Towards a Harmonic Complexity of Musical Pieces Ladislav Mark 1 , - - PowerPoint PPT Presentation

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Towards a Harmonic Complexity of Musical Pieces Ladislav Mark 1 , Jaroslav Pokorn 1 , Martin Ilk 2 1 Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic 2 Vienna University of Technology, Vienna, Austria

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Towards a Harmonic Complexity

f Musical Pieces

Ladislav Maršík1, Jaroslav Pokorný1, Martin Ilčík2

1 Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic 2 Vienna University of Technology, Vienna, Austria

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Categorization

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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New mathematical model for harmony analysis Distinguish complex and simple music – defining Harmonic complexity Analysis of music in MP3 format, interesting results

Our results

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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Music classification: Possible new descriptor Music recommendation: New recommender systems Musicology: Comparing artists, genres and periods How we did that? Creating a mathematical model based on Tonal Harmony

Motivation

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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Tonal harmony – basic harmonic functions

„Most important in music is its harmony.“ Ilja Zeljenka Tonic Subdominant Dominant

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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Folk song: Slovenské mamičky Basic harmonic functions T – D – T – D

Simple harmony

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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Complex harmony

Modifications of basic harmonic functions Dp - Tp - Sp - Dp

T7 - Dp - D7 Sp - Dmi Tp-Sdim - Dp

Sp - Dp - S7 Hiromi: 010101 (Binary System)

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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Complex harmony

Bedřich Smetana – Moldau T – SP – TP – S- T – D - T (D) - (T)

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Model of harmonic complexity

TSD model

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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Model of harmonic complexity

Similar to formal grammars Basic harmonic function = start sentential form 2 rules applicable on sentential form: ADD – adds a new tone ALTER – alters the tone Example:

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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Chord complexity

Chord complexity = length of derivation = distance from the root harmony

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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Transition complexity

Transition complexity (TC) = steps needed to create a harmony from previous one

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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Implementation methods

Query method (localization of the 2 harmonies) Graph method (preprocessing, BFS)

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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Example analysis

Hiromi 010101 (Binary System)

CEbBb DbGb DbGb DEAbBb

Complexity:

DG DG C#F# C#F# CEFA DGAB D#EAb DbGb DGAB DGAB CBb CBb DGbAbBb DGbAbBb

7 1 7 2 4 7 1 7 1 3

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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Example analysis

Hiromi 010101 (Binary System) Complexity: 1 3 7 1 7 2 (0) 4 7 1 7

TCAVG = 4,24

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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Experiments

Rock, Pop, Jazz (5 best-selling artists) Classical music periods 3 parts TCAVG for different genres and music periods TCAVG for different artists TCAVG for different songs (The Beatles, Queen)

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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1. Genres and Music Periods

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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2. Artists

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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3. Songs – Queen, The Beatles

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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New mathematical model for harmony analysis Distinguish complex and simple music – defining Harmonic complexity Analysis of music in MP3 format, interesting results

Conclusion

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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Thank you for your attention

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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System Harmanal - diagram

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.

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Chord Transcription Example

Chroma features extraction Beat locations Haas et al. (Utrecht University)

Maršík, Pokorný, Ilčík: Towards a Harmonic Complexity of Musical Pieces

DATESO 2014, 18.4.