I've been looping a C major chord on an app, and tried to play the F minor scale on that. Why does this work? I know that A minor is the relative scale of C major and that should sound good. But why does F minor sound so good on a C major chord?
A C major chord has a close relationship to the F minor scale. The dominant of F minor is C. Also, although E is flat in the key signature of F minor, as the leading note (just before the tonic F), it is often before raised to E natural. So, a C major chord is common in F minor and will lead to the tonic chord F minor.
Well, we will have to agree to disagree. I really don't think most of the F minor notes sound good at all against a C major chord. There are 3 notes which fit exactly - C F and G, but the others are a semitone away from any in the C scale, and the E♭ clashes against the major 3 of C. This in itself is no big deal: blues often uses the m3 against the major version of a chord. It also uses B♭, but those apart, nothing else works - in my opinion. And opinions aren't really what the site is about!
I am going to assume that by "F minor scale" you mean the F natural minor scale, not F melodic minor, F harmonic minor, or some other minor mode.
The notes of the F natual minor scale are also the notes of the C Phrygian scale: C Db Eb F G Ab Bb. Now a C triad contains the notes C-E-G; the only problem is that C has an E natural in it, but C Phrygian has an Eb which would seem to clash with the third of the C.
A Diversion Into the Diminished Whole Tone Scale
This reminds me of what is called the altered scale, also known as the diminished whole tone scale. The altered scale is the scale derived from the seventh mode of the melodic minor scale, so the C altered scale would be: C Db Eb Fb Gb Ab Bb. Here is some tablature to compare the two:
$A 3 4 6 $D 3 5 6 $G 3 5
C altered (C diminished whole tone)
$A 3 4 6 $D 2 4 6 $G 3 5
This C altered scale is usually paired with what is called a C7alt chord. But, in this application, the C altered scale isn't spelled the way I have spelled it above, but rather using an enharmonically equivalent spelling: C Db D# E F# G# Bb (giving a C7(#5b9#9#11) chord) or C Db D# E Gb Ab Bb (giving a C7(b5b9#9b13) chord). That is, you can construct a C7 chord with the 5th and all of the extensions altered any way you like, so long as they are altered.
You can play a C altered scale over a C7 chord (or even over a C chord in some circumstances). These altered scales are usually played over an altered dominant seventh chord, i.e. C7b9, C7#9, C7#9#11, and so on. Often in a jazz chart you will find a C7alt chord which means that the exact alterations to the seventh chord are left up to the player, but an altered scale is appropriate here. Generally speaking, altered scales are a little bit tricky to use.
Returning to the Phrygian Scale: Poor Man's Altered Scale?
The C Phrygian scale was: C Db Eb F G Ab Bb, but instead we could spell it as C Db D# F G Ab Bb. This gives a C7(b9#9b13) chord, except that the third (E) is missing. But since the scale is played over a C chord, that E is present in the harmony. In this sense the C Phrygian scale is something of a poor man's C altered scale.
In this interpretation, the C Phrygian scale provides a way to elaborate a C7 chord. By playing C Phrygian over a C chord, you are converting it to a C7 chord, with some alterations.