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If I am in C major I will often see the b6 described as "mode mixture" in my text books or a borrowed note from the natural minor scale. However if I am in the key of C and play a III chord with a major 3rd, this will be notated as a #5. Under which circumstances do we see #5 and under which circumstances do we see b6?

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I recommend thinking of at least two issues for this question: the harmonic function/environment of the tone and its resolution.

By "harmonic environment of the tone" I mean its role in the current harmony. If you have a major III chord built on E in the key of C, the major third above E is a G♯ and not an A♭, because a third above E is some kind of G. (The A♭, meanwhile, would be a diminished fourth above E.) Similarly, if you want to play a minor iv in the key of C, your root will be F, meaning the third above must be A♭ and not G♯ (the latter of which would only be a second above F).

As for the tone's resolution, there's a general rule in tonal music that raised notes resolve up and lowered notes resolve down. There are various factors that get in the way of this rule, but it's still largely followed. So if this pitch ends up resolving up to A, it will likely be spelled as G♯; if it's resolving down to G, it will likely be spelled as A♭.

Thus a I–III–IV–I progression will have a G♯ going up to A from III to IV, whereas a I–iv–V–I progression will have an A♭ going down to G from iv to V.

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Notate your example and the answer will be apparent. III is a major triad, and will be notated to LOOK like a major triad with a major third (♯5 of the scale), not a flattened fourth. The other commonly altered triad, iv, is a minor chord, so will be written with a minor third.

Think of your other question about diminished 7th chords. Those 4 notes can be spelt in several different ways, and take the harmony in several different directions. Likewise that black note between G and A. Don't worry about what it IS - notice what it DOES.

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  • Ok so even though the note is "borrowed" from the minor mode it can appear in the major mode as a raised 5th or lowered 6th..... the fact that it is ^6 in minor is not important?
    – armani
    Aug 17 at 17:37
  • I agree. Notating the two pitches (and then completing the triads) makes clear you will be dealing with two different chords, two different roots. Aug 17 at 19:10
  • If you really want to justify these common chromatic chords as 'borrowed', III is the dominant of the relative minor. The G# is 'borrowed' from either the Melodic or Harmonic forms of the A minor scale. But I wouldn't get too hung up on 'borrowing'. It can explain ANY note with a bit of ingenuity.
    – Laurence
    Aug 17 at 19:11
  • @armani, "...the note..." be careful to not think of it as ONE pitch just because they are enharmonic equivalents. It's two different scale degree alterations first and the enharmonic equivalence is coincidence. Also, note the different functions. Sharp ^5 forms dominant harmony while flat ^6 forms subdominant harmony. Aug 17 at 19:15
  • Michael, if they are to be seen as two separate pitches I cant see how they come from the minor scale, can you?
    – armani
    Aug 17 at 19:43
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Taking your key as an example, the III (or more accurately V/vi) will be G♯ - the M3 of that chord E. Hence here it is ♯5.

If the chord at the time is, say Fm, then the m3 will be A♭, so will be written as ♭6. Same note, different harmonic setting.

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  • 1
    Could you explain why?
    – armani
    Aug 17 at 10:58
  • I thought I did. When the note is part of, say, an E chord, it won't be Ab. When part of an Fm chord, it won't be G#. It may be part of C+, so will have to be G#, as G# is the note that is part of C+, while Ab isn't. How could it? Has nothing to do with borrowed anything, or modal stuff.
    – Tim
    Aug 17 at 11:22
  • Now, the funny part is that the precise chord you're borrowing suddenly gets important when it comes to notating a seeming Bb7 in C major as either Bb-D-F-Ab (e.g. V7/bIII) or Bb-D-F-G# (Ger. Aug. 6 of ii).
    – Dekkadeci
    Aug 17 at 15:30
  • @Dekkadeci - err, yes, Fm is borrowed! It's a chord I sort of expect to find in key C, and, yes, it's borrowed. I prefer the former of your two.
    – Tim
    Aug 17 at 16:17
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One of the underlying ideas in "music theory" is that chords are constructed out of thirds. Thus E-G#-B is a chord within the theory, but E-Ab-B is not and would require additional justification to fit within the principles of Tonality and Functional Harmony.

The F minor chord occurs "naturally" in the key of C minor, meaning it's made up entirely of notes from that key. So, when F minor appears within the context of C major, it's considered "borrowed".

E major does not appear in C minor, so it cannot be seen as borrowed from that key.

A b6 would appear in chords arising out of the minor scale: iio, iio7, or ii7b5; iv; VI; or viio7

#5 would appear in chords which require that pitch: I+; III#; or #Vo. However, III# would typically be interpreted as V/vi, and #Vo would most likely be interpreted as viio/vi. Only I+ has a clear meaning within functional harmony.

Where one might see E-Ab-B would be as a chromatic passing tone leading to E minor (iii). E-Ab-B, however, wouldn't be considered a chord in its own right; just an incidental result of horizontal movement.

E-Ab-B as passing chord

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