Quantifying and Visualizing Tonal Complexity. Weiß, C. & Müller, M. In Proceedings ofthe 9th Conference on Interdisciplinary Musicology, Berlin, 2014. ![Quantifying and Visualizing Tonal Complexity [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper abstract bibtex In Western classical music, the structure of a piece is reinforced by the contrasting harmonic nature of its sections. The structural parts are characterized by the presence of certain chords or chord changes. A section that is harmonically stable may be followed by a contrasting section that feels unstable or tense. In the sonata form, for example, the unstable development part is located between the stable exposition and recapitulation phases. In this paper, we try to measure this kind of harmonic stability and present visualizations for such analyses. To this end, we propose novel features for quantifying tonal complexity and discuss their musicological implications. The features are based on statistical measures calculated from chroma representations of the music recording. The characteristics of tonal complexity apply to different time scales. To illustrate this time scale dependence for the proposed features, we use hierarchical visualizations based on previously introduced scape plot representations. On a fine temporal level, tonal complexity is related the character of chords or scales. For example, in a modulating transition phase, we usually find more complex chords than at the beginning of a piece. To analyze such differences, we study the feature values for isolated chords. Looking at a coarser level, the presence of modulations is an indication for a segment's complexity. In the sonata form, for example, the development usually contains several modulations. To account for this property, we calculate the complexity features based on a coarse resolution of the chroma features. For evaluation of this coarse-scale complexity, we analyze Beethoven's sonatas where we find higher complexity in the development parts.
@InProceedings{ wei.ea2014-quantifying,
author = {Wei{\ss}, Christof and M{\"{u}}ller, Meinard},
year = {2014},
title = {Quantifying and Visualizing Tonal Complexity},
abstract = {In Western classical music, the structure of a piece is
reinforced by the contrasting harmonic nature of its
sections. The structural parts are characterized by the
presence of certain chords or chord changes. A section
that is harmonically stable may be followed by a
contrasting section that feels unstable or tense. In the
sonata form, for example, the unstable development part is
located between the stable exposition and recapitulation
phases. In this paper, we try to measure this kind of
harmonic stability and present visualizations for such
analyses. To this end, we propose novel features for
quantifying tonal complexity and discuss their
musicological implications. The features are based on
statistical measures calculated from chroma
representations of the music recording. The
characteristics of tonal complexity apply to different
time scales. To illustrate this time scale dependence for
the proposed features, we use hierarchical visualizations
based on previously introduced scape plot representations.
On a fine temporal level, tonal complexity is related the
character of chords or scales. For example, in a
modulating transition phase, we usually find more complex
chords than at the beginning of a piece. To analyze such
differences, we study the feature values for isolated
chords. Looking at a coarser level, the presence of
modulations is an indication for a segment's complexity.
In the sonata form, for example, the development usually
contains several modulations. To account for this
property, we calculate the complexity features based on a
coarse resolution of the chroma features. For evaluation
of this coarse-scale complexity, we analyze Beethoven's
sonatas where we find higher complexity in the development
parts.},
address = {Berlin},
booktitle = {Proceedings ofthe 9th Conference on Interdisciplinary
Musicology},
keywords = {music analysis with computers},
mendeley-tags= {music analysis with computers},
number = {January 2014},
url = {https://www.researchgate.net/publication/303667504_Quantifying_and_Visualizing_Tonal_Complexity}
}
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In this paper, we try to measure this kind of harmonic stability and present visualizations for such analyses. To this end, we propose novel features for quantifying tonal complexity and discuss their musicological implications. The features are based on statistical measures calculated from chroma representations of the music recording. The characteristics of tonal complexity apply to different time scales. To illustrate this time scale dependence for the proposed features, we use hierarchical visualizations based on previously introduced scape plot representations. On a fine temporal level, tonal complexity is related the character of chords or scales. For example, in a modulating transition phase, we usually find more complex chords than at the beginning of a piece. To analyze such differences, we study the feature values for isolated chords. Looking at a coarser level, the presence of modulations is an indication for a segment's complexity. In the sonata form, for example, the development usually contains several modulations. To account for this property, we calculate the complexity features based on a coarse resolution of the chroma features. For evaluation of this coarse-scale complexity, we analyze Beethoven's sonatas where we find higher complexity in the development parts.","address":"Berlin","booktitle":"Proceedings ofthe 9th Conference on Interdisciplinary Musicology","keywords":"music analysis with computers","mendeley-tags":"music analysis with computers","number":"January 2014","url":"https://www.researchgate.net/publication/303667504_Quantifying_and_Visualizing_Tonal_Complexity","bibtex":"@InProceedings{ wei.ea2014-quantifying,\n author = {Wei{\\ss}, Christof and M{\\\"{u}}ller, Meinard},\n year = {2014},\n title = {Quantifying and Visualizing Tonal Complexity},\n abstract = {In Western classical music, the structure of a piece is\n reinforced by the contrasting harmonic nature of its\n sections. The structural parts are characterized by the\n presence of certain chords or chord changes. A section\n that is harmonically stable may be followed by a\n contrasting section that feels unstable or tense. In the\n sonata form, for example, the unstable development part is\n located between the stable exposition and recapitulation\n phases. In this paper, we try to measure this kind of\n harmonic stability and present visualizations for such\n analyses. To this end, we propose novel features for\n quantifying tonal complexity and discuss their\n musicological implications. The features are based on\n statistical measures calculated from chroma\n representations of the music recording. The\n characteristics of tonal complexity apply to different\n time scales. To illustrate this time scale dependence for\n the proposed features, we use hierarchical visualizations\n based on previously introduced scape plot representations.\n On a fine temporal level, tonal complexity is related the\n character of chords or scales. For example, in a\n modulating transition phase, we usually find more complex\n chords than at the beginning of a piece. To analyze such\n differences, we study the feature values for isolated\n chords. Looking at a coarser level, the presence of\n modulations is an indication for a segment's complexity.\n In the sonata form, for example, the development usually\n contains several modulations. To account for this\n property, we calculate the complexity features based on a\n coarse resolution of the chroma features. 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