ElevenLabs Music
twitter.com
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A single song's lyrics easily fits into the context window of virtually any LLM, and with some of the bigger and better ones (Opus) you could probably feed it every known song's lyrics in your desired genre before asking it to create a new set of verses.
If they want higher quality work and not just trolling "make a song about how @octopoc is fat and needs to get a job" level of creation, they need to allow more inputs into the process.