The maths of music: Mariah Carey in numbers
By: Kelvin Tan
Tags: Music, Pop Culture, Machine Learning, Data Science, Data Analysis

Interestingly, the only two Mariah Carey songs that are within the averages of the other songs at the time are Vision of Love and We Belong Together. Both of these songs were at pivotal moments of her career, with Vision of Love being her debut single and We Belong Together cementing her comeback and continued reign.

A majority of her earlier songs had higher acoustic scores, slightly lower danceability, energy and valence scores compared to its peers. This coincides with the early focus of the production on her technical mastery of her voice. In addition, as many of Mariah’s songs touch on love and heartbreak, the lower valence scores tell us that people turn to her to seek solace in times of need, and that this aspect of her music was one of the reasons for her popularity at the outset of her career. While Mariah was clearly in tune with the sound of the moment following the release of The Emancipation of Mimi, this period also saw her tap into the different timbres of her voice more confidently and creatively to achieve a more understated, but no less effective delivery of tension and release.

She Came to Have a Party

Despite being one of the most prolific songwriters of all time, Mariah Carey does not receive nearly half the credit she deserves, having only been inducted into the Songwriters Hall of Fame in 2020. Known for being a prodigious topliner, she has assembled a growing list of writers and producers to achieve her creative vision.

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From the plot above, we see how she started off her career with a small number of close collaborators and which eventually evolved to having 40 other writers listed as she worked with an increasingly diverse array of talent. For Mariah Carey, she tapped into the trove of songs she had written with Ben Margulies in high school and through her label, enlisted the help of Walter Afanasieff to produce. Due to the album’s success, her label gave her more creative freedom to seek out new directions in her later albums. Daydream marked the start of her gaining control over incorporating hip-hop and R&B in her music, with the Fantasy remix which featured Ol’ Dirty Bastard solidifying her status as an innovator in fusing the genres of hip-hop, R&B and pop. This album also saw her first introduction to Jermaine Dupri, another would-be longtime collaborator, in addition to heavily incorporating rap elements in her music.

In 2005, the one-two punch of the Jermaine Dupri-penned tracks It’s Like That and We Belong Together from The Emancipation of Mimi saw her back at the top of the charts and ushered in a new era of experimentation. Together with The Dream, Mariah scored her 18th number 1 with Touch My Body from the album E=MC², which then led to more fruitful sessions when he co-wrote and produced most of the tracks on Memoirs of an Imperfect Angel. Her latest offering Caution saw her in the studio with producers she had never collaborated with before such as Skrillex, Poo Bear and Blood Orange, which was met with critical acclaim, and the album appeared on numerous year-end best of lists.

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Taking a step back from her catalogue, we go back to the Billboard Hot 100 dataset to measure her impact on her peers.The Fantasy remix released in 1995 had a significant cultural impact on pop music, as it set the blueprint for the subsequent records that had a strong hip-hop influence, and paved the way for artists such as Beyonce, Christina Aguilera, Rihanna and many others today. As a simple metric, we count the number of songs with features below, and it is clearly evident there was a huge explosion in 1996, and this has only continued to rise over the years.

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The Art of The Songwriter

If we were to take one thing away from Mariah Carey’s songs, it’s that she understands the multiple facets of love, whether it assumes the form of emotions so strong that you believe that it is not just a fantasy but a sweet destiny, or the nuances of a breakup that could result in a former lover being a part of yourself indefinitely, or to be told to simply get the fuck out.

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The word clouds above do indeed show that love is a central theme in each of her albums, but what kinds of love exactly is she referring to? We turn to Natural Language Processing to dig deeper into her lyrics, and with the help of a technique called Non-Negative Matrix Factorization, four interesting topics emerge. The top 10 words for each topic are as follows:

believe, find, inside, end, need, know, heart, love, understand, hurt boy, play, girl, good, wanna, leave, ya, tell, mariah, mean touch, heaven, dream, need, feeling, want, love, long, wait, tonight away, light, open, far, walk, fade, run, night, rain, shine

The first topic’s lyrics remind us of why we turn to Mariah: soaring power ballads to lift us out of our darkest hour. The second topic clearly showcases her affinity for collaborating with hip-hop and R&B artists in producing club-ready jams (Mariah may be a diva, but she’s definitely not singing her own name). The third topic is about imagining what the paragon of love would look like while the last topic strikes a more reflective and wistful tone. For conciseness, I’ve renamed them as:

Power ballads R&B/Hip-hop aficionado Love and limerance Introspective escapism

The top tracks with the highest scores in each are:

As we referenced earlier, Daydream was a turning point in Mariah’s career which saw her venture into R&B/hip-hop and also begin to pen more intimate songs such as Underneath the Stars. We also see a consistent decline in Power Ballads over the years as she broke free from her labels constraints on her as a traditional ‘pop’ artist.

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Finally, we use Spotify’s audio features in addition to the topics above to cluster Mariah Carey’s songs in order to see if any patterns emerge. We use a simple k-means clustering algorithm with 4 clusters as we would expect the audio features to line up broadly with the topics above. A few audio features were dropped such as Instrumentalness as this did not have much variation; Liveness and Loudness to allow each song to be treated as a standard studio effort; Mode was dropped as any intended effect of a major/minor key would be encapsulated by Valence.

As opposed to simply applying a blanket rule to categorise a song from the lyrical analysis above, we retain the raw scores and apply k-means clustering in order to account for other audio features which may also be an influence in the overall appreciation of the song. The plot below is the output from the clustering algorithm, where each cluster has been labelled after the lyrical category that has the highest average.

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Not unexpectedly her R&B leaning tracks score the highest in Danceability Energy, and Valence but the Love and Limerance songs are not far behind. Her Power Ballads score the highest on Acousticness as these songs show off her ability to convey a tapestry of emotions through the technical use of her voice, without the need for any accompaniment that might divert attention away.

Looking at how her number 1s have been classified, she has an equal number of tracks in Power Ballads and Love and Limerance and the least in Introspective Escapism. This category however has a number of lamb-favourites such as Fourth of July, Underneath the Stars and Close My Eyes. Mariah Carey’s grand displays of emotion appeal to the masses while her confessionals resonate with her fans.

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Conclusions

Mariah Carey is a living legend — we already knew that she was a record-breaking, genre-defying trailblazing singer-songwriter already, but quantifying these accomplishments has only made her success seem more incredible. We then tried to break down her music using maths to understand if there are underlying patterns and identified a few common themes in her songwriting and production. None of these will surprise her devout fans, as they will already have subconsciously internalised the different facets to her music, but maths has given us a way to evaluate this numerically. It’s a wrap!