harmony-analyser. org-Java Library and Tools for Chordal Analysis

Tags: distances, chord, Tonal Pitch Space, distance, chroma vectors, results, CEUR Workshop Proceedings, Music Information Retrieval, Cover Song Identification, chord progressions, chord distances, Java library, music analysis, International Computer Music Conference, H. Dictionary, Oxford University Press, chord progression, musical piece, TPS, plugins, Chord Transition Tool, International Society, Universitat Pompeu Fabra, WAV file format, Music Audio Signals
Content: HARMONY-ANALYSER.ORG - JAVA LIBRARY AND TOOLS FOR CHORDAL ANALYSIS Ladislav Marsнk Dept. of Software Engineering, Faculty of Mathematics and Physics Charles University, Malostranskй nбm. 25, Prague, Czech Republic [email protected]
ABSTRACT
We present a new Java library and tools for analysis of music harmony focused on chords, chord progressions and chroma vectors. The underlying model is capable of creating, naming and analysing chords, as well as evaluating chord distances including Tonal Pitch Space, geometric distances on Tonnetz grid, or chord complexities. Special attention is given to the experimental distances between chroma vectors. Our system can take input in the form of text, MIDI input device, or the WAV file format. We provide tools for chordal analysis and for creating visual representations chord segmentations or line graphs of chord or chroma distances. The system is extensible by creating additional plugins and provides an easy way of incorporating C++ based Vamp plugins, thus forming a suitable framework for Music Analysis in Java. Our JHarmonyAnalyser library and tools under harmony-analyser.org can be used for music analysis or as a Feature Extraction for retrieval tasks.
1. INTRODUCTION
Automatic chord estimation has been a major task in
Music information retrieval (MIR) in the 21st century.
Fujishima has first compared the chroma vectors to a
chord dictionary and obtained chord progressions in 1999
[6]. Since then, effort have been put not only towards
great variety of techniques for chord estimation [11], but
also towards improving recent MIR tasks by analysing
chroma or chord sequences. Notable examples are in
cover song identification task, where using reduced
chroma information, such as averaging chroma for every
beat [5], or chroma landmarks [1], yields good results.
Similarly for chord sequences, extracting and comparing
fingerprints is a proven way to search for a cover song [8].
While comparing chroma or chord sequences looks to be a
standard way for today's harmony analysis, new ideas
have arisen in the distances between
past years, pioneering similarity and chords themselves [4][13] and calling

for further research on this topic. The paradigm shift is to
look at the chord as a point in the space, and treat progression in musical piece as a path in this space. Our work is following up on these efforts. We provide library and tools capable of creating, naming and analysing chords and visualize chord progressions. Furthermore, we gather all relevant chord distances and provide tools for their comparison. We also pioneer new distances between chroma vectors, offering multiple options to approach this novel concept. The paper is structured as follows. In Section 2, we look at the known chord distances and form suggestions towards chroma distances. In Section 3, we show the contents of ou r JHarmonyAnalyser library and explain more in depth the new models we have developed (chord complexity distance, chroma vector distances). In Section 4 we present how new plugins can be created and added to the system, in order to achieve custom analysis. We wrap up by showing snapshots of GUI tools in Section 5, and our course for future work in Section 6. Fig. 1. Tonal Pitch Space model proposed by Lerdahl [9]. Chords are visualized in five levels, from (a) to (e): octave, fifths, triadic, diatonic, and chromatic level. Depicted is the space of a C major chord in the C major key context. Distances between chords are then calculated as a sum of number of shifts on levels (c) and (d) and number of non-common pitch classes on levels (a) to (e) between the two chords. We refer the reader to [9] or [4] for more information. 2. CHORD AND CHROMA DISTANCES In music theory, the concept of chord distance is long-known as Tonal Pitch Space (TPS), introduced by Lerdahl in 2001 [9] (Figure 1). Only recently, TPS was used to improve chord estimations by Rocher et al. [13], and music similarity tasks by De Haas et al. [4]. Notable
models, distinct from TPS, are the ones based on Tonnetz grid (Figure 2), from which the most developed is Chew's spiral model [2]. There are also other ways to represent chord distances, out of the scope of our work, all summarized in the work of Rocher et al. [13]. In the literature, we often encounter comparisons of chroma-like structures and chord or key candidates. Distinct from chord-to-chord distance, i n this use case, we first derive a so called pitch class profile from the musical piece or its part. An example can be averaging chroma vectors for the whole piece. Resulting structure is a vector of floats, similar to chroma vector. We then estimate the key for the musical piece, by comparing the pitch class profile to the profile of the key candidate [7]. A similar use case is that of estimating a chord for a given set of chroma vectors. Chord candidates are typically chosen from a suitable dictionary, such as 24 major and minor chords. Commonly used methods are Euclidean distance, or weighted sums [6], the latter being an inverted distance (higher the sum, closer is the queried vector to the chord candidate). In these examples we can see that distance measures are meaningful between chroma-like structures and chords. But we need to keep in mind that chroma vectors and chords occur on different levels: chroma vectors are obtained by a Fourier transform and represent a short frame of music, while chords can be obtained by processing chroma vectors and represent the changes in harmony. While distances between adjacent chords in a musical piece have been proposed for improving MIR tasks [13], to the best of our knowledge, distances between two (adjacent) chroma vectors have not been extensively studied, although they can represent meaningful information. Above mentioned methods can be easily applied, however, it is questionable if they will be valid for transition between two short instants. More interestingly, musicology-based methods such as TPS can be employed to obtain chroma vector distances. We elaborate these new topics in the harmony-analyser.org system.
Fig. 2. Tonnetz grid as proposed by Riemann [12] in 19th century. Highlighted is the C major chord.
3. LIBRARY OVERVIEW harmony-analyser.org is a home for JHarmonyAnalyser library as well as simple GUI tools to present its main functions, together forming a cohesive system for chordal analysis. It contains two main packages: chord_analyser package, containing Java classes for evaluating chord distances chroma_analyser package, containing Java classes for evaluating experimental chroma distances Both packages have a similar structure, and fulfil these common requirements: 1. The packages contain base classes, that supply them with the representations of tones, intervals and scales (typically one Java class for each entity). 2. The packages contain the main classes, Chord and Chroma respectively for chord_analyser and chroma_analyser package. Various constructor inputs are supported, including text input. 3. The packages provide methods to derive distances between its main entities. For this purpose, multiple model classes are provided, representing some model of computation (e.g. TPS model). To ease the work with a real-life input, services package is included, containing tools for reading WAV files, or interpreting MIDI input from external MIDI instrument (e.g. MIDI keyboard). We show how all the packages work together in an example scenario: let us consider MIDI input keyboard plugged in to our machine. Classes available in services packages are able to get the keyboard and decode its input. We may use chord_analyser package to construct chord, or chroma_analyser package to construct chroma from the input on the keyboard. We choose to proceed with playing two chords (e.g. C major and G7) and creating two Chord objects. Then, using TonalPitchSpace model located in chord_analyser, we calculate distance between C major and G7, outputting result to a text area in GUI. We explain the main contents of each package in the subsections below. 3.1. chord_analyser package With JHarmonyAnalyser library being updated on a regular basis, new models are being included to the packages, to achieve an up-to-date selection. brief summary of the current model classes contained in
chord_analyser package in version 1.2 of
JHarmonyAnalyser are:
TonalPitchSpace - as defined by Lerdahl [9],
with symmetricity fix as described by De Haas et
al. [4].
ChordComplexityDistance (CCD) - defined in

our previous work [10] as a complexity of
transition between two subsequent chords, this

experimental distance treats the added dissonant
tones on the top of major or minor chord as

additional layers of complexity. Rules are
d efined to add/remove/modify the dissonant
tones. Resulting distance is defined as the
complexity of constructing the next chord from
the previous chord and is similar to edit distance
of two strings. Figure 3 shows the distance
between C major chord with the added a tone,

and C major chord with the added f# tone.
Tonnetz - implementation of the Tonnetz grid and
distances of major and minor chords on the grid
(see Figure 2).

Fig. 3. Diagram showing the Chord Complexity Distance (CCD) between two chords. First, the a tone needs to be removed to obtain common ancestor for both chords, which is C major chord in a C major key. Afterwards, we add the f tone from the same key, and alter it to f# outside the key. Resulting complexity of the transition is 3. For more information we refer the reader to [10].
3.2. chroma_analyser package
In this package we provide classes to calculate
experimental distances between chroma vectors. Example
models in version 1.2 of the library are:
EuclideanDistance,
WeightedSumDistance,
SimpleDifference and ComplexityDifference. As described
in Section 2, Euclidean distance and weighted sums are
commonly used for chord estimation. chroma_analyser
package allows us to reuse these distances for two
subsequent chroma vectors in the musical piece. In
addition to these basic concepts, we offer
SimpleDifference sd(x,y) for chroma vectors x and y as: 12 sd(x, y) = |xi - yi| i=1
Motivated by the levels present in Tonal Pitch Space (Figure 1) and chord complexity distance presented in Section 3.1, we propose ComplexityDifference cd(x,y) for chroma vectors x and y as: 12 cd(x, y) = |w(x)ixi - w(y)iyi| i=1 In this definition, w(x) and w(y) are weight vectors, which have their 12 values dependent on the context for the transition from x to y. To explain how to find the weights, we define c(x) as a function that returns chord estimate for a given chroma vector x, and k(c, d) as a function that returns common key for chords c and d. Both functions k and c have their return values in the form of boolean vectors of size 12 (for a chord estimate c(x) of a chroma vector x, c(x)i = true if the pitch class i belongs to c(x), c(x)i= false otherwise). Usually for a vector returned by function c, 3 values will be true and for a vector returned by function k, 7 values will be true, which are the standard numbers of tones for chords and keys. As an example transition, we can imagine x and y both being estimated to C major chord (c(x) = c(y) = C major chord) and C major being the common key (k(c(x), c(y)) = C major key). Weight vector w(x) is defined as follows1: w(x)i = 0 c(x)i = true w(x)i = 1 k(c(x), c(y))i = true c(x)i = false w(x)i = 2 k(c(x), c(y))i = false c(x)i = false In other words, using the weight vector w(x), we suppress the changes in between chord tones (w(x) = 0), we take into account changes in between the non-chord tones from the key (w(x) = 1), and we assign highest weights to the non-chord and non-key tones (w(x) = 2), to emphasize the non-diatonic movements in music. This way, we can observe the complexity of movements in Tonal Music. 4. EXTENSIBLE PLUGINS The system under JHarmonyAnalyser library can also act as an easy-to-use framework for creating plugins for music analysis in Java (not necessarily related to chords or chroma vectors). There are ready-made plugins available in the plugins package of the library. Custom plugins can be created simply by following the proposed structure. Plugins form one of the core parts of the system, since they are responsible for opening and analysing WAV files using the models from the rest of the library. While distances between chords and chroma vectors can be calculated simply by calling a method from the model 1 We can get w(y) by the same equation, only swapping chroma vectors x and y.
class, analysis of WAV file format, usually, takes more
subsequent steps in order to achieve the desired result. For
example, we first need to derive chroma vectors from the
WAV file, and then we need to get distances between
subsequent chroma vectors. Optionally, we may want to
plot a line graph of the resulting distances. The resulting
3-step process would be unfit for one wrapper method,
especially if we want to observe the partial results.
Custom and ready-made plugins serve this purpose of
layered analysis.
Inspired by GNU GPL licenced C++ Vamp
plugins (http://vamp-plugins.org), a plugin has its own
unique key and analyses the whole WAV input in its
specific manner, producing results that are well
documented. In fact, thanks to Java wrappers provided by
Queen Mary University, we include a selection of
Java-wrapped Vamp plugins in the plugins/vamp_plugins
package. Differently from Vamp plugins, results from one
plugin are very often taken by another plugin to continue
with higher-level analysis (chroma vectors picked up by
chord estimator, chord progression picked up by chord
distance plugin). Each plugin needs to meet the following
requirements:
1. It needs to have a pluginKey, a unique key for the
plugin, e.g. chord_analyser:tps_distance.
2. It needs to provide a list of input files and their
extensions.
3. It needs to provide a list of output files and their
extension.
4. It needs to implement analyse method, which
takes all the input files, and creates correct output
files.
Example plugins are (for full list, please refer to
the documentation on harmony-analyser.org):
chord_analyser:tps_distance
implementing
Tonal Pitch Space model analysis for a WAV
file.
chord_analyser:chord_complexity_distance
implementing CCD analysis for a WAV file.
chroma_analyser:complexity_difference
implementing chroma vector distance analysis by
ComplexityDifference model for a WAV file.
5. GUI TOOLS
Along with the library and plugins, harmony-analyser.org also provides simple GUI tools (jointly named harmony-analyser), developed using java.awt package, to show the main library functions. Screenshots of some of the main tools are on Figures 4 and 5. Example tools are: Chord Transition Tool - using MIDI or text input to analyse chords or chroma vectors.
Audio Analysis Tool - batch analysis using selected plugins for an input folder with WAV files. Visualization Tool - plotting graphs and diagrams with chord or chroma vector distances for a WAV file. Fig. 4. Visualization Tool from harmony-analyser.org: selection of plugins and the resulting line graphs. Analysis of Wonderwall from Oasis is shown, containing results for both TPS and CCD distances on one screen. We can observe some chord distance peaks captured by both models, and some singled out by only by TPS or CCD distance. CCD peaks are around 30th, 90th and 160th second correspond to the A5 chord followed by B7sus4 chord. Fig. 5. Chord Transition Tool from harmony-analyser.org: capturing the MIDI input and outputting chord labels and distance information. C major and G7 chords were captured on a piano keyboard.
6. CONCLUSION AND FUTURE WORK We provide a maintained, tested and publicly available Java library and tools for chordal analysis, under harmony-analyser.org domain. JHarmonyAnalyser library can be used for feature extraction, visual analysis of musical pieces, or comparison of chord and chroma distances, as well as a simple framework for development of music analysis software in Java. As a future work we will focus on comparing the proposed distances, and obtaining results for MIR tasks such as cover song identification. We plan to add new models to the chord_analyser package, starting with the model proposed by Elaine Chew [2]. We will also broaden the plugin base with plugins and smoothing filters. Our other goal is the ease of installation (Linux) and availability in Java repositories (Maven). By providing these free tools we hope to encourage future research in the chordal analysis field. 7. ACKNOWLEDGMENTS The study was supported by the Charles University in Prague, project GA UK No. 708314. 8. REFERENCES [1] Bertin-Mahieux, T. and Ellis, D. P. W. "Large-Scale Cover Song Recognition Using Hashed Chroma Landmarks" In: IEEE Workshop on the Applications of signal processing to Audio and Acoustics (WASPAA 2011), 2011 [2] Chew, E. Mathematical and computational modeling of Tonality. Springer US, 2014 [3] De Haas, W. B., Magalhгes, J. P., and Wiering, F. "Improving Audio Chord Transcription by Exploiting Harmonic and Metric Knowledge" In: Proceedings of the 13th International Society for Music Information Retrieval Conference (ISMIR 2012), 2012 [4] De Haas, W. B., Veltkamp, R. and Wiering, F. Tonal Pitch Step Distance: "A Similarity Measure for Chord Progressions" In: Proceedings of the 9th International Conference on Music Information Retrieval (ISMIR 2008), 2008 [5] Ellis, D. P. W., and G. E. Poliner. "Identifying `Cover Songs' with Chroma Features and DynamiC PROGRAMMING Beat Tracking" In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2007), 2007 [6] Fujishima, T., "Realtime Chord Recognition of Musical Sound: A System Using Common Lisp Music" In: Proceedings of the International Computer Music Conference (ICMC 1999), 1999
[7] Gуmez, E. Tonal Description of Music Audio Signals. PhD thesis, Universitat Pompeu Fabra, 2006 [8] Khadkevich, M. and Omologo, M. "Large-Scale Cover Song Identification Using Chord Profiles" In: Proceedings of the 14th International Society for Music Information Retrieval Conference (ISMIR 2013), 2013. [9] Lerdahl, F. Tonal Pitch Space. Oxford University Press, Oxford, 2001 [10] Marsik, L., Pokorny, J. and Ilcik, M. "Towards a Harmonic Complexity of Musical Pieces" In: Proceedings of the 14th Annual International Workshop on Databases, Texts, Specifications and Objects (DATESO 2014), CEUR Workshop Proceedings, Vol. 1139, 2014 [11] McVicar, M., Santos-Rodriguez, R., Ni, Y. and Bie, T. D., "Automatic Chord Estimation from Audio A Review of the State of the Art" In: IEEE/ACM Trans. Audio, Speech & language processing 22 (2), pp. 556­575, 2014 [12] Riemann, H. Dictionary of Music. Augener Ltd., London, 1896 [13] Rocher, T., Robine, M., Hanna, P. and Desainte-Catherine, M. "A Survey of Chord Distances With Comparison For Chord Analysis" In: Proceedings of the International Computer Music Conference (ICMC 2010), 2010

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