How do I silence incoming texts on Iphone 5 with IOS 8.1

I cannot answer the question about the text tone silence, since my tones are rather short and I cannot test it.

However, in response to your second question regarding tones when on the phone, the only setting you can use for that is to use the mute button temporarily, or Do Not Disturb temporarily. There is no setting to disable text tones while on the phone.

Actually 😉

Since OP is saying that only certain text tones are bothersome - s/he has the option to go into that conversation - hit the i and get into details and toggle the Do not disturb

It will silence that particular conversation until you reverse the toggle

You will see the DND half moon in the left column of that conversation

The only way to cut down on tones during a conversation is round about

IF you turn on DND and choose to accept phone calls from favorites - you will have effectively silenced the tones but the calls from favorite contacts will come through - Please see that there are limitations to this approach

What happens if you tap the power button? That works for silencing the phone ringer.

However, if this is a new text, not from someone they can do that to in a conversation, it would still come through. I do not like to assume this is an ongoing conversation.

As usual Chris - you are absolutely right - it does have its limitations but at least something for the OP to consider and hence I threw it out there

This has been a "limitation" that many have talked about in the past, finding a way to silence a text tone while on the phone. OF course, I believe this one to be compounded slightly because they are using tones of greater length. I believe there should be a way for the device to distinguish when the user is on the phone to temporarily silence other notifications. Of course, that is something for Apple to address and users can use the feedback link to suggest this to Apple at www.apple.com/feedback and click on the appropriate subject.

Have a nice day.