I’m looking for ways or tools to change the pitch of audio without messing up the sound. Ideally, it should work for vocals or full tracks without adding noticeable noise or distortion.
Perfuse your speakers with Helium and record the output.
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You can take a look at TS2 by ircamlab, it can do crazy things, but is also nice in subtle stretch
Just out. I also think Ableton’s algorithms are pretty good.
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There is always going to be some kind of artefact and different algorithms are better or worse for different types of audio (which is why DAWs often offer a choice), but I find Serato’s Pitch and Time very good.
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It mostly depends what and how much you wanna pitch. Pitch shifting vocals or drums are two very different needs. The same way for stretching a sample or full track.
For vocal and full mixes iZotope Radius (Logic / RX) seems to be rated as the most efficient at preservation of audio but more CPU greedy.
For general real-time stretching Zplane Elastique Pro is used in Ableton, Reaper and FL Studio IIRC and is generally considered as a good compromise regarding CPU need, audio preservation, phase issues, etc.
Yet, shifting to a full octave can’t go without premises.
Depends on what “quality” means.
Audio quality:
Should be possible with high resolution FFT algorithms (1024 resolution in fourier space and upwards). First analyis of the sound, get the frequency spectrum right, and pitch it up or down.
Reproduction of an instrument:
No, if an instrument has different frequency spectra for different pitches. Example: A piano has one string for bass, two strings for mid-range, and three strings for upper and soprano-range. Those sounds have quite different frequency distribution structures. If pitched too far away from the recorded pitch a re-pitching will create quite noticable artifacts.
Yes, if the above doesn’t matter much 
Ever heard of formant preserving pitch shifting?
(On the other hand, General Midi Soundsets with one sample every five or less pitches are a thing and people seemingly didn’t complain, altough I deeply dislike [hate] whatever came out of that.)
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Serato has a good tool for this.
Edit: oops, sorry didn’t see it mentioned above.
freq shifter
I still haven’t heard a pitch shift that didn’t sound like an effect rather than pitch shift. (if that makes any sense 
)
Some are better than others, and some sound more interesting than others, but if you’re looking for something that JUST shifts pitch without losing or adding from/to the original signal as a byproduct, I don’t know that it exists. I’m sure there will be something soon that uses machine learning in the same way that “fake frames” are generated for something like GPUs that would be able to do it. Still haven’t heard anything 100% convincing though.
Luckily for me it’s not something I really need for anything I do, but could see it being useful for some. 
Yes, I think just a rate conversion shift is probably the most natural sounding until you get into chipmunk territory. However, then you’re dealing with time shifts as well. I guess it depends on the application as to whether it works or not.
Well I guess not …
random youtube video demonstrating it
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The instruments sound decently pitched. You can still hear it, but not bad. The vocals though, you can hear the effect quite a bit. Maybe it’s because I know what to expect there though. Still not bad compared to other pitch shifting I’ve heard. Might be just what the OP is looking for.
Who knows what is possible in fidelity since the 7 years this video was uploaded
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I know professional (very high end ) mix engineers who swear by this - but it ain’t cheap!