2

In melodic minor you get a #6 (and #7) ascending.

Do composers commonly use the #6 to build a chord on? Are there exceptions?

So in a min you'd get an diminished triad like (F# A C) which would probably sound pretty dissonant.

Doesn't seem like their style?

But what even further confuses me: if you create a melody that had the f# played on a strong beat over a normal VI (F,A,C) it would sound even more dissonant.

6

Let's straighten out a bit of terminology to start with. Let's call the melodic degrees in question 6 and 7 when used in the major, and ♭6 and ♭7 when used unsharped in the minor. You're talking about the substitution of 6 for ♭6. Also, there's nary a major third to be seen in F♯-A-C - the chord is diminished, not augmented.

Normally F♯ is going to be a passing note in a rising scale segment from 5 to 1. However, it does present a possibility of being interpreted as part of a strong predominant. A diminished chord on F♯ would fall into this category fairly neatly (as shown in ex. a), as it would tend to suggest a truncated version of vii°7/V (ex. b) or V♭9/V (ex. c). So here, the diminished triad is standing in for the dominant of the dominant. I can't pull out an example in the literature off the top of my head, but the voice leading is so unexceptional that I don't doubt that it has been done.

enter image description here

Diminished chords are generally considered only moderately dissonant - they form, after all, part of the dominant seventh chord.

6 against ♭6 does show up in the literature, generally where ♭6 is falling to 5 and 6 is rising to 7. There is a rather baldfaced example in 2 voices in Domenico Scarlatti's Sonata in A minor K. 3:

enter image description here

Take a look at what is happening in ms. 17, 21 & 25. These all use 6 of the current key in the bass againgst a held ♭6 in the soprano. Yes, it is dissonant, probably more dissonant than it would be if mellowed by accompanying thirds, but it makes sense in the context of the voice leading. I haven't run across this cross relation used in exactly the way you posit, but I don't see anything inherently wrong with it, provided the voice leading works:

enter image description here

This uses your cross relation transposed by a fifth to fill out the Scarlatti example.

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    I edited my post to reflect dim instead of aug. – Kolob Canyon Nov 6 '16 at 15:16
  • There is a rather terrible parallel fifth in your example a (doubling the a instead of the f sharp should solve this). As for a literature example, I assume any rising faulx-bourdon by a baroque composer would use the raised sixth. – 11684 Nov 6 '16 at 23:38
  • Maybe a better fix would just be to resolve to V6 doubling the b. – 11684 Nov 6 '16 at 23:50
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    @11684, not a parallel fifth, a direct fifth - that's a diminished fifth (C over F♯) moving to a perfect fifth, using an inner voice at the top of the fifth, and that is quite common and quite "legal" in common practice harmony. – user16935 Nov 7 '16 at 0:00
  • The cross relation is fairly common, but examples that pit 6 directly against ♭6 (sounding at the same time) are a bit rare: 7 against ♭7 is more common. – user16935 Nov 7 '16 at 0:12

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