# How can French A6 and V7b5/b5 be seen as the same?

While I was reading about commonalities between French A6 and tritone substitute, I kept bumping into the similarities between French A6 and V7b5/b5.

French A6 is ^b6 ^1 ^2 ^#4 and V7b5/b5 is ^5 ^7 ^b2 ^4.

Their scale degrees and interval structure are different. But what similarities are there to draw between them?

• I thought the French sixth had a normal second scale degree, not a b2 in it. That would give them the same interval structure a half step apart. Commented Jul 8 at 11:32
• yeah you are right. I will change it
– Sean
Commented Jul 8 at 21:47

Note the passage's wording carefully. The French Augmented 6th in question spans ^♭2 to ^7 instead of the usual ^♭6 to ^♯4. This means that the French Augmented 6th in question contains ^♭2 - ^4 - ^5 - ^7. These are the same notes as in V7♭5 in second inversion.

You can look at it two ways. Let's take an example in `C` minor where the French augmented sixth chord will be spelled `A♭ C D F♯`:

• `A♭ C D F♯` can be enharmonically respelled to `A♭ C E𝄫 G♭` which is `A♭7♭5`.
• `A♭ C D F♯` can be viewed as an altered `iio7` chord, which would be spelled `D F A♭ C`, where the alteration is raising the chord's third to create `D F♯ A♭ C`, which can then be put in second inversion for the common `Fr+6` voicing `A♭ C D F♯`, and also it can be viewed as yet another altered dominant, because `D F♯ A♭ C` is `D7♭5`.

In the quote you posted, the concluding "more rarely..." part is new to me and interesting. I would recommend comparing those resolutions to the resolution of a common tone diminished seventh chord to a major tonic triad, where the common link between the various chords is the shared tritone of `^6` and `♯^2` or `^1` and `♯^4`.

The two rare chords the author presents are analogous to a tritone substitution of a dominant chord, except the chords described are tritone substitutions of a common tone diminished seventh chord.

There is a lot of wacky enharmonic spelling changes, substitutions, and re-arrangement of pitches involved with these concepts. If something isn't clear I can add additional detail.

Of course the very, very important thing to distinguish is how these chord resolve. The `Fr+6` standard resolution is to a dominant chord, and to be very standard it will be a triad with a half cadence feel. The point is they are subdominant or pre-dominant in function. Compare that with a jazz tritone substitution which is dominant in function, and the plagal resolution of the "more rarely" used chords.