Idk about staggered cadence, as that kinda sounds like overengineering a solution to me. But when I'm having trouble sleeping because of thoughts racing in my head (AuDHD, common problem for me), any audio with human speech is pretty good at disrupting that. My go-to is softly spoken ASMR videos, but I've also fallen asleep watching chill cartoons like Futurama and 90s Batman. I've also had it work with audiobooks but this is suboptimal because then I lose my place.

My theory is that it works because my thoughts are like a voice in my head being spoken by my internal dialogue, and it's hard to hear two people talking over eachother. So introducing another voice occupies the language-processing part of my brain and therefore blocks my ruminating thoughts.

There is an app https://github.com/trynoice (F-droid, Playstore, on the web) that

'Noice is an app that allows you to create personalised sound environments. It enables you to combine different sounds at different volume levels to create perfect ambient atmospheres. These custom sound surroundings let you drown out distractions and allow you to concentrate. You can also use it to generate a serene, peaceful aura that encourages you to relax and fall asleep.'

As well as nature sounds there are things like 'conversation' and 'coffeeshop'. You might try that

Dunno about staggered cadence but when I've been hearing voices I've found listening to very boring Buddhist dharma talks on podcast to help. They block out the voices and the dull, drone of the bikkhu lulls me to sleep.

Worth a try?

I use TMSoft's White Noise which runs on most platforms, or stream. It has plain white noise, yes, but it also has a wide range of other sounds that you can use (brown noise, railroad, city street, stream, etc). You can also upload your own sound, get sounds/mixes from other users, or make your own mix.

My personal mix has a mild background of pink noise, with both a thunderstorm and some rain mixed in: the pink noise filters out common background, the rain helps with masking as well, and the thunder helps me sleep through bass sounds like lawn mowers and trucks.

Do you find the sound of rain and distant thunder relaxing? If so there are plenty of recordings on YouTube and YT music that are hours long and not loops. Search for keywords with "rain forest".

For some reason, listening to Knowledge Fight helps me sleep

Why not just a second white noise, or other white noise adjacent sound? Even if they're both looped they're not going to have the same loop length and that will be a changing rhythm that way.

Update 2 days later: Many useful comments. I now have text doc filled with apps, software, podcasts, etc to research, try out.

This posted question was weird, obscure. Could've been ignored, ridiculed. Barely slept in 4 weeks cuz hearing voices. Desperately hoping against hope.

So, small group of random internet strangers taking question seriously, offering constructive solutions instead of ridicule? You've helped a lot. Thank you.

There's podcasts like Sleep With Me that occupy the same place as white noise.

Ocean sounds don't exactly have a specific rhythm, and are a popular white noise that people have used to go to sleep.

Not sure if it's what you're looking for, butI have a free app called White Noise lite (Android) that let's you 'remix' multiple white noises by combining them. You can add up to 5 different noises at once, with customized settings that include variance. Here's some shots of what that looks like in the app:

wtf