Assuming that the ISP that provides a dynamic IP renews every 72 hours
Renewing a dynamic IP address is not the same as changing a dynamic IP address.
With good ISPs, even if you obtain the dynamic address using DHCP, then the same lease can be renewed again and again essentially forever – as long as the client router doesn't let it expire, it will keep having the same address for years. (This is standard DHCP behavior, as long as the ISP doesn't actually impose deliberate restrictions.)
Some other ISPs do enforce daily or weekly address changes (in some countries), but that is not inherent in having a dynamic IP address.
will the audio stream be affected by the IP change? For example, with a micro-cut that takes the audio streams down for a moment
It depends on the streaming technology, but in most cases (especially with basic TCP/HTTP-based streams), if an address change is forced, the connection will be completely cut off until the client notices a timeout and reconnects to the new address.
(Most transport protocols simply don't have any "roaming" features built in, and it's not guaranteed that the streaming server will even be aware of the address change at all, especially if the server is behind NAT and the address actually belongs to the router and not the server.)
1Are people subscribing to your stream? Or are you subscribing to someone elses stream? – spikey_richie – 2019-09-30T12:54:12.907
I'm using my internet connection to stream from my computer to an external Icecast server. – nicozica – 2019-09-30T12:59:15.357
Please consider using the 'fallbacks' functionality of Icecast (see its documentation). It helps you avoid listeners being dropped due to source client connection issues. – TBR – 2019-10-01T12:38:41.720