Finding Cadences through Boundary Entropy

<http://purl.org/ontology/chord/symbol/Ds:min7(*b3,9)/5> a chord:Chord; chord:root [ a chord:Note; chord:modifier chord:sharp; chord:natural <http://purl.org/ontology/chord/note/D> ];

chord:bass [ a chord:ScaleInterval; chord:degree 5 ];

1 Chord Transcriptions

Retrieve chords from transcribed chord collections in RDF• Beatles Transcriptionsall studio albums, 180 songs (Harte et al., 2005)

• MMA file collection• Goldsmiths’ Extracted LabelsSeveral file types can be converted to the Chord Ontology (Sutton et al., 2007) RDF format, which our Java code reads in. A conversion tool for Band-in-a-Box files will soon be available and will allow access to a large number of freely available, manual transcriptions from the internet.2 Pre-Processing & Trie

• Reduce chords to classesWe map chords with and without extensions onto the chord classes major (without dominant chords), minor, dominant, diminished, augmented, suspended and neutral (≈ open fifth). Consecutive chords that are equal (after this procedure) are joined. At present we ignore bass notes.

• Transposition to start on CWe make the assumption of invariance to transposition, i.e. we regard the chord changes C-F and D-G as equivalent. That’s done to every sub-sequence.

• Insert into TrieWe use a tree structure known as a trie or n-gram tree (see right) into which we insert all sub-sequences of a song collection to depth n+1. Every sequence is stored only once.

Bb Eb C F Bb6.

C F D G C . C A D G .

C F Bb.C F .

C .

C F D G C .

3 Results: “Cadences”

Abstract

•Calculate Boundary Entropy of 3-gramsWe adapt an approach devised by Cohen & Adams (2001) for segmentation of text into episodes. Given one particular chord 3-gram we consider the chord that immediatly follows it, i.e. the fourth chord. Intuitively, if the 3-gram is in the middle of a cadence, the fourth chord will nearly

Dm G C Dm G

...

always be the same. If the 3-gram constitutes the last three chords of a cadence, since it occurs in different songs or before different parts of the same song, more different chords will occur and the distribution of chords is flatter. A measure for the flatness of a distribution is the entropy, and it can be easily calculated from the trie.

Matthias MauchDaniel Müllensiefen

Geraint WigginsSimon Dixon

References

•Rank 3-gramsThe only thing left to do is to rank the chord 3-grams according to their entropy value.

Highest ranking boundary entropy 3-grams over 180 Beatles songs (possible functional interpretation in brackets)1. 0 MIN → 5 MAJOR → 10 MAJ (ii-V-I)2. 0 MAJ → 2 MAJOR → 7 MAJ (IV-V-I)3. 0 MAJ → 5 MAJOR → 0 MAJ (I-IV-I)4. 0 MAJ → 0 MINOR → 7 MAJ (IV-iv-I)5. 0 MAJ → 5 MAJOR → 10 MAJ (II-V-I)6. 0 MAJ → 7 MAJOR → 0 MAJOR (I-V-I)7. 0 DOM → 5 MAJOR → 10 MAJOR (II7-V-I)

The identification of recurrent patterns in chord progressions into meaningful units is a useful tool for a variety of tasks in automatic music processing and analysis, e.g. for the identification of song sections and the induction of song structure, sytle identiication and analysis, cover song detection, and the modelling of harmonic expectations. We propose an unsupervised approach that identifies cadences (i.e. recurrent patterns that indicate harmonic closure) from entropy profiles of chord progressions from symbolic harmony annotations for pop songs. Results indicate a large overlap between the most highly ranked progressions of 3 subsequent chords and well-known cadences from music theory. Further research will go into segmentation of chords into meaningful episodes, n-gram models and semantic clustering.

Cohen, P. & Adams, N. (2001). An Algorithm for Segmenting Categorical Time Series into Meaningful Episodes. Lecture Notes in Computer Science 2189, Springer, 198-207

Harte, C., Sandler, M., Abdallah, S. & Gomez, E. (2005). Symbolic representation of Musical chords: A Proposed Syntax for Text Annotations. ISMIR Proceedings.

Sutton, C., Raimond, Y., Mauch, M. (2007): The OMRAS2 Chord Ontology, http://motools.sourceforge.net/chord_draft_1/chord.html

C(5)

F(3) A(1)

D(1)

G(1)

C(1)

D(1)

G(1)

Bb(1)

Trie of depth 3+1, level 5 in pale grey. Numbers in brackets indicate how many sequences go through the node

Almost all of these 3-grams correspond to meaningful harmonic "episodes" as they appear in harmonic cadences. Most of them have proper names in music theory, e.g.: 1. "2-5-I" cadence; 2."Perfect cadence"; 3. "Plagal cadence", 6. "Authentic cadence".