When I first started figuring out the 15-year excitement cycle, I quickly hit on the tendency for harmonic rather than melodic music during the vulnerable phase of the cycle. Lots of layers, droning, sighing, ethereal, floaty, dreamy -- like coasting down a lazy river ride at a water park. Perfect for audiences who are in a refractory phase, and who don't want much stimulation or else their nervous systems will overload.
For more detail, see these earlier posts on the pattern for both indie and pop genres, here and here.
My examples from the early 2000s vulnerable phase were a bit sparse, because I was going from memory, and as it turns out, most of the key examples were from R&B, and I never listened to it that much at the time or since. But I've been reliving the y2k sound lately, and quite a few examples jumped out, which I would not have recalled from memory.
Only one is technically from the early 2000s, but the other three are from '99 -- they were ahead of the curve, leading into the early 2000s, and do not sound like the rest of the late '90s manic phase (techno, Eurodance, Britney Spears, etc.). The point is that they show the fatigue from the late '90s manic phase was setting in, and the cycle was just about to crash into a refractory state.
The late '90s and early 2000s was pretty weak for rock, compared to earlier eras, and electro dance music wasn't nearly as popular as it would become by the late 2000s and 2010s. The R&B and rap genres were a lot more central to the zeitgeist than before or after, so if you don't know what was going on in those genres, you'll miss a lot of the y2k vibe.
I won't do an in-depth analysis of each song, just a few notes about what they all have in common. As usual with the dream-pop sound, there are zillions of layers, both vocal and instrumental. There's not much melody or even hooks / riffs, but rather sleepy, trance-inducing repetitive motifs (like the harpsichord line in "If You Had My Love"). The rhythm section isn't very danceable, and there is minimal accenting of the off-beat, unlike the UNH-tsss percussion of late '90s techno / Eurodance (and no replacement of the hi-hats with other rhythmic instruments).
Vocal delivery is pretty low-energy and ethereal -- not because it's rap, and not meant to have lots of intonation changes, but because it's a dreamy ethereal time for R&B, rather than the belting-it-out style. Only "Thong Song" has an intense vocal passage, and it's only near the climax, not sustained throughout the song. All of them are written in a minor key, as per yoozh with the dreamy droning don't-disturb-me style.
For comparison, "Believe" by Cher from a bit earlier ('98) has the beginnings of the ethereal soundscape approach, but only in the intro and occasionally afterward. It has the standard UNH-tsss, hi-hat accenting the off-beat, super-danceable rhythm of the techno of its time. And the vocal line is more melodic, has much greater intensity, and is more uplifting. Also, written in a major key.
The songs that follow are quite a radical departure, and showed where the mood would be during the start of the new millennium, as excitement levels plunged into a refractory state.
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"Genie in a Bottle" by Christina Aguilera (1999):
"If You Had My Love" by Jennifer Lopez (1999):
"Thong Song" by Sisqo (1999):
"Try Again" by Aaliyah (2000):