How do I tell which octave the displayed note is in on the Boss tu-12h tuner? I want to avoid breaking guitar strings.
There is no indication of octave on the TU-12H. If you’re tuning a guitar that was recently in tune, it’s probably only a few notes away from the correct note at worst. Also, usually all the strings are a bit flat when retuning, and usually the whole guitar is either sharp or flat. So if you have to flatten one string to get it in tune, you’ll probably have to flatten all of them. It would be unusual for some to be flat and others sharp.
If you’re tuning up a new set of strings, it can be a bit more challenging. When you have some experience, you’ll just know which octave is the right one from tension and sound. In the meantime, tune the low E string first, up until it makes sound and then tune it to the lowest octave that can hold the note. If you’re not sure it’s too low, leave it in that octave and use it to find the right octaves for the other strings. At some point either one of the strings will feel obviously wrong or they will all seem about right. If they are right, you’re done. If one is clearly wrong, then you probably have to try the next octave up.
When I buy new strings I always buy two sets and always have at least one extra set on hand. If something goes wrong with a new string I can replace it right away.
You’ll get the hang of it fairly quickly. The difference in tension and feel between two adjacent octaves is a lot, so if you are tuning too low you’ll know it’s too low, and if you’re going too high you’ll start to feel nervous about it and it will get really hard to turn, at least on the lower strings.
I've seen many tuner apps for mobile phones that display the octave. You can also compare it to another instrument like for example another guitar (same octave), a bass (one octave up), or a piano. And after some experience, even if you don't have absolute pitch, you will be able to tell if it's off by an octave.