I'm studying in an online game music course, and I'm experimenting Modes to add unusual sound to the music. I'm a complete newbie in music. So let's have the Locrian mode, the root chord is a dimished one, so the V is dimished. As far as I read, power chord are created with a V, so, if I want to play a power chord on the root in locrian mode, do I have to use the dimished fifth, or have I to use the fifth, playing a note that does not belong to the key? I tried the two: strangely the one with the fifth, playing the note out of key sounds better ( ie, it produce a dark feeling ) but is it correct to play?
If you want to be 'faithful' to the mode/scale you are in (in your case the Locrian Mode), you have to use the diminished fifths. For instance, the Power chords would be B-F (diminished fifth), C-G (natural fifth), D-A (natural fifth) etc..
It's not uncommon though to use notes outside the mode. You can use the Power Chord B-F# which is a natural fifth. Musicians do this all the time.
Really depends on what you want to create. My suggestion would be to try both out and see what you like best. In some cases you might like the diminished sound and in some other cases, you might want the neutral sounding natural fifth.
The term 'Power chord' normally means a perfect 5th. It can sound like a reinforced single note, because of the way harmonics work. But then it's often played on guitar with a distorted sound, so the harmonics are all mussed up anyway! Whatever. We know what a 'Power chord' sounds like.
You are perfectly at liberty to play a diminished 5th in a 'power chord' sort of way. It won't have the same effect of reinforcing the harmonics of the bottom note. It would probably be inaccurate to call it a 'Power chord'. But that doesn't matter. If you like the sound, use it.
Don't worry about theory 'allowing' you to do things. Theory describes, it does not command. (I say this a lot, and will continue saying it until it sinks in :-) If you're thinking harmonically, and are going for a Locrian feel, it may be better to keep all notes within the mode. Or you can belt out a Locrian scale, each note played as a 'Power chord' with the (perfect) 5th above added. Theory will help you describe what you're doing. It won't tell you WHAT to do.
As Laurence Payne said, it's only a power chord if you use a pure fifth. Any chord you put through distortion will give you not only the frequencies actually played, but also new components that weren't originally there at all, via intermodulation.
plotWindow . distortionCompare $ sineSig 163 ^+^ sineSig 308
Recall that even a single note on an instrument like guitar corresponds to a whole bunch of sinusoidial frequencies, however because these are in neat integer ratios those actually line up perfectly with the new distortion-frequencies, that's why distortion works fine on single guitar notes – it simply gives a more agressive, overtone-rich spectrum but doesn't change the harmonic content itself:
plotWindow . distortionCompare $ stringSig 100
Similarly, if you distort a powerchord (in which the fundamental frequencies are in a neat 3:2 ratio) the result has merely a “filled up” spectrum, but the new frequencies align perfectly with the already-there harmonic content, thus you get a very fat and agressive, but still clear sound:
plotWindow . distortionCompare $ stringSig (note "A2") ^+^ stringSig (note "E3")
In fact, all the frequencies you see here are integer multiples of 55 Hz, i.e. of A1. Therefore, this sound actually makes sense even in A-Locrian, despite the E that isn't supposed to fit in that scale.
Incidentally, the harmonic-alignment effect still kind-of works with a major third:
plotWindow . distortionCompare $ stringSig (note "C3") ^+^ stringSig (note "E3")
Here, the new frequencies fit pretty well in the spectrum, but are significantly “smeared out”, which makes the signal dirty in a way that starts to resemble white noise. That's actually an artifact of the tuning system: I've used the common 12-edo tuning above, which handles thirds pretty badly. In the correct just intonation, major thirds distort in fact very nicely:
plotWindow . distortionCompare $ stringSig (note "C3") ^+^ stringSig (5/4*note "C3")
Anyway, for something as dissonant as a tritone, all bets are off:
plotWindow . distortionCompare $ stringSig (note "B2") ^+^ stringSig (note "F3")
Here, the intermodulation frequencies are all over the place. There's nothing the ear can really cling to anymore, so it won't sound powerful anymore but just annoying.
So no, it doesn't make a lot of sense to play diminished fifths when accompaning Locrian mode on electric guitar. Better just play powerful deep single notes if you want a dark sound, or indeed standard powerchords, as already suggested.
Alternatively: it is actually possible to re-tune a tritone-near interval to something that can be resolved in just intonation, namely the 7:5 ratio that also occurs in the harmonic seventh chord (aka Barbershop seventh):
plotWindow . distortionCompare $ stringSig (note "B2") ^+^ stringSig (7/5*note "B2")
You can achieve that by tuning the F note of the B-Locrian scale down by 17 cents from its 12-edo frequency. That's not really feasible on a 12-edo guitar, but it can be done on a many-fretted microtonal instrument. 31-edo is definitely capable of this. 22-edo might also work.
The only difference between the Phrygian and Locrian modes is that the fifth scale degree of the Locrian mode is 1 semitone flat from the Phrygian one. At this point, unless you want your Locrian music to sound like it's in the Phrygian mode instead, I'm afraid you're stuck with diminished fifths for playing "power chords" on the root.