Local Harmonic Agreement based on Recurrent Patterns (LHARP)
A novel method for harmonic similarity that emphasises shared repeated patterns among symbolic chord sequences, to accommodate a wide set of applications. Compared to other harmonic similarity methods on symbolic music, LHARP enables more explorative studies, as it can establish links when local harmonic patterns are found repeated in both sequences, while retaining global information to a lesser extent. This is also complemented with “The Harmonic Network” a computational tool allowing users to explore music collections by visualising harmonic similarities among tracks and interacting with the resulting graph to discover nontrivial relationships among authors, composers, and pieces.
Introduction to LHARP
The proposed harmonic similarity in this chapter is formulated in a way to emphasise shared repeated patterns among two arbitrary symbolic sequences, hence it provides a general framework for the analysis of symbolic streams based on their local structures. As illustrated in the diagram above, the domain-specific parts are the pre-processing and encoding steps, whereas the downstream part of the pipeline – including pattern extraction and matching operations, can generalise to arbitrary symbolic (uni-modal) sequences.
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Harmonic reduction. Chord progression are simplified before comparison – the bass note is removed as this operation improves the generalisation capabilities of the next steps, thereby producing more consistent similarity scores), and consecutively repeated chords are removed. This provides a “bird’s eye view” on the global harmonic properties of each piece.
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Key-based normalisation. Chords labels/classes in a progression need to be contextualised according to the key of the piece (defined by the tonic and the scale) before any comparison is possible. Therefore, all chord progressions are transposed to the same key: C major. This last transformation concludes the pre-processing operations.
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Decomposition of chords. The normalised harmonic sequences are then prepared for the encoding step, so that they can be used as input to the any computational procedure. Rather than further simplifying the symbolic musical content, a new encoding procedure was designed to retain the fundamental internal structure of each chord. More precisely, every chord label is decomposed into its pitch constituents – the individual pitches it is made of. For example, a C major is encoded as a multi-hot vector where the elements corresponding to the active pitches are equal to 1; all the others are 0.
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Enumeration of pitch simultaneities. To reduce the complexity of any potential polyphonic model using such sparse local representations of chords, each unique decomposition is then assigned to an index (an integer value). As it can be observed, this is akin to the common encoding approach used in natural language processing for word tokens. This results into chord tokens defined over the vocabulary of all possible chord decompositions.
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Harmonic thumbnailing. To identify the areas/regions of chord progressions that can be deemed as “harmonically memorable”, we extract the n-grams of all possible orders – starting from tri-grams, that repeat at least once within the progression. We call them “harmonic thumbnails”, as they represent harmonic structures per se.
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Shared harmonic patterns. Finally, chord progressions are compared for similarity based on the agreement between their harmonic thumbnails. In particular, the longest harmonic structures they share is compared to the order of the longest thumbnail that occurs within each progression, independently. Therefore, depending on the harmonic patterns the two chord progressions have in common – in relation to their internal structures, the similarity function will return a value between 0 and 1 (the higher the value, the stronger the similarity) together with the longest harmonic patterns they share.
The Harmonic Network
As illustrated in the figure above, in the harmonic network nodes correspond to tracks in chord music datasets, whereas edges connect nodes if their value of harmonic similarity is greater than 0 (an harmonic match was found). To simplify the inspection, a grey-scale colourmap visually projects the value of harmonic similarity expressed by edges: from light grey (low similarity) to plain black (high similarity). Instead, nodes are sized according to their degree – the number of connections/edges they have. As the graph is undirected, considering that similarity is symmetric by definition, the degree is equal to the number of tracks sharing harmonic structures. A distinct border colour also differentiate nodes according to the music dataset they come from. The harmonic network also provides features for the exploration of the graph; a demo LIVE version can be found at this link.
Setup, data, and examples
All required packages and dependencies are listed in the requirements.txt file. To setup your environment, just create a new virtualenv or conda environment from your local system, clone this repository, and install all dependencies by running the following command.
git clone https://github.com/polifonia-project/lharp.git && cd lharp
pip install -r ./requirements.txt
Getting chord datasets
To replicate our experiments, or simply to compare the chord progressions in the current version of the harmonic network with those of your own collection, you first need to clone our dataset repository (run the command below).
cd .. && git clone https://github.com/polifonia-project/datasets.git
The dataset used for this project were:
- Isophonics (pop/rock songs from Beatles and Queen)
- JAAH (jazz songs from various artists)
- Schubert Winterreise (classical tracks from Schubert).
How to use LHARP
You are now ready to use LHARP. Please check our demo notebook for an example run. We have also implemented a documented API where each function corresponds to one of the main steps for the computation of the harmonic similarity (see the diagram above). These functions can be found at this link and they also allow to compute LHARP among tracks in a given collection (harmonic_similarity_intra) and against those tracks we used for our experiments (harmonic_similarity_inter).
Attribution
Please, cite this paper if you use the code in this repository as part of a published research project:
inproceedings{deberardinis2021lharp,
title={A local harmonic similarity function based on shared repeated chord structures},
author={de Berardinis, Jacopo and Meroño-Peñuela, Albert and Poltronieri, Andrea and Presutti, Valentina},
booktitle={Manuscript under review},
year={2021}
}
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.