[danpat]

https://en.wikipedia.org/wiki/Wideband_audio

and more specific to cellular phones:

https://en.wikipedia.org/wiki/Adaptive_Multi-Rate_Wideband

Search for "HD Voice" from the big cellular companies in the US. It usually requires handset support.

[X86BSD]

I believe apple has supported this with the iPhone for several years now.

[DiabloD3]

As has Android, but AT&T and Verizon tend to lock out features like HD Voice and Wifi Calling to be iPhone only.

[X86BSD]

T-Mobile is what I have. I think they were the first? But it sounds great on T-Mobile. I usually just talk to the wife both of us on iPhones and T-Mobile. And then I get the occasional call from someone else and I am like "What the !@# get a decent connection/phone/whatever!"

[ubersync]

It is correct that both parties need this for better quality?

[redditplebs]

It is, yes (and both possibly need to be on the same network - at least, I know this is the case for Verizon's HD calling).