When I place a call I hear the traditional rotary dial phone ringing sound until the person at the other end, whose ringtone most likely is completely different, answers. What I was wondering is, can I set a ringtone for the person placing the call to hear until the other party answers? If so, can such "ringtone" be set differently for every person called?
The sound someone hears when they call a phone is dependent on the person they are calling. This is why, no matter where in the world you are, when you call a US number, you get the US "ringing" tone, whereas if you call a European number, you get the European "ringing".
The providers of the person you are calling are what provides the ringing tone. Some carriers, like Verizon, offer the ability for you to set tones for others to hear, usually for an added monthly fee. Verizon would essentially answer the call and play the music while it continues to try and reach you. Once you answer (or it is sent to voicemail), then the music would end and Verizon would connect the call on their end. This might be manageable on the phoen via an app from Verizon, but you would be changing their settings for your phone number that is stored on their servers.
Nothing locally on the phone is capable of changing what the incoming caller will hear for a ringtone.
I believe what you're asking about are similar to the Verizon ringback tones, right? Ringback tones are not set from a phone level, they are a feature added and managed by the carrier. Your wireless carrier could probably change it for you, but there is no way you could manage it all from your phone. I know Verizon offers ringback tones, if that's the feature you're looking for you could ask about that.
Would be a cool feature, if it were possible.