How a chord is analyzed as a "chromatic mediant of the V"?

Question

In the video How To Analyze Songs from the channel 12 tone, the guy wisely separates the task of labeling from analyzing. There's a comment where he lists some possible analysis options of the label bIII:

• Modal interchange

• Chromatic mediant of the root

• Passing chord between ii and iii
• New root in a direct modulation
• Chromatic mediant of the V chord
• Tritone substitution resolving to ii
• Secondary-axis substitute for V chord
• Secondary dominant of tritone substitution of V chord
• It's all just atonal
• Someone also says: part of an extended plagal cadence bIII bVII IV I

I'd like to know, how a bIII (the Eb chord in the key of C) functions different when analyzed as a modal interchange chord and a chromatic mediant chord? And also how would you differentiate the chromatic mediant of V and of I. I thought chromatic mediant was just a label of a chord distant a minor/major third apart from a degree (not being diatonic), but aparently there's also a semantic issue involved because a chord would "function" as a chromatic mediant and not as a modal borrowing. What should I look for to determine this classification? Thanks.

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EDIT

I believe the "Chromatic mediant" wikipedia article shed some light on my question.

"Some chromatic mediants are equivalent to altered chords, for example ♭VI is also a borrowed chord from the parallel minor (...), with context and analysis revealing the distinction."

And that was exactly my question: What to look for in the context to distinguish both? The article quotes:

"Chromatic mediants (...) provide color and interest while prolonging the tonic harmony, proceed from and to the tonic or less often the dominant"

So, is "being surrounded by the same chords" a necessary condition for a chord to receive the chromatic mediant terminology?

Answer 1

'Chromatic mediant' isn't an analysis, just a description. 'Modal interchange' is often merely an excuse. (Yes, a chord that isn't diatonic in this key will probably be diatonic in some other key. So what? We're in THIS key, the chord needs a reason to exist in THIS key!)

The sort of analysis that wants every chord to have a dominant relationship to the next one can run into problems with much commonplace modern harmony. Look carefully at what a chord DOES, in context, before assigning it a functional description.

C, F, Fm7, Bb7, Eb. A journey from C major to Eb major. Fm7 and Bb could be usefully analysed as 'borrowed' from Eb major. (But note that we can get to ANY new tonal centre by putting its ii7, V7 in front of it - there's nothing particularly special about this being a trip to the 'chromatic mediant')

Or let's just go C, Eb, with a common melody note of G. Yes, that works. It works particularly well when the common note is the tonic or dominant of the home key. C, Ab with the common note C is nice too. (Are we beginning to sniff a reason why 'chromatic mediant' is 'a thing'? But be careful, we could come up with something just as plausible for just about any other chord.)

C, E, Eb, D, (G7, C). Let's be honest, a guitarist was just sliding a full barre chord shape along the fingerboard. Sounds fine, but analysis of the Eb as a 'chromatic mediant' or a 'b5 substitute dominant of D' would be ludicrous. (The excuse for this is 'planing'.)

Answer 2

V and I do not share all their chromatic mediants, so there are chords that are chromatic mediants of V but not I. For example, in C major, B major and B flat major chords are chromatic mediants of V (G major) but not I.

As for bIII as chromatic mediant vs. modal interchange, I generally only classify bIII as a chromatic mediant when it is tonicized/modulated into, it resolves immediately to I, or it resolves directly from a dominant-function chord. Otherwise, it sounds more like it was borrowed from the tonic minor (one of the prime cases of modal interchange).