“Formation” Live Chromagram

An important part of Coachella history (and history in general) is Beyoncé’s “Homecoming” live album, which is her headline performance from Coachella 2019. This epic show was almost two hours long, and had the production quality of a Super Bowl halftime show. A Netflix documentary was made to immortalize the performance, something that is extremely rare for Coachella artists. Here, we will look at chromagrams for one of the songs she performed, “Formation”, and use dynamic time warping to observe how the life performance differs from the album version.

“Formation” Recording Chromagram

Here we see a chromagram, which, at any given time window in the music, tells us how much of each pitch we are hearing relative to the others. Looking at this chromagram, for example, we can see that for most of the song we are getting strong values from the F key. We can attribute that to the constant wobbly electronic tone. Interestingly, we see almost a full scale in the first 20-30 seconds. I’m not exactly sure why this happens — there is a two note echoing sound playing and her voice a cappella. With the voice having such a broad range of harmonics, this may explain the multiple notes, but not the ascending scale. There are low drone notes that rise, but over shorter periods of time. The ascending here looks like a very clean, distinct scale.

Dynamic Time Warping

Unfortunately, the DTW is too large of a computation to render in ggplotly, so an image is included in its place.

Proper alignment in a DTW visualization will look like a diagonal line, which we can very, very faintly see at certain time windows in the graph. This means that at some points in the performance, it was very well matched up to the original recording, and vice versa. However, with the differences in timing between the two performances, it may be hard to accurately compare them. The dynamic time warping at each point can be thought of as a cost function regarding how costly it would be to make some sort of edit to align the tracks perfectly — a similar problem to the edit distance problem.. A dynamic programming approach is used in both sequence-aligning problems.

Cepstrograms

In order to further explore the range of Coachella’s headliners, we may want to explore how their music differs. To analyze song structure, instrumentation, and more, we can conduct a chroma and timbre analysis of songs by two of the three 2023 headliners. Here is an analysis of “Futura Free” by Frank Ocean, and “Butter” by BTS, through the lens of cepstrograms and self-similarity matrices.

Here in the cepstrograms, we can see how Butter by BTS is split into about 5 sections. The intro has some different elements than the rest of the song, and we can discover upon listening that the intro is the one part in the song that has very little instrumental, mainly just voice and drums. Once the instrumental comes in, the first few MFCC’s become more present.

In the cepstrogram of Futura Free by Frank Ocean, there is a lot going on, but maybe most interesting is around 280-315 seconds, when almost all the MFCC’s are below 0.5 except C02. Upon listening, this is around 2:38 when the instrumental swells up, there is distorted noise, then we hear a focus on Frank’s voice over very light, sparse piano chords. The section from 315 onwards is an audio collage of different interviews and mainly speaking.

“Butter” Self-Similarity Matrices

Now onto the self-similarity matrices. The purpose of comparing these two headliners is to show that the headliners encompass a range of genres. BTS is more standard pop music, with most of their music sounding formulaic in the genre of pop. Frank Ocean is more experimental and complex in his instrumentals. Using a self-similarity matrix is a great way to compare these overall complexities.

For BTS, we see a distinct checkerboard pattern. Here, we can use that to say there is a lot of homogeneity in the song. There are blocks in the song to represent different sections, but overall there is a lot of similarity between early and late sections in the song, chroma-wise. In the timbre section, the brighter crosses represent novelty, or something new in the song. We don’t see much of this, and the timbral analysis shows that most of the song has fairly similar instrumentation, apart from the initial 25 or so seconds.

“Futura Free” Self-Similarity Matrices

For Frank Ocean, we see a lot more complexity. In this case, this is shown with a lot of dark blue and little yellow — the magnitude of similarity at many points in the song is low, meaning there are few repeated sections or little homogeneity in the track. The timbral analysis shows a similar insight, with a novel musical moment around 315 seconds (this is the aforementioned speaking collage). Listening is always important because while this may signal to us that there will be some crazy different instrumental section at this point, it is in fact more visible because it is only vocals, which happens only at this section. Instead of an “interesting” musical moment, you could describe this moment as an “uninteresting” moment among an otherwise interesting song timbre-wise, so it stands out in the self-similarity matrix.

Melody: A Chordogram

Coachella is full of electronic music. Electronic music as a genre can range from highly melodic complex tonal music to very limited techno beats that may only really sound like drums and bass. I would like to analyze Opus by Eric Prydz, a 9 minute masterpiece with an abnormally long buildup, and see how the chordogram recognizes the tonal changes, if any. We see the song start out hovering around A major and F# minor, which is classified to be F# minor by Chordify. We then see something interesting — at about 120 seconds, we see the tonal center start to become less pronounced. The clear F# minor is no longer so clear. This may be because the drums start coming in, which continue for the rest of the song. Drums can add a lot of harmonics that would throw off the pitch values. We can still see a center around that F#min block, but there is also activity in the Gb7, and the Eb7 regions. It should be noted that these values were computed using David Temperley’s key profiles, a reconsideration of the classic Krumhansl-Schmuckler Key-Finding Algorithm.

Tempo: A… Tempogram

If the last slide didn’t inspire you to pull up the track and hear the changes and follow along, maybe this one will. Not only does Eric Prydz have a very interesting melodic visualization, but when we visualize the tempo of the song using a Fourier based, cyclic tempogram, we get a pretty stunning result. We see here how the song is analyzed to start out around the 80bpm mark or below, and slowly starts ramping up. In fact, it’s a build up that starts at the beginning of the song and continues until around 3 minutes and 10 seconds where it settles on its main tempo of about 126 beats per minute. The extra lines that we see above and to the left are what is called tempo harmonics — listening to the song, we can confirm the true tempo line is the main one we see in the middle, but if we were to zoom out on this graph we would see the horizontal line repeated around 252 beats per minute, exactly double of where we see it on this graph. This is because the software is unsure whether to count the beat for its value, or double, or half, or another way. We also see the tempo fade back down starting at around 400 seconds. There is a bit of a breakdown at 330 seconds, or 5 minutes and 30 seconds, which is audible but in my opinion is very unnoticeable compared to how pronounced the drop is on the tempogram.