How do I make Android continue playing the ringtone music instead of restarting it as peer calls again? Device receives a call, but there is no reply. In 3 minutes, there is another ring from the same peer.

How do I make long ringtone music continue from some point instead of starting from scratch when the phone is ringing soon enough?
I haven't tried doing this yet; but I believe you might be able to do it with this app called Automated Device, you can setup some rules to change the ringtone, and by cutting your song into chunks, and then using the flag functionality to define which rule is active at each moment, you could setup a rotation of ringtones that together play the full song.

Something like (pseudocode):

If phone is ringing, and the flag "ringtone step" is zero;
then change ringtone to cut 2 but only after 29 seconds, 
and set the flag "ringtone step" to 1.

If phone is ringing, and the flag "ringtone step" is 1;
then change ringtone to cut 3 but only after 29 seconds, 
and set the flag "ringtone step" to 2.

If phone is ringing, and the flag "ringtone step" is 2;
then change ringtone to cut 1 but only after 29 seconds,
and set the flag "ringtone step" to 0.


The 29 seconds thing is so it won't skip to the next chunk without completing the current one (if an action is delayed and the conditions stop being true, it won't execute). I'm not sure what happens if you try to change the ringtone while the phone is ringing though.

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For doing anything complex with it, it is a bit like programming, but a lot more awkward. But simpler stuff is quite easy.

Perhaps there might be other apps; I haven't looked for an alternative in quite a while; this one is what I'm familiar with.