Yeah so you're right about Brown not coming from the color, but I believe this was still done on purpose.
Pink noise has an inverse proportion to frequency, so defined by f^{-x} where 0 <=x<=2 (so at best, an inverse square). Now the problem with this is that sensitivity of human hearing is not flat across frequencies. There's a sharp uptick from 1kHz to 3kHz (peak) and you gotta get to 9kHz before you're back down to the level of 1kHz (which 100Hz - 1kHz is fairly flat). Here's a random graph[0], take it with a bit of a grain of salt but as far as I know it is reasonable. But remember that dB is logarithmic so this is significantly louder.
Because of this, Pink Noise is created to be "flat" with respect to the human ear[1]. I mean there's approximations going on for this but think of it as a lazy version of that if we didn't know the more complex response curve from [0]. While white noise is flat across frequencies, the perception is that higher frequencies are louder.
In short, pink noise will sound like it is raining on a metal surface or by rapids in a river. You can hear the low frequencies but you got lots of high ones too. Brown noise will be like sitting in the forest when it is raining, it hitting the soft dirt. Or a lot like being near the ocean.
So if you want that comfort slow pace feeling, turn up the low frequencies, so 10Hz to 500Hz, and I like to cut-off anything above 600Hz.
It can be good to play with single tones too[2]. I like about 65Hz (I can hear about 21Hz to 17kHz on this site with some good headphones but who knows. All that isn't flat and I'm a tad over 30). But the site I sent you previously has a lot to play around with. I'm not sure there's a high quality refined tone specification site but if you find one let me know.
Pink noise has an inverse proportion to frequency, so defined by f^{-x} where 0 <=x<=2 (so at best, an inverse square). Now the problem with this is that sensitivity of human hearing is not flat across frequencies. There's a sharp uptick from 1kHz to 3kHz (peak) and you gotta get to 9kHz before you're back down to the level of 1kHz (which 100Hz - 1kHz is fairly flat). Here's a random graph[0], take it with a bit of a grain of salt but as far as I know it is reasonable. But remember that dB is logarithmic so this is significantly louder.
Because of this, Pink Noise is created to be "flat" with respect to the human ear[1]. I mean there's approximations going on for this but think of it as a lazy version of that if we didn't know the more complex response curve from [0]. While white noise is flat across frequencies, the perception is that higher frequencies are louder.
In short, pink noise will sound like it is raining on a metal surface or by rapids in a river. You can hear the low frequencies but you got lots of high ones too. Brown noise will be like sitting in the forest when it is raining, it hitting the soft dirt. Or a lot like being near the ocean.
So if you want that comfort slow pace feeling, turn up the low frequencies, so 10Hz to 500Hz, and I like to cut-off anything above 600Hz.
It can be good to play with single tones too[2]. I like about 65Hz (I can hear about 21Hz to 17kHz on this site with some good headphones but who knows. All that isn't flat and I'm a tad over 30). But the site I sent you previously has a lot to play around with. I'm not sure there's a high quality refined tone specification site but if you find one let me know.
I hope this helps.
[0] https://www.compadre.org/nexusph/course/images/OscillationsA...
[1] https://en.wikipedia.org/wiki/Colors_of_noise#Pink_noise
[2] https://www.szynalski.com/tone-generator/