Structure perception is a fundamental aspect of music cognition in humans. Historically, the hierarchical organization of music into structures served as a narrative device for conveying meaning, creating expectancy, and evoking emotions in the listener. Thereby, musical structures play an essential role in music composition, as they shape the musical discourse through which the composer organises his ideas. In this paper, we present a novel music segmentation method, pitchclass2vec, based on symbolic chord annotations, which are embedded into continuous vector representations using both natural language processing techniques and custom-made encodings. Our algorithm is based on long-short term memory (LSTM) neural network and outperforms the state-of-the-art techniques based on symbolic chord annotations in the field.
One of the main factors that influence music perception is the hierarchical structure of music
compositions. Regardless of their level of musical knowledge and harmonic sensitivity [
Music structuring is one of the tools used by composers to tell a story. According to [
Figure 1 shows the structure of Helter Skelter by The Beatles, highlighting the musical chords
of the song. In the example, by means of the alternation between verse and refrain the artist
establishes a common repetitive pattern. The addition of an instrumental section after the
second refrain and the repetition of the intro reinforces the repetitive aspect of the composition.
The upcoming outro section denies the expectation of a new verse, right before the song ends.
Expectation and the way it is fulfilled or denied is an essential part in musical enjoyment [
Music structure segmentation is a broad term related to the study of musical form, which
describes how musical pieces are structured. In particular it can be divided in two main
categories: phrase-structure segmentation and global segmentation [
Most of the recent methods and research approaches are based on audio analysis techniques
[
In this paper, we focus on the music structure segmentation task by only taking into account harmonic information extracted from symbolic notations (music chord annotations). The assumption behind this approach is that the identification of harmonic sub-sequences (harmonic patterns) can be influential in defining the structure of a song and the sections of which it is composed. For instance, by taking a closer look at Figure 1 it is easy to notice how harmonic information can provide valuable information in the structure segmentation task: all verses are roughly based on the same harmonic progression (E, G, A, E) while refrains are based on a diferent harmonic progression ( A, E, A, E, E). A segmentation strongly based on those recurrent patterns is likely to be coherent with the way the composer shaped the progression in the first place.
The objective of this paper is threefold: (i) we propose pitchclass2vec, a novel chord embedding method; (ii) we use this encoding with a recurrent neural network on a corpus of musical chords; and (iii) we compare the performance of the encoding with the state-of-the art methods in the ifeld.
The chord embedding method proposed, pitchclass2vec, encodes a chord using a one-hot
encoding of the notes that compose it by making use of word embedding techniques. Each
embedded chord is defined to be similar to the embedding of its neighbouring chords in an
harmonic progression. This formalization is supposed to approximate the semantic meaning of
a chord [
The paper is organised as follows: Section 2 introduces the related works, Section 3 describes the novel chord embedding method and the recurrent neural network used for the segmentation task. Section 4 presents the experiments performed and Section 5 gives an overview of the obtained results. Finally in Section 6 we discuss the results and new research directions to be explored.
Automatic segmentation on audio signal is a prolific research field in which many diferent
solutions have been presented, ranging from self-similarity matrices [20, 21] to neural network
based methods [22, 23, 24]. Harmonic content has been used to improve those methods both
using probabilistic models [25] and transformer based models [26]. Significant research has
been performed on phrase-level structural segmentation based on melodic [27, 28, 29] as well as
polyphonic content [30]. However, to the best of our knowledge, the only approach proposed
in literature for global music segmentation on symbolic harmonic content is FORM [
FORM performs structural segmentation by exploiting repeated patterns extracted from
harmonic progressions encoded as sequences of strings. Each string represent a chord. In the
original work chord labels are transformed into 24 class of chords, 12 major chords and 12 minor
chords, while every other chord feature is removed. In this paper, FORM is re-implemented
in order to compare the results of the proposed method with the current state of the art (see
Section 5). FORM pattern detection algorithm is based on sufix trees. Each node on a sufix
tree represents a (possibly recurrent) sub-sequence of a string. FORM extracts sub-sequences
appearing in at least two position in the analyzed harmonic progression. A partial segmentation
is obtained by labeling each sub-sequence as a new section. The final segmentation is obtained
by labeling remaining sub-sequences as their preceding neighbouring section. The results are
compared with a random baseline that generates arbitrarily long structures and to a heuristic
that assigns to each composition the typical pop song structure ABBBBCCBBBBCCDCCE [
Our structure segmentation method is based on our novel chord representation method,
pitchclass2vec, based on continuous word representation. The core idea of continuous word
representation is based on the Distributional Hyphotesis [
∑ log ( =1 ∈ | ), function ( where represents the indices of the words that appears as context of the word and the | ) is parameterized using -dimensional vectors in ℝ , respectively u and v .
The problem can be framed as a binary classification task in which words are predicted to be present (or absent) from the context of . A similarity function ( , ) between two words and , can be computed as the scalar product u v . The representations obtained by training the described method on a large corpus correctly approximates the semantic meaning of words. In the last few years, continuous word representation has been applied in a growing number of application areas, achieving state-of-the-art results in the natural language processing field [31] in tasks such as part of speech tagging[32], named entity recognition[33] and document classification[ 34].
The described approach has been first proposed by the
word2vec skipgram model [
Word2vec, however, is limited by the lack of morphological knowledge of a word. When computing the representation of a word, none of its morphological components are taken into account. Let’s take for instance two morphologically similar words, house and housing. Their computation does not share any common element and the final representation of the words will not be influenced by their similarities. Fasttext [17] was presented as a solution to this issue and has proven to be more efective in the representation of a word using continuous representations. The novel aspect is in the way representations are computed. At first the n-grams that compose a word are extracted. For each n-gram a continuous vector representation is computed, using the same methodology as word2vec. The representation of the original words is finally obtained as the sum of its n-gram components. Using this technique, the final representation of a word is conditioned by its morphological structure. When two words share one or more n-grams their vectors will be the sum of at least one common element, which will bias both vectors in being more similar to each other. An additionally advantage of the fasttext approach is the way out-of-vocabulary words (words that never appear in the training corpus, and whose representation is hence unknown) are handled. When using fixed approach such as word2vec, (a) word2vec (b) fasttext out of vocabulary words are represented as a static vector, usually randomly sampled from a normal distribution. Fasttext instead is able to compute the representation in a meaningful way, given that at least one of the n-grams in the out-of-vocabulary term has been computed previously in the training corpus. Figure 2 shows a visual comparison between word2vec (Figure 2a) and fasttext (Figure 2b).
Continuous word representations have already been applied to chord symbols with promising results. In chord2vec [35] the authors obtain state-of-the-art results on the log-likelihood estimation task. Log-likelihood estimation is the task of correctly estimating, given one element in a sequence, the probabilities of another element being the upcoming element in the sequence. Chord2vec is inspired by the word2vec method, in which chords are represented by the notes that they are composed of. The representation model proposed by chord2vec is similar to pitchclass2vec. Instead of computing chord representations with the notes that compose a chord, the representations of pitchclass2vec takes into account the relationship between the notes that compose each chord. An in depth discussion is presented in section 3.
More recently, word2vec-based approach on symbolic chord annotations has been analyzed by [36]. Chord representations are based on the chord label without taking into account the notes that compose it. The encoding is then used on two diferent tasks: chord clustering and log-likelihood estimation. The log-likelihood estimation task is used to investigate the historical harmonic style of diferent composers. The log-likelihood results strongly correlates with current musicological knowledge. For instance the model finds dificult to predict chords from artists that make a sporadic use of common harmonic progressions [36]. The chord clustering task highlights how it’s possible to observe similarities between functionally equivalent chords (chords that shares notes between each other) and a well defined diference between functionally diferent chords. Continuous word representations are hence adequate to encode chords in the ifrst place, and more importantly they are able to autonomously internalize relations between chords that have been previously observed by domain experts.
Embedding approaches used in natural language processing have obvious limitations when it comes to dealing with musical content, such as musical chords. While relying on purely syntactical representations has been show to correctly encapsulate some forms of domain knowledge [36], more advanced representations are needed to obtain accurate results when dealing with harmonic progressions [35].
There are, however, some ambiguous cases in which both vector representations might C:maj131, whose notes are respectively C:maj = {, , } and C:maj13 = {, , , , , } introduce wrong similarities between chords. Let us take for instance the chords C:maj and . Both chords’ labels only difer by two characters, however the diference between the notes that they are composed of can’t be neglected. A method exclusively based on syntactical information would wrongly represent the vectors as similar between each other. Conversely, only relying on the notes that compose a chord results in ambiguous representations of some particular classes of chords, called enharmonic chords. For instance, the enharmonic chords C:dim and Eb:dim share the exact same set of notes, C:dim = Eb:dim = {, , , } represented as diferent chords as they serve diferent harmonic purposes.
but need to be Chord2vec would wrongly represents both chords as the same exact vector.
In order to overcome the aforementioned limitations, we propose an encoding which requirements can be summarised as follows: 1. it has to be based on the constituent notes of a chord, rather than its label; and 2. it must take into account the relation between those notes instead of the notes themselves.
The proposed encoding is grounded on tonal music theory: each chord is composed of a set of notes ⊂
, where is the set of all notes and is called the pitch class of a chord.
An important distinction is represented by the root note, which names the chord and plays an important role in its harmonic function.
We encode each chord as the Cartesian product ℐ = root × between the root note and the pitch class of the chord. The vector representation u of a chord is computed as u = ∑ u
∈ℐ where u is the vector representation of the tuple ∈ ℐ . See Figure 3b for a visual reference on how pitchclass2vec handles enharmonic chords and Figure 3a on how chords with common components are handled. This formalization can be seen as an extension of the chord2vec [35] method, in which the chord inner structure is taken into consideration as well.
Nevertheless, the label of a chord has a well-defined semantic. Chords composed of the same
set of notes may have diferent harmonic functions. For example, the chords
G:min7 and Bb:6,
despite diferent labels contain the exact same notes: G:min7 = Bb:6 = {, , , }
problem is particularly evident in datasets containing annotations made by experts, where the
. This
1In Harte[
(b) C:dim and Eb:dim chord embeddings. Both chords are composed of the same notes but using mostly diferent components. choice of label is the result of a meticulous analysis. For this reason, we have implemented two diferent variants of pitchclass2vec: (i) a variant combining the approach proposed by word2vec with pitchclass2vec; and (ii) a variant combining fasttext with pitchclass2vec.
In order to obtain mixed embeddings we test diferent hybrid combinations before passing the new representation to the LSTM model: (i) concatenating the embeddings; (ii) concatenating the embeddings and projecting the result in a -dimensional vector, using a fully connected layer; (iii) projecting the embeddings in the same -dimensional space by using two diferent fully connected layer and summing the -dimensional vectors; (iv) computing a new representation of each embedding by using two separate LSTM layers and summing the resulting vectors; (v) computing a new representation of each embedding by using two separate LSTM layers and concatenating the resulting vectors.
None of the combination used proved to be able to outperform the others and we decided to
stick to the first simpler and faster approach.
3.1. Implementation details
The model is implemented using pytorch. We train the model on a set of ≈ 16000 chord
progressions (with a total number of over 1 chord instances), taken from the Chord Corpus
(ChoCo) dataset [37]. ChoCo is a chord dataset consistsing of more than 20000 tracks taken
from 18 diferent professionally curated datasets. All datasets have been parsed in JAMS [ 38]
format and converted in Harte Notation [
This section shows how the proposed model compares to FORM [
Although in literature there are neural network architectures that have proven to perform
better in similar task [
We split our dataset in the usual training, validation and test split (respectively 800, 178 and 89 elements) and fine-tune each model hyper-parameters (number of LSTM stacked layers, LSTM hidden size, dropout probability) to obtain the best results on the validation set. The final configuration of each model is summarised in Table 2. Training is performed using an NVIDIA RTX 3090 with a batch size of 128. Each model takes at most few minutes to train and average less than 2 milion parameters.
We compare the proposed embedding model to fasttext and word2vec as well, in which both
methods are trained on the string labels of chords in Harte format. Both the models are trained
using the highly optimized gensim [
The results of the experiments are summarised in Table 3. We evaluate the segmentation results
by computing pairwise precision, recall and F1-score ( , and 1 in Table 3) [
Pairwise metrics are computed as the usual precision, recall and F1 scores on the set of
identically labeled pairs in the sequence. Precision and recall can be interpreted as the amount
of accuracy that is influenced respectively by under-segmentation and over-segmentation. On
the other hand under and over-segmentation scores are computed by taking into account the
normalized conditional entropy of the segmentation. In short, gives a measure of how much
information is missing in the predicted segmentation, given the ground truth segmentation while
gives a measure of how much noisy information are the result of the predicted segmentation
[
We evaluate our models based on the 1 and 1 scores of Table 3 since both metrics gives a balanced measure of over and under segmentation.
FORMsimple detect repetitive patterns from simplified chord labels, as shown in [
(a) High over-segmentation example. = 1 since if we take each chord in the sequence pairwise then each chord that should be in the same section is indeed in the same section. = 1 since the accuracy of the prediction can be easily explained by the over-segmentation phenomena. Conversely, = 0.53 and = 0.53 clearly show how the prediction is not able to capture all the needed segments but rather merges ground truth segments together. (b) High under-segmentation example. The exact opposite of Figure (a) is displayed. The prediction is not able to capture segments and rather place each chord on its own segment. (c) , and , compared. In this edge case the main diference between the two measures is highlighted. While and suggests a decent segmentation and clearly states a completely wrong segmentation. Pairwise metrics can be misguiding in absence of and .
All the neural models in table 3 outperforms FORM. Even though each neural model shows some diferences in term of metrics, the clear trend is that syntactical-based models ( fasttext and word2vec) yield overly segmented results, as the low score suggests, while the approach taken by pitchclass2vec produces a more balanced segmentation, as suggested by the 1 score. Surprisingly, fasttext and word2vec under-performs when compared to the FORM baseline on 1 metric. The model is not able to generalize enough over the representation and cannot detect patterns that are detected by FORM. Finally, the combination of pitchclass2vec with either fasttext or word2vec doesn’t bring any remarkable benefit to our novel representation. Even though an higher 1 score is obtained by using an hybrid approach, the lower 1 score suggests that it has an underlying less accurate segmentation, similar to example (c) in Figure 5.
In this article, we presented a new embedding method for musical chords, pitchclass2vec, that considers the component notes of the chord (also called pitchclass), instead of the chord label, as used in embedding methods in the natural language processing field. In addition, we proposed hybrid embedding forms, which combine embedding on the chord label and the novel pitchclass2vec. We compared diferent embedding models, including pitchclass2vec with the state-of-the-art approach in the field of music structural segmentation. We used ChoCo, a dataset of chord annotations, for training the embeddings and Billboard, a dataset of structurally annotated tracks, for the music segmentation task. We used the diferent types of embeddings on a recurrent neural network (LSTM). The results obtained by using our embeddings outperform the state of the art in every case, with the best result obtained by pitchclass2vec, achieving a pairwise F1 score of 0.548 and an over-under-segmentation F1 score of 0.538.
Pitchclass2vec is efectively able to learn the harmonic relationships that ties diferent chords together. Even though the experiments based on fasttext and word2vec proves to be efective as well, the musical theoretical approach upon which we base pitchclass2vec is an essential factor that needs to be taken into account. The presented embedding model proves to be a promising method to improve results in MIR tasks that can be complemented with harmonic information. Moreover, it provides a valuable tool to better understand and analyse harmonic progressions, since it allows a richer comparison between chords and chord sequences when compared to string labels.
There are additional information that we plan to integrate on pitchclass2vec to obtain a richer and more accurate representation. For instance, one of the main limitations of our approach stems from the fact that we do not take temporal information into account. We plan to test this possibility by using the temporal information directly in the embedding process and further modify the LSTM model to condition the classification of the section of a chord based on its duration. As discussed in Section 3, chord labels have their own semantic as well. Since the hybrid models proposed did not directly result in more accurate results, we plan on expanding the pitchclass2vec method to take into account the label of a chords as well directly in its embedding model. To obtain a semantically richer representations we plan on enhancing pitchclass2vec by using deep contextual word embeddings [50] along with knowledge enhancement techniques [51] that combines domain-specific ontologies, such as [ 52], with deep contextual word embeddings.
Moreover, we plan an in-depth analysis of pitchclass2vec training parameters, described in
section 3.1, since in [
It is worth mentioning that the LSTM model that we implemented for the structure
segmentation task does not take advantage of two fundamental aspect of the task itself: the segmentation
of a musical piece should be conditioned by its musical genre. In fact, the annotation guidelines
provided in [
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