic similarity metricsMelodic similarity metrics

Tree edit distance O( |T1| |T2| h(T1) h(T2) )

Previous prunning process helps to overcome this complexity

(Zhang & Shasha, “Simple fast algorithms for the editing distance between trees...”. SIAM J Comput., 8(6): 1245-1262. 1989)


Tree representationTree representation

Use key information of the melody in the labels: interval from tonic

Propagation of keys based on melodic rules (P.Roman et al.

ICMC’07)

Development of algorithms to learn the tree edit distances costs

European network of excelence (Pascal) project:

“Pump Priming. Learning Stochastic Edit Distances from

Structured Data: Application in Music Retrieval”

Current workCurrent work

Part IIPart II

Tree model of symbolic music for tonality guessing

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Polyphonic tree representationPolyphonic tree representationRecall tree representation.

Process repeated for each voice

{C,G}

{C} {F}

C F CG

G E

{G} {C,G,E}{C,F,G}

{C,E,F,G}


Polyphonic tree representationPolyphonic tree representationBetter tree summarization:Use harmonic profiles + rhythmic weights Multiset

E.g. Applying rhythmic weight= 1/level

{C=0.5,E=0.5,G=0.5}

{C=0.25} {F=0.25}

{C=0.25,F=0.25,G=0.5}

{C=0.75,E=0.5,F=0.25,G=1}

Krumhansl-Schmuckler profiles multiply the rhythmic weight: worse results

Polyphonic tree representationPolyphonic tree representation Whole song representation for comparison

– Ordered forest with a tree for each bar

0.5| 1|0 …. 0.3|0|0.3… 1|10|0|0.5|…0|1….0|0|1|0.3|… 1|0|0.2|…

. . . . .

Bar 1 Bar 2 Bar 3 Bar 4 Bar N

Layers distance: -Let be a tree level ot tree T, compose a sequence S(T) with all nodes at that level in the forest

-Distance between 2 songs A and B at a level d(A,B, a, b)= stringDistance(Sa(A), Sb(B))

-Global distance d(A,B) = min0i, 0j d(A,B,i,j)

Complexity: O(|barsA| * |barsB| * 2)

Also other measures:LCS

Shasha tree edit distanceSelkow tree edit distance

Drawback:- metered music required- use Melisma to get bars from unmetered music

Sa

Label substitution costLabel substitution cost

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Graphical representationsGraphical representations

P1, P2, P3 algorithms from Ukkonen, Lemström, Makinen ‘03

P2v5, P2v6: indexed versions of P2– Not published

yet


Classifier combinationClassifier combination


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ExperimentsExperiments Different corpora:

– Helsinki: 7 different polyphonic tunes Covers made up of polyphonic piano files + “Band in a box” variations 68 files

– Theme_variations_classical Bach Goldberg variations Bach english suites variations Some Tchaikowsky variations 78 files, all polyphonic

– Corpus1000_with_queries MIDI files downloaded from internet 80 files, almost all polyphonic, some monophonic

Leave one out– Avoid very good / bad queries

ResultsResults

Corpus ICPSCorpus ICPS


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Corpus HelsinkiCorpus Helsinki

ResultsResults


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ResultsResults

Corpus Theme Variations ClassicalCorpus Theme Variations Classical


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Conclusions and future (current) workConclusions and future (current) work

Tree methods are 24 times faster when the tonality is known: they are also more accurate

Very hard task when MIDI files are real ones– Preprocess songs:

Use automatic tonal analysis + trees to remove non-important notes in songs

Improve results by combining different classifiers Tune the tree comparison measures

– Current learnt similarity measures Add LCS fast implementation from Hyyrö ‘04 Add confidence values to LCS Add the G.Valiente bottom-up tree edit distance

Query

MIDI

tree structured representation of music for polyphonic music information retrieval

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