( But what if the root note is not on the scale? If we saw an Eb Chord in the key of C, we would likely call that a bIII Major (or bIII Maj). A Bb Chord in the key of C would be a bVII Major. An F# Minor would be a #IVmin. This is a rare one )
I dint understand this part . It’s confusing.
Like Eb chord in key of C - will call it as bIII minor not bIII major ( because minor diatonic Roman number is I, III, VI ( but it’s written bIII major . How come ?
By convention, chords without any kind of qualifier are assumed to be major. When you see C, Eb, A, D#, etc. without any elaboration, they are assumed to refer to major chords.
Whether we’re talking about diatonic or non-diatonic chords is another matter. As you pointed out, knowing the key is important.
The scale degrees of diatonic chords are the following:
I, IV, V: major
II, III, VI: minor
If we’re talking about an “Eb chord” in the key of C major, (1) we know it’s a non-diatonic chord in that key and (2) it has to be assumed to be a major chord as there are no other qualifiers mentioned (minor, sus, dominant 7, etc.) If one was talking about the bIII min chord in C major, the chord would be named as Eb minor explicitly.