# Automatic Detection of Moral Values in Music Lyrics

###### Abstract

Moral values play a fundamental role in how we evaluate information, make
decisions, and form judgements around important social issues. The possibility
to extract morality rapidly from lyrics enables a deeper understanding of our
music-listening behaviours. Building on the Moral Foundations Theory (MFT), we
tasked a set of transformer-based language models (BERT) fine-tuned on 2,721
synthetic lyrics generated by a large language model (GPT-4) to detect moral
values in 200 real music lyrics annotated by two experts. We evaluate their
predictive capabilities against a series of baselines including out-of-domain
(BERT fine-tuned on MFT-annotated social media texts) and zero-shot (GPT-4)
classification. The proposed models yielded the best accuracy across
experiments, with an average F1 weighted score of 0.8. This performance is, on
average, 5% higher than out-of-domain and zero-shot models. When examining
precision in binary classification, the proposed models perform on average 12%
higher than the baselines. Our approach contributes to annotation-free and
effective lyrics morality learning, and provides useful insights into the
knowledge distillation of LLMs regarding moral expression in music, and the
potential impact of these technologies on the creative industries and musical
culture.

##  1 Introduction

Figure 1: Model Structure for predicting Moral Foundations (MFT) in Lyrics,
fine-tuned on out-of-domain social media data, and synthetically generated
lyrics with GPT-4.

Lyrics play a crucial role in how we experience music, affecting our emotions
and actions. Positive lyrics can motivate and elevate listeners, whereas
negative or aggressive content in songs may negatively impact mood and
behaviour [1]. Social, political, and cultural issues, such as racial
inequality and gender discrimination, are often reflected in the music lyrics
of their time [2, 3]. Songs that feature in successful campaigns typically
include uplifting melodies and lyrics that reflect the ideals of a nation,
representing values of optimism and progress towards a better future [4].
Moral rhetoric in lyrics has been used to advocate for what is perceived to be
a necessary societal change [5], promote peace and unity [6], and raise
awareness for marginalised groups [7]. These narratives are closely related to
moral judgements and beliefs, yet their relationship to music listening
behaviors has received limited attention by music scientists.

In the field of Music Information Retrieval (MIR), lyrical content analysis
has focused primarily on genre classification [8], mood prediction [9],
emotion dynamics [10], and lyrics-to-audio alignment [11, 12]. Recent works
have elaborated on less attended psychological characteristics of music
lyrics, including moral valence. For example, insights into personal values
and personality traits derived from lyrics can enhance various MIR tasks,
including genre classification, audio tagging, and music recommendations [13].
Preniqi and colleagues [14] showed that moral valence extracted from lyrics
can to some extent predict listeners’ moral values, in some cases more
accurately than audio features. The possibility to extract morality rapidly
from lyrics can enable a deeper understanding of our music listening
behaviours.

Inferring moral values from song lyrics is a complex natural language
processing (NLP) task from the start due to the subjectivity of our
perceptions and interpretations. The progress is further hindered by the lack
of annotated lyrics for training new or fine-tuning pre-trained models, and
for benchmarking. Using models fine-tuned with out-of-domain annotated texts
(e.g., from social media [15, 16]) to predict moral values in music lyrics
faces significant challenges due to the unique structure of lyrics compared to
other textual forms (e.g., greater use of repetition, metaphor, imagery, and
other poetic devices).

In light of the above, we investigate the novel task of automatic detection of
moral values in music lyrics using an integrated approach that leverages the
strengths of two distinct NLP technologies. Specifically, we leverage the
generative capabilities of GPT-4 (Generative Pre-trained Transformer) to
create morally nuanced synthetic lyrics—a process required only once—and
employ BERT (Bidirectional Encoder Representations from Transformers), which
demands fewer computational resources, to learn from the synthetic data
structure.

Following recent related work [17, 14, 15], we operationalize morality drawing
on Haidt and Graham’s Moral Foundations Theory [18], which outlines five core
moral traits, or foundations, divided into “virtue” and “vice” based on moral
polarity: Care and Harm, Fairness and Cheating, Loyalty and Betrayal,
Authority and Subversion, Purity and Degradation. We developed a corresponding
set of 10 single-label classification models, each customized to predict the
presence or absence of one moral value in lyrical text. MFT is a
straightforward yet comprehensive model for understanding moral values,
uniquely characterized by well-developed term dictionaries [19].

We present a dataset of 200 real song lyrics human-annotated with MFT. To the
best of our knowledge, this is the first such dataset. It serves as the basis
for evaluating our proposed method. We make the real and synthetic lyrics
datasets, and the paper code fully available via a GitHub
repository.111https://github.com/vjosapreniqi/ismir-mft-values

We report a comprehensive comparison of the proposed models against BERT fine-
tuned with out-of-domain human-annotated moral text data and zero-shot
classification with GPT-4. Figure 1 summaries the overall pipeline of this
work. The proposed models yielded the best accuracy across experiments, with
an average F1 weighted score of 0.8. This performance is, on average, 5%
higher than out-of-domain and zero-shot models. When examining precision in
binary classification, the proposed models perform on average 12% higher than
the baselines. Our approach contributes to annotation-free lyrics morality
learning, and provides useful insights into the knowledge distillation of
large language models such as GPT-4 regarding moral expression in music.

##  2 Related Work

The field of music and moral expression has received limited attention.
However, recent studies have shown a link between an individual’s moral values
and their preferences for lyrics and music, suggesting significant
implications for tailoring personalisation in streaming services [20, 14, 17].
Further research has delved into how moral values and lyrical preferences
manifest within specific music communities. For example, Messick and Aranda
[21] demonstrated that moral values could explain a unique and significant
portion of the variance in lyrical preferences among fans of different metal
music sub-genres.

Given the understanding that verbal expressions more effectively convey
morality than non-verbal forms [17, 22], initial studies introduced lexicons
[23, 24] as an extension of Moral Foundations Dictionary (MFD) [25] for
identifying words and lemmas that accurately depict moral foundations. More
recent studies focused on examining moral values in texts using human-
annotated social media datasets[26, 27, 28], and introducing more advanced
Natural Language Processing (NLP) approaches to detect moral dimensions in
textual content[16, 15]. Trager et al.[27] introduced baseline models for
predicting moral values, employing a pre-trained BERT model fine-tuned on the
Moral Foundation Reddit Corpus. Guo et al. [16] proposed a multi-label model
for predicting moral values with Twitter and news data, incorporating the
domain adversarial training framework suggested by Ganin et al. [29] to align
multiple datasets and generalise for out-of-domain predictions. A similar
approach was taken by Preniqi et al. [15] in predicting moral values in
different social media domains.

However, a main challenge that persists is the ability of these models to
generalise across various domains. Lisco and colleagues[30] demonstrated that
text classifiers perform better when domains are similar. This poses a major
obstacle when predicting morality in lyrics because there is no prior study
that has presented an annotated lyrics dataset with moral values. Further,
manually annotating extensive text demands substantial time, resources, and
deep understanding of Moral Foundations Theory (MFT).

To overcome these limitations, we employ GPT-4, an advanced LLM, to generate
lyrics infused with various moral undertones, which helps in fine-tuning a
moral classifier. This minimises the need for laborious manual annotation of
extensive lyric databases, enabling us to utilise a smaller, human-annotated
dataset to validate the effectiveness of knowledge distilled from GPT-4. The
capacities of LLMs for music tasks are being actively explored for the moment.
Doh et al.[31] similarly employed a large language model such as GPT-3 for
generating pseudo captions from tags to mitigate the problem of data scarcity
in the field of automatic music captioning. While Zhang et al [32] evaluated
the quality and correctness of generated music lyrics via GPT-3. Sawicki et
al. [33] investigated the possibility of using GPT-3 models to generate high-
quality poems in a specific author’s style while suggesting that GPT-3 can be
a useful tool in assisting authors.

##  3 Method

###  3.1 Human-Annotated Lyrics

For this work, we annotated 200 song lyrics, categorising them into 10
different moral foundations. This annotation process was conducted by two
skilled annotators: the lead author of this study and an external researcher
with a background in music and sound design, both of whom agreed to
contribute. Before starting, the annotators were informed about their
participation rights, including the option to discontinue their involvement at
any point. Each annotator was assigned with 125 songs for annotation. To
evaluate the agreement between annotators, 50 songs were annotated by both
annotators. The inner-annotator agreement was assessed using Cohen’s kappa
coefficient for each moral label. This resulted in an almost perfect agreement
[34] with an average score of 0.86 across all moral categories identified
within the lyrics of the chosen songs. We selected the songs for the moral
values annotation from the Wasabi Dataset [35], known for its extensive
collection of 2 million songs including lyrics, artist gender, and musical
genre among other data. This dataset spans over five decades, enabling the
selection of songs from various eras. The process of selecting the songs
involved a semi-random approach, with efforts made to retain the distribution
of genres, and the timeline of song releases as found in the original dataset.
Among the 200 songs annotated for moral values, 18 were from the 60s and 70s,
78 from the 80s and 90s, and 116 from the post-2000 era. The chosen songs
represented a balanced mix of genres including Rock, Pop, Hip-Hop, R&B, Soul,
and Country. Figure 2 depict the distribution of Moral values in the human-
annotated song lyrics with the proportion of genre for each MFT value.

Figure 2: Distribution of Moral Foundations in 200 song lyrics dataset
annotated by human annotators with genre proportions for each moral value.

###  3.2 Predicting Morality in Lyrics with Domain Adaptation

Initially, we tried to predict moral values in lyrics by fine-tuning a BERT
model with out-of-domain social media data, following the approach used by
Preniqi et al. [15]. We utilised 20,628 tweets from the Moral Foundation
Twitter Corpus (MFTC) [26]; 13,995 posts from the Moral Foundations Reddit
Corpus (MFRC) [27]; 1,510 posts from Facebook vaccination dataset [28].
Preniqi’s and other work have demonstrated that predicting moral values using
a single-label approach—predicting one MFT value at a time—results in higher
accuracy [27, 15]. Informed by these findings, we developed a set of single-
label classification models tailored to predict individual moral foundations
in lyrics.

As a baseline model, we apply a similar approach to the MoralBERT [15]. We
identify the polarities (virtues and vices) of moral foundations, as opposed
to just identifying the mere presence or absence of moral values. We
incorporate the domain adversarial method aiming to improve the models’
ability to generalise effectively in predicting moral values in lyrics [16,
15]. Adopting this model, we start by deriving a domain invariant
representation $h$ from the BERT CLS embedding $e$:

$h=W_{inv}e$

where $W_{inv}\in\mathcal{R}^{768\times 768}$ is a learnable matrix. Next, we
calculate moral values predictions $\hat{y_{m}}$ using:

$\hat{y_{m}}=Softmax(W_{1}(ReLU(W_{2}h)))$

with $W_{1}\in\mathcal{R}^{768\times 768}$, $W_{2}\in\mathcal{R}^{768\times
c}$ representing 2 learnable matrices, $c$ being the number of classes, $ReLU$
is the rectified linear unit activation function and $Softmax$ is the
normalised exponential function. A domain classification head is also included
for obtaining domain predictions $\hat{y_{d}}$:

$\hat{y_{d}}=Softmax(W_{3}(ReLU(W_{4}h)))$

with $W_{3}\in\mathcal{R}^{768\times 768}$, and
$W_{4}\in\mathcal{R}^{768\times d}$ learnable matrices and with d being the
number of domains in the training set. The main rationale of the adversarial
network is increasing the loss from the domain head while minimising the loss
from the moral values prediction. Hence, the model is “forced” to learn
domain-invariant representations. This is achieved by integrating a gradient
reversal layer before the domain classification head, while using standard
training for minimising moral prediction loss. Cross-entropy ($CE$) loss is
used for both the moral and domain classification heads. The final loss is
expressed as:

$L=CE(\hat{y_{m}},Y_{m})-CE(\hat{y_{d}},Y_{d})+L_{norm}+L_{rec}$

with and $Y_{m}$ and $Y_{d}$ as the ground truth for moral values and domain,
respectively. Two regularisation terms from [16] are added: L2 norm
regularisation and reconstruction loss:

$\displaystyle L_{norm}=||W_{inv}h-I||^{2},\quad L_{rec}=||W_{rec}h-e||^{2}$

similar to $W_{inv}$ (defined above), $W_{rec}\in\mathcal{R}^{768\times 768}$
is also a learnable matrix and $I$ is the identity matrix. These
regularization losses are combined with moral and domain classification
losses. The regularization terms are not applied when training MoralBERT on a
single domain (e.g., when trained on just synthetic lyrics).

The binary setting we use implies the model should learn from highly
unbalanced datasets, where the neutral label (negative class) is far more
represented than the single moral value to be predicted in each instance
(positive class). To address the class imbalance, we employed two methods.
First, weights are assigned to classes[36]:

$weight_{c}=\frac{N-N_{c}}{N}$

where $N$ is the total training samples and $N_{c}$ is the count of samples
per class $c$. Second, similar to [37], we employed a separate threshold
$\theta_{v}$ for each moral value $v$, so that we use $\hat{y_{m}}$ to obtain
the final prediction $\hat{m}$:

$\hat{m}=\begin{cases}1&\text{if $\hat{y_{m}}>\theta_{v}$}\\\
0&\text{otherwise}\end{cases}$

with $\hat{m}=1$ indicating the moral value is present in the lyrics and
$\hat{m}=0$ indicating it is not. The optimal value $\theta_{v}$ for each
moral value $v$ was found by optimizing for binary F1 during training,
searching in the search space 0.05 to 0.95 with a step of 0.05. The models
were trained for 20 epochs using a single Nvidia T4 GPU, a learning rate of
5e-5, and the Adam optimiser for all MoralBERT experiments.

###  3.3 Synthetic Lyrics Generation for Moral Assessment

There is a growing interest in knowledge distillation from large pre-trained
language models via synthetic text generation [38]. Here we apply a similar
knowledge distillation approach by utilising GPT-4 for synthetic lyrics
generation. This method eliminates the need to collect real-life data, which
is often difficult to gather for a specific NLP task and with a specific input
distribution [39]. Initially, we assessed GPT-4’s familiarity with Moral
Foundation Theory [25], confirming its fundamental understanding of moral
values. We tasked GPT-4 with generating lyrics by formulating a prompt, as
follows:
Prompt: You are an assistant to a songwriter, you need to assist in writing
lyrics related to the Moral foundations described in the Moral Foundation
Theory. Given the {Moral Foundations Tags} , which represent {Description
Tags}, write original lyrics of a song expressing these moral foundations. DO
NOT directly mention these moral foundations. DO NOT explicitly talk about
morality. Write it in the style of {Artist Tags}.

We assigned a “role” (songwriter assistant) for the model and provided three
types of “input tags”. The {Moral Foundations Tags} comprise any of the 10
moral values. The resulting lyrics can represent 1, 2, or 3 moral values. We
determined this based on the moral combinations observed in our human-
annotated lyrics dataset. The {Description Tags} represent fundamental
concepts of each moral value. The {Artist Tags} represent the names of artists
whose styles we employ to diversify the lyrics. Initially, we intended to
commence the lyrics generation task solely using moral categories and genres
as tags. However, we observed that the lyrics were more uniform and generic
compared to when we incorporated the artist’s style. To tailor the lyrical
style using various artists, we employed MusicOSet [40], a collection of
musical elements (e.g., music, albums, artists, genres and popularity)
suitable for music data mining. To capture the nuances of different genres, we
organized the artists according to their popularity and grouped them into
prevalent genres like Rock, Pop, Country, Hip Hop, R&B, Soul, Folk, Blues, and
Jazz. These genres align very closely with those in the song lyrics we
selected for human annotations. We chose to utilise this dataset because it
offers detailed data on artist genres and sub-genres, as well as an artist
popularity metric that we employ in developing lyric styles. We acquired a
dataset comprising 2,721 artificially generated lyrics, each aligned with
moral categories similar to our human-annotated lyrics dataset. On average,
the generated lyrics had 146 words, with a total of 10,305 unique words across
the synthetic lyrics dataset.

###  3.4 GPT-4 in Moral Classification Task

In addition, we wanted to assess the capability of the 0-shot GPT-4 model in
classifying morality in actual song lyrics while comparing it to our proposed
model. To do so, we prompted the task as follows:

Prompt: You will be provided with song lyrics. The song lyrics will be
delimited with #### characters. Classify each lyric into 10 Possible Moral
Foundations as defined in Moral Foundation Theory The available Moral
Foundations are: {Moral Foundations Tags}. The explanation of the moral
foundations is as follows: {Description Tags}. This is a multi-label
classification problem: where it’s possible to assign one or multiple
categories simultaneously. Report the results in JSON format such that the
keys of the correct moral values are reported in a list.

The song lyrics utilised for the GPT-4 model classification are the same as
the ones annotated by human annotators. In this way, we can compare the human
annotations with those of the model while assessing the general performance of
GPT-4 for the classification task.

##  4 Experiments

| F1 Scores Weighted Average | F1 Scores Binary
---|---|---
|  | MoralBERT
---
GPT-4 | BERT SL |  | MoralBERT SL
---
| MoralBERT
---
GPT-4 | BERT SL |  | MoralBERT SL
---
Care | .80 ± .03 | .68 ± .03 | .81 ± .03 | .83 ± .03 | .68 ± .05 | .64 ± .04 | .68 ± .05 | .75 ± .04
Harm | .68 ± .03 | .75 ± .03 | .71 ± .03 | .70 ± .03 | .62 ± .05 | .71 ± .04 | .63 ± .05 | .69 ± .04
Fairness | .55 ± .03 | .73 ± .03 | .73 ± .03 | .74 ± .03 | .30 ± .05 | .39 ± .06 | .41 ± .06 | .38 ± .06
Cheating | .84 ± .03 | .80 ± .03 | .86 ± .02 | .69 ± .03 | .27 ± .09 | .16 ± .07 | .52 ± .08 | .32 ± .06
Loyalty | .69 ± .03 | .67 ± .03 | .77 ± .04 | .79 ± .04 | .38 ± .06 | .34 ± .06 | .21 ± .08 | .27 ± .09
Betrayal | .81 ± .02 | .72 ± .03 | .89 ± .02 | .84 ± .02 | .34 ± .07 | .31 ± .06 | .40 ± .11 | .37 ± .08
Authority | .77 ± .03 | .75 ± .03 | .77 ± .03 | .84 ± .03 | .45 ± .06 | .42 ± .06 | .35 ± .07 | .39 ± .09
Subversion | .80 ± .03 | .72 ± .03 | .80 ± .03 | .71 ± .03 | .44 ± .07 | .39 ± .06 | .40 ± .07 | .43 ± .06
Purity | .77 ± .03 | .86 ± .02 | .89 ± .02 | .90 ± .02 | .41 ± .06 | .56 ± .07 | .55 ± .08 | .63 ± .08
Degradation | .74 ± .03 | .81 ± .03 | .81 ± .03 | .86 ± .03 | .34 ± .06 | .40 ± .07 | .30 ± .07 | .32 ± .10
Average | .75 ± .03 | .75 ± .03 | .80 ± .03 | .80 ± .03 | .42 ± .06 | .43 ± .06 | .45 ± .07 | .46 ± .07
Table 1: F1 scores of prediction models with standard deviation estimated via
1,000 bootstraps. Weighted average scores account for both moral and non-moral
(neutral) classes, while binary scores only for moral classes. SL = Synthetic
Lyrics.

Figure 3: Precision scores for binary classification with standard deviation
estimated via 1,000 bootstraps.

We started by analysing the MoralBERT technique [20] and fine-tuned models
using social media data from Twitter, Reddit, and Facebook. The total number
of text records was 35,887. We found that 51% of the texts were neutral and
49% of them were labeled with one or more moral values. This indicated a
significant skew towards neutral texts, which we addressed by adding the class
weighting technique. After that, we evaluated the BERT models fine-tuned with
only GPT-4 generated lyrics. We call these models "BERT SL". We also fine-
tuned the models with a combination of out-of-domain social media data and the
generated lyrics data which we call "MoralBERT SL". We used the Domain
Adversarial module only when fine-tuning BERT with multiple domain data,
including synthetic lyrics. When fine-tuning solely with synthetic lyrics,
this module was not utilized. Lastly, we evaluated GPT-4’s zero-shot
classification capabilities against our models on the manually annotated song
lyrics.

The results show that the models achieving the highest performance were BERT
SL and MoralBERT SL. These models performed on average 5% better across all
moral values in terms of F1 weighted score which accounts for both moral and
non-moral prediction classes. While for the binary F1, these models were
marginally better than GPT-4. For harm foundation, GPT-4 performed slightly
better, possibly due to the synthetic lyrics’ lack of natural variability when
expressing this foundation. The fact that MoralBERT SL and BERT SL
performances are similar to the one from GPT-4 for binary F1 is expected as
the same latent knowledge of GPT-4 has been distilled into BERT by using the
generated lyrics. The improvements from MoralBERT SL and BERT SL are
significant for what concerns weighted F1, suggesting that given the
supervised setting of these models, they were also able to learn the higher
prior probability of non-moral (e.g., neutral) instances, which generally
outweigh moral instances. The same is evident if we look at Figure 3, which
compares the binary Precision scores of the various models. From the figure,
it is evident that MoralBERT SL and BERT SL exhibit significantly higher
Precision surpassing GPT-4 and MoralBERT by 12% on average. These models,
then, are often correct when labelling lyrics with moral values (even though
results vary according to which moral value), while being more cautious in
assigning a moral value, given the preponderance of neutral cases. For the
evaluation metrics, we report the standard deviation estimated via
Bootstrapping which is a statistical resampling technique used to estimate the
variability of the metrics. We used 1,000 bootstraps which is typically
sufficient to achieve a reasonable approximation of the standard deviation.

Song Name |  Artist |  Human Annotations |  MoralBERT |  GPT-4 |  BERT SL MoralBERT SL
---|---|---|---|---|---
“Take This Heart of Mine” |  Foghat |  Care, Purity |  Care, Purity |  Care, Loyalty |  Care, Fairness, Purity
“Who’s Cheatin’ Who” |  Charly McClain |  Cheating, Betrayal |  Cheating, Betrayal, Loyalty, Purity |  Cheating, Betrayal |  Cheating, Betrayal
“Samurai Showdown” |  RZA |  Harm, Authority |  Harm, Betrayal, Authority, Purity |  Harm, Loyalty, Authority |  Harm, Authority
“Man In The Mirror” |  Mark Chesnutt |  Care, Fairness |  Fairness, Loyalty, Authority |  Care, Fairness, Loyalty, Authority |  Care, Fairness
Table 2: Examples of moral values detected in song lyrics by human annotators
and model predictions.

Our findings show that BERT-based models are still comprehensible with larger
models such as GPT-4, when fine-tuned properly they can excel in specified
tasks. GPT-4 demonstrated a very good performance even without any fine-tuning
(zero-shot approach) which was anticipated given its state-of-art performance
in multiple tasks and its training on an extensive amount of data. These
models have been trained on diverse text sources such as Wikipedia, GitHub,
chat logs, books, and articles [41], enabling them to comprehend language
across various domains [31]. The earlier model, GPT-3, contains 175 billion
parameters, a figure vastly greater than BERT’s 340 million parameters [42].
Such models demand significantly more computational resources than BERT
models. In contrast, the BERT model is cost-free, easier to modify, and offers
greater control over the models due to its open-source nature. On the other
hand, BERT models need fine-tuning, which presents its own challenges due to
the necessity for manual labelling and data annotation. Therefore, a hybrid
approach like the one we suggest offers an optimised solution that combines
the best of both worlds.

Table 2 presents four song examples annotated for moral values by both human
annotators and prediction models. These examples show that MoralBERT SL and
BERT SL (not shown in the table as it shares the same outcomes as MoralBERT SL
for these instances) aligned most closely with human moral assessments. From a
general observation of the song lyrics that were annotated by humans and
tested with these models, it was noted that MoralBERT and GPT-4 tend to assign
more moral attributes per song while increasing their chances of correctly
guessing moral labels but also misclassifying neutral ones. In contrast,
models trained with synthetic lyrics more accurately identified neutral (non-
moral) lyrics, aligning with the quantitative observations of the F1 weighted
score. Typically, human annotators did not assign more than three moral values
per song. To control the number of assigned moral values per song, we adjusted
the thresholds [37] for our prediction models, ensuring optimal accuracy. When
lacking ground truth data, a post-processing can be applied for cutting moral
labels with lower probabilities. Here we present only F1 and Precision scores.
For further details, refer to the project’s results page on
GitHub.222https://github.com/vjosapreniqi/ismir-mft-values/tree/main/Results

##  5 Conclusion

In this paper, we presented an integrated approach for the automatic detection
of moral values in lyrics. We created a synthetic lyrics dataset using GPT-4
which we used to fine-tune the BERT-base model alone (BERT SL) and in
combination with out-of-domain social media corpora (MoralBERT SL). We
introduced a dataset of 200 song lyrics sourced from the WASABI dataset
annotated for moral values by two experts, serving as the basis for evaluating
our moral prediction models. We also assessed the performance of models
trained with synthetic lyrics in comparison to those trained solely on social
media data (MoralBERT) and a zero-shot GPT-4 classifier. We found that models
trained with synthetic lyrics generally achieved significantly better binary
Precision and higher weighted F1 scores compared to the GPT-4 classifier and
MoralBERT, along with marginally better binary F1.

Our research has some limitations. To begin with, the synthetic lyrics is
created via GPT-4, a powerful model but not an open-source, which limits our
control of the model. We prompted GPT-4 to create unique lyrics in the style
of various artists across different genres. Yet, adding musical composition
details, lyrical themes [43], or visual images as descriptors [44], could
enhance both the quality and diversity of the generated lyrics. However, we
only employ this method for fine-tuning to make BERT models learn the
structure and moral expressions in lyrics. The creation of truly creative
lyrics for artistic purposes requires greater sophistication and rigorous
human review [44]. Further, we analysed the overall moral expressions in the
song lyrics without differentiating between structural elements such as
verses, bridges, and choruses. Lastly, we focus on inferring moral values in
English lyrics, which limits our ability to understand moral expressions in
music lyrics from non-Western cultures.

Understanding how lyrics can convey moral values is important for the MIR
field, as it can enhance how we experience and interact with music, including
improving music tagging and recommendation systems [45]. Addressing challenges
in automatic detection of moral values in lyrics can further push the
boundaries of current technologies in natural language processing and machine
learning applied to music and other creative tasks. Further, as lyrics often
reflect societal values and cultural norms, tools for extracting morality
rapidly from lyrical text enable researchers to gain insights into the
prevailing moral attitudes of different times or cultures. This can be useful
in sociological studies, helping scholars understand how music influences and
is influenced by societal norms and changes.

##  6 Ethics Statement

In this study, we employed large language models (LLMs) to generate synthetic
lyrics. Given the vast amount of data on which these models are trained, there
is a potential for bias transfer from the training datasets. Additionally,
these models may inadvertently contain copyrighted literary works within their
training data, necessitating meticulous steps to prevent plagiarism,
particularly if the generated lyrics are utilised beyond fine-tuning for
artistic and creative outputs [46, 47].

We engaged two human annotators to label 200 songs with moral values based on
the Moral Foundations Theory (MFT). These annotators signed a consent document
that detailed the project’s objectives, their roles, and the nature of their
tasks. They were informed of their right to withdraw from the study at any
time without consequences. To protect their privacy, all data from the
annotators were anonymised.

While powerfull language models like BERT and GPT-4 offer significant
potential to enhance communication and support social campaigns, they also
pose risks if used for manipulative purposes. Our research is committed to
advancing the understanding of moral expressions in music and fostering the
responsible development and use of AI in creative contexts.

## References

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# Binary Black Hole Encounters, Gravitational Bursts and Maximum Final Spin

Matthew C. Washik  James Healy  Frank Herrmann  Ian Hinder  Deirdre M.
Shoemaker  Pablo Laguna  Center for Gravitational Wave Physics
The Pennsylvania State University, University Park, PA 16802  Richard A.
Matzner  Center for Relativity and Department of Physics
The University of Texas at Austin, Austin, TX 78712

###### Abstract

The spin of the final black hole in the coalescence of nonspinning black holes
is determined by the “residual” orbital angular momentum of the binary. This
residual momentum consists of the orbital angular momentum that the binary is
not able to shed in the process of merging. We study the angular momentum
radiated, the spin of the final black hole and the gravitational bursts in a
sequence of equal mass encounters. The initial orbital configurations range
from those producing an almost direct infall to others leading to numerous
orbits before infall, with multiple bursts of radiation while merging. Our
sequence consists of orbits with fixed impact parameter. What varies is the
initial linear, or equivalently angular, momentum of the black holes. For this
sequence, the final black hole of mass $M_{h}$ gets a maximum spin parameter
$a/M_{h}\approx 0.823\,$, with this maximum occurring for initial orbital
angular momentum $L/M^{2}_{h}\approx 1.176\,$.

###### pacs:

04.60.Kz,04.60.Pp,98.80.Qc

A few years ago, after a decades-long period of development, breakthroughs
were made in computational modeling of strong gravitational fields that now
allow numerical relativists to successfully simulate binary black holes (BBH)
from inspiral through merger. In general terms, there are now two
computational recipes to follow. One of them is based on a generalized
harmonic formulation of the Einstein equations Pretorius (2006, 2005) and uses
_excision_ Brandt et al. (2000); Shoemaker et al. (2003) of the black hole
(BH) singularities. The other recipe, called the moving puncture recipe,
involves a BSSN Shibata et al. (1992); Baumgarte and Shapiro (1999)
formulation, _punctures_ to model BH singularities and a gauge condition for
these punctures to move throughout the computational domain Campanelli et al.
(2006a); Baker et al. (2006). Using these recipes, many studies involving
interacting BHs and their generated gravitational radiation have been carried
out, including gravitational recoil Baker et al. (2007a); Gonzalez et al.
(2007); Herrmann et al. (2007a); Baker et al. (2006); Campanelli et al.
(2007a); Pollney et al. (2007); Koppitz et al. (2007), spin hang-up Campanelli
et al. (2006b) and matches to post-Newtonian (PN) approximations Baker et al.
(2007b); Hannam et al. (2007). Most center on astrophysical implications and
connection to future gravitational wave observations.

BBH simulations also enable studies of strong non-linear phenomena regardless
of traditional gravitational astrophysics consequences. A recent example is
the work in Ref. Pretorius and Khurana (2007) on the self-similar behavior
found in the approach to the merger/flyby threshold of BBHs. Similar merger
thresholds in BBH encounters or scatterings form the context for our work.

We consider orbits in which the BHs initially fly past one another, but then
fall back to orbit and merge. We focus on the gravitational waveform and the
angular momentum radiated from such encounters. Serendipitously, we find
significant astrophysical implications, both the existence of a maximum in the
final BH spin and of multiple encounter orbits with associated multiple bursts
of gravitational radiation. Ref. Pretorius and Khurana (2007) considered only
the first close encounter or “whirl,” and the study did not extend the
evolutions to find possible fall-back orbits such as those here considered.
The work in Ref. Pretorius and Khurana (2007) and our work here have to date
been the only studies considering these highly eccentric orbits; while there
have been high-order PN studies of inspiral, cases studied so far have
described relatively smooth inspirals Königsdörffer and Gopakumar (2006).

All our orbits are parabolic or hyperbolic encounters. Depending on the
merger, the fraction of angular momentum radiated varies significantly
($0.05\lower 2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}J_{rad}/L\lower
2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}0.55$ with $L$ the initial orbital
angular momentum of the binary). This emission of angular momentum sets an
upper limit of $a/M_{h}\approx 0.823\,$for the spin parameter of the final BH;
this maximum occurs when $L/M^{2}_{h}\approx 1.176\,$, with $M_{h}$ the mass
of the final merged BH.

As in our previous BBH studies Herrmann et al. (2007a, b); Herrmann et al.
(2007), we use a code based on the BSSN formulation and the moving puncture
recipe. The results here were obtained with a $634^{3}\,M$ computational
domain consisting of 10 refinement levels, with finest resolution of $M/52$.
We set up nonspinning equal mass BHs using Bowen-York initial data Bowen and
York (1980). The mass of each BH is $M/2$, computed from $\sqrt{A_{ah}/16\pi}$
with $A_{ah}$ their apparent horizon area. The data have the BHs on the
$x$-axis: BH± is located at $\pm 5\,M$ and has linear momentum
$\vec{P}_{\pm}=(\mp P\,\cos{\theta},\pm P\,\sin{\theta},0)$. We keep the angle
constant at $\theta=26.565^{\circ}=\tan^{-1}(1/2)$; thus the impact parameter
is $\sim 4.47\,M$. The total initial orbital angular momentum is given by
$\vec{L}/M^{2}=10\,(P/M)\,\sin{\theta}\,\hat{z}$. We obtain a one-parameter
family of initial data by varying the magnitude of the initial momentum in the
range $0.1145\leq P/M\leq 0.3093$. At the lower limit of the momenta, merger
occurs within less than half an orbit of inspiral. We then consider
successively higher initial momentum until we find solutions that will clearly
require a very long, “infinite” time to merge.

The results are summarized in Figs. 1 and 2. The top panel in Fig. 1 shows the
spin $a/M_{h}$ of the final BH as a function of the initial orbital angular
momentum $L/M_{h}^{2}$. The spin and mass of the final BH were computed using
the apparent horizon formula Campanelli et al. (2007b); Herrmann et al.
(2007b). The bottom panel of Fig. 1 displays the fraction of angular momentum
radiated ($J_{rad}/L=1-a\,M_{h}/L$). Figure 2 shows, as a function of
$L/M_{h}^{2}$, in the top panel the final mass $M_{h}/M_{adm}$ relative to the
total ADM mass and in the bottom panel the fraction of energy radiated
$E_{rad}/M_{adm}=1-M_{h}/M_{adm}$. The vertical lines in Figs. 1 and 2 denote
the value of $L/M_{h}^{2}$ where $a/M_{h}$ is maximum. We have also calculated
both the radiated angular momentum and energy via the Weyl tensor. The results
are consistent with those in Figs. 1 and 2. However, the values obtained form
$J_{rad}/L=1-a\,M_{h}/L$ and $E_{rad}/M_{adm}=1-M_{h}/M_{adm}$ are more
accurate because they are not as susceptible to resolution effects as those
derived from wave extraction. We have carried out simulations at resolutions
of $M/45$, $M/48$, $M/52$ and $M/64$ for ten representative cases in Figs. 1
and 2 to check convergence and make error estimates. We found that the results
are consistent with the 4th-order accuracy of our code and that the errors in
the quantities displayed in these figures are not larger than 3%.

We have selected six encounters that are representative of the different
behaviors in our series. These six cases are $L/M^{2}=$ 0.512, 1.208, 1.352,
1.376, 1.382 and 1.387 or equivalently $L/M_{h}^{2}=$ 0.521, 1.282, 1.522,
1.480, 1.498 and 1.554. We will refer to them as encounters Ea, Eb, Ec, Ed, Ee
and Ef, respectively. Cases Ed, Ee and Ef correspond to the last three points
in Figs. 1 and 2.

Figure 1: Top panel, spin of the final BH $a/M_{h}$ and, bottom panel, angular
momentum radiated $J_{rad}/L$ vs the initial orbital angular momentum
$L/M_{h}^{2}$. Figure 2: Top panel, mass of the final BH $M_{h}/M_{adm}$ and,
bottom panel, energy radiated $E_{rad}/M_{adm}$ vs the initial orbital angular
momentum $L/M_{h}^{2}$. Figure 3: BH tracks of the encounters. The coordinate
dimensions of the top four panels are $12\,M\times 12\,M$ and $16\,M\times
16\,M$ for the 2 bottom panels. Figure 4: Waveforms for the Ea, Eb and Ec
encounters.

For $L/M_{h}^{2}\lower 2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}0.8$, the
radiated angular momentum is $J_{rad}/L\lower
2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}0.15$, so the final BH has
$a/M_{h}$ close to $L/M_{h}^{2}$. The evolution is rather simple in these
cases: immediate merger, with minimal inspiral. For instance, in case Ea (Fig.
3), $L/M_{h}^{2}=0.521$, and $J_{rad}/L=0.05$; thus most of the angular
momentum goes into the final BH, $a/M_{h}=0.496$. Fig. 4.Ea shows the
corresponding radiated gravitational wave ($M\,r\,$Re$\Psi_{4}^{2,2}$). All
waveforms were extracted at radius $50\,M$.

As the initial angular momentum increases, the radiated angular momentum also
increases, suppressing and limiting the spin of the final BH. Eventually for
large enough initial angular momentum, so much angular momentum is radiated
that, as seen in Fig. 1, the final spin reaches a maximum of $a/M_{h}\approx
0.823\,$at $L/M^{2}_{h}\approx 1.176\,$. Fig. 3.Eb shows the tracks of the BHs
in the neighborhood of this maximum. Fig. 4.Eb shows the corresponding
radiated waveform. For even larger initial angular momentum, the spin of the
final BH actually decreases for increasing $L/M_{h}^{2}$. The reason is that
the merger is not only preceded by several hang-up orbits Campanelli et al.
(2006b); Pretorius and Khurana (2007), but also the merger yields a highly
distorted BH that radiates copiously as it settles down. Case Ec with
$a/M_{h}\approx 0.68$ and $L/M_{h}^{2}\approx 1.522$ represents this situation
in which almost 50% of the initial angular momentum is radiated (see path in
Fig. 3.Ec and radiated waveform in Fig. 4.Ec).

A persistent feature of the mergers with $L/M_{h}^{2}\lower
2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}1.3$ is that the separation between
the BHs (the coordinate distance between the punctures) decreases
monotonically with time (monotonic inspiral). Comparing cases Ea, Eb and Ec in
Fig. 4, we see general qualitative agreement: inspiral-generated gravitational
waves with frequency and amplitude increasing in time, followed by essentially
fixed-frequency ringdown waves. There is, however, a hint of disappearance of
the monotonic spiral in case Ec. The amplitude of the gravitational radiation
has a “shoulder” at about time $\sim 110\,M$. For a period of time equal to
two wave oscillations, the decline of the amplitude ceases and then
recommences. The relative orbital separation as a function of time (Fig. 6.Ec)
clearly shows there is a plateau in the separation centered at time $\sim
50\,M$, which is absent for cases Ea or Eb. For a brief period of time there
is a closely circular phase in which the BHs “want” to fly apart, but just
manage to stay at roughly constant separation.

The last three points in Figs. 1 and 2 are the cases labeled Ed, Ee and Ef.
They describe orbits without immediate merger but “escape” and recapture; they
all show initial approaches followed by increasing mid-evolution separations
of $14\,M$, $25\,M$ and $42\,M$ before the final merger (see Figs. 3 and 6).
Because the interaction involves two close approaches, there are two bursts of
gravitational radiation, one from the first flyby Yunes et al. (2007) and the
other from the merger (see Fig. 5). We are currently investigating
astrophysical implications of detections of these multiple gravitational
bursts and hangups in globular clusters Kocsis et al. (2006).

For the Ef case, there is an approximate hangup with separation $\sim 4-5\,M$
around time $\sim 950\,M$ similar to the shoulder seen in Fig. 6.Ec around
time $\sim 50\,M$. This structure shows up in the waveform for this Ef case;
we actually see a (lower amplitude) precursor to the radiation burst
associated with the merger, a hint that orbits with many repeated bounces are
possible. For even slightly ($0.1\%$) greater initial angular momentum than
case Ef, the BHs complete approximately one loop and then escape. This is a
possible indication of chaotic behavior (exponential dependence on initial
conditions, c.f. Ref. Pretorius and Khurana (2007)). Repeated bounce orbits
would have to be found with initial angular momentum very slightly above that
which resulted in Fig. 3.Ef. As with all critical phenomena, the problem
becomes one of careful tuning of the parameters. Note that these interactions
of nonspinning BHs produce chaotic orbital dynamics, in contrast to the chaos
found in spin evolutions Levin (2000); Hartl and Buonanno (2005).

One of the main conclusions of our work is that there is an upper limit on the
Kerr parameter for the final merged BH from nonspinning BH merger. For our
sequence this maximum is $a/M_{h}\approx 0.823\,$. We can understand this
observation by examining the timing of the formation of the final BH and the
radiation from the merger. It appears that the merger occurs through an
intermediate excited state which is essentially a highly distorted BH. We say
“essentially” because a substantial amount of angular momentum is also
radiated in the plunge immediately before the apparent horizon forms. This is
consistent with close limit BBH calculations Price and Pullin (1994) that show
merging BHs behaving like a perturbed BH, even before a common apparent
horizon forms, so long as the merging BHs are inside the peak of the effective
potential of what will be the final BH. This intermediate state emits the
largest part of the radiated energy and angular momentum. Because this
mechanism is universal (excitation of such a state is inevitable, and it will
inevitably radiate), it suggests that no merger of equal mass (or presumably,
roughly equal mass) BHs can lead to a final BH with maximal spin parameter
$a/M_{h}\approx 1$. This result does not directly affect spin up by accretion
since mass accretion will not excite the low $l$ modes that strongly radiate
angular momentum. Thus typical gas accretion can in principle lead to final
spins much closer to the limit $a/M_{h}=1$.

Figure 5: Waveforms for the Ed, Ee and Ef encounters. Figure 6: BBH coordinate
separation for the Ec, Ed, Ee and Ef encounters.

Work was supported by NSF grants PHY-0653443 to DS, PHY-0653303, PHY-0555436
and PHY-0114375 to PL and PHY-0354842 and NASA grant NNG 04GL37G to RAM.
Computations under allocation TG-PHY060013N, and at the Texas Advanced
Computation Center, University of Texas at Austin. We thank M. Ansorg, T.
Bode, A. Knapp and E. Schnetter for contributions to our computational
infrastructure.

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