New lesson: Tritone subs

[Beginner Bass]

Good lesson!

 

[monroe55]

Hi there Mr. Ross,

Good description.

I would add that the essence of a tri-tone sub is the enharmonic re-evaluation of TWO intervals: dim 5th <=> Aug 4, AND m7 <=> Aug 6th.

ie. C, E, Bb, <=> C, E, A#

So while 3rd+7th = 7th+3rd...which you wrote, it's also true that root and minor seventh = root and augmented sixth.

C-Bb = m7 <=> C-A# Aug 6th

In a tonal context as part of a V7 chord, C +Bb resolve (inward) to F and A (or F and Ab);

while C and A# resolve (outward) to B and B.

C7 is also CAug6th and they each resolve melodically to tonic chords that are tri-tones apart from each other. (ie. F and B )

It's a 18thC way of thinking, (where the Aug6th also passes through a 6-4 chord before resolving), but it's a sound that started way back then, then got taken and put everywhere later on.

Huh?

 

[bigfatbass]

As a full time roots player, (definitely NOT a I-IV-V band www.casablancos.com) I use this all the time to keep a progression moving under solos. I try to pick spots where the soloist might dabble in the same voicings, and then follow along with the little bursts of chromaticism, in what is normally pentatonic territory. So, I know about HOW to use it, and WHERE to use it (I hope!), but now I know a lot more about WHY it works.

Thanks for the knowledge y'all!

 

[Richard Lindsey]

Huh?

What he's saying is that for the voice resolution to make sense in standard terms for a tritone substitution--for example, Db7 to C instead of G7 to C--the "7th" in the tritone sub should technically be thought of as an augmented 6th rather than a minor 7th. Thus, Db-F-Ab-B rather than Db-F-Ab-Cb (Db-B is an aug 6th, Db-Cb is a min 7).

The reason is that as these things are commonly taught, Cb doesn't resolve to C; however, B does resolve to C (leading tone to tonic).

This may or may not matter to you.

 

[mambo4]

.... the essence of a tri-tone sub is the enharmonic re-evaluation of TWO intervals: dim 5th <=> Aug 4, AND m7 <=> Aug 6th....etc

Technically correct, sure.
But the essence of a tri-tone sub?
I Disagree strongly.
It works harmonically because of the 3rd and the b7.
Change those pitches and you no longer have a functioning dominant chord.
So the 3rd and the b7th are what I would call the "essence", at least as far as harmonic functionality...
the other stuff is just coloration, and not nearly as important.

YMMV, IMHO and all that...

 

[Richard Lindsey]

Technically correct, sure.
But the essence of a tri-tone sub?
I Disagree strongly.
It works harmonically because of the 3rd and the b7.
Change those pitches and you no longer have a functioning dominant chord.
So the 3rd and the b7th are what I would call the "essence", at least as far as harmonic functionality...
the other stuff is just coloration, and not nearly as important.

YMMV, IMHO and all that...

But I think that's kind of what he's saying already.

His point was that in a dominant 7th chord, the distance between the 3 and the 7, if we look at the pitches in a row, is a diminished 5th (eg, F to Cb). Also, the distance between the root and the 7 is a minor 7th (Db to Cb).

For the voice leading to make sense, the minor 7th should be an augmented 6th (Db to B), which means that the diminished 5th would become an augmented 4th (F to B). As we know, a tritone, such as the one between the 3 and the 7 of a dominant 7th chord, can be expressed either as a diminished 5th or an augmented 4th.

The poster was not arguing against the key role of those two pitches in a tritone substitution. He was saying that in terms of how we think about chord construction, we tend to think of that Db7 as a dominant 7th chord, and thus of that central interval as a diminished 5th, but for the purposes of voice leading, the chord may be better thought of as an augmented 6th chord, making that same tritone an augmented 4th. (Granted, we tend not to see an augmented 6th chord in rock/jazz/pop/country charts, but it is an accepted term in harmony. There are even three--or is it four?--different types, German, Italian, French....)

 

[esoomssab]

Richard -

As I learned it there are 3 augmented sixth chords but the German has two forms that sound the same.

Relative to the tonic, the first German Augmented Sixth contains the b6, 1, b3, and #4 and the second contains the b6, 1, #2, #4

The Ger+6 in the first form can resolve to the dominant, or tonic 6-4; the second form must resolve to the tonic 6-4, due to the #2 being a tendency tone because of the way it's written.

As I remember and understand it - but anyways, it's still a bit fuzzy. The difference between the two is really just theoretical, just like the reworking of the Db7.

 

[Richard Lindsey]

Richard -

As I learned it there are 3 augmented sixth chords but the German has two forms that sound the same.

Relative to the tonic, the first German Augmented Sixth contains the b6, 1, b3, and #4 and the second contains the b6, 1, #2, #4

The Ger+6 in the first form can resolve to the dominant, or tonic 6-4; the second form must resolve to the tonic 6-4, due to the #2 being a tendency tone because of the way it's written.

As I remember and understand it - but anyways, it's still a bit fuzzy. The difference between the two is really just theoretical, just like the reworking of the Db7.

That sounds about right. I don't think I've thought about this for 20 years or more.

 

[longfinger]

Richard -

Relative to the tonic, the first German Augmented Sixth contains the b6, 1, b3, and #4 and the second contains the b6, 1, #2, #4

Thanks Richard for adding some extra clarity to what I wrote.


--
For the above, this may just be for the German 6th chord in a minor key (b6, 1, b3, #4) and in a major key (b6, 1, #2, #4).

They both need to pass through a cadential 6-4 chord to avoid parallel 5h between the b6 ->5, and the b3 (#2) -> 2.
For minor keys b3 stays where it is, and for major keys #2 climbs to 3. Then they both pass down to 2.

 

[HaVIC5]

Thanks Richard for adding some extra clarity to what I wrote.


--
For the above, this may just be for the German 6th chord in a minor key (b6, 1, b3, #4) and in a major key (b6, 1, #2, #4).

They both need to pass through a cadential 6-4 chord to avoid parallel 5h between the b6 ->5, and the b3 (#2) -> 2.
For minor keys b3 stays where it is, and for major keys #2 climbs to 3. Then they both pass down to 2.

Except of course, when it doesn't pass through the cadential 6-4 chord and creates (gasp!) parallel fifths. Mozart was known to do this, and this sort of parallel fifth is know as the "Mozart Fifth" for that reason.

http://en.wikipedia.org/wiki/Consecutive_fifths#Mozart_fifths

It's interesting to note the parallels between the augmented sixth chords and tritone substitutions, although it wasn't until later on in the common practice that augmented sixth chords gained the flexibility that tritone subs have with jazz music today. Academia would have you believe that the only kinds of augmented sixths ever to exist were the German, Italian and French varieties which always resolved to some sort of dominant structure (or cadential 6-4). This would make them (roughly) enharmonic to subV/V. For example, the German augmented sixth chord in the key of C would be spelled Ab C Eb (D#) F#, which is enharmonic to Ab7. Ab7 is the tritone sub of D7, the V7 of V.

However, come the mid to late 19th centuries, composers started playing with this structure a LOT more, and no longer was it limited to resolving to the V7. You could have, say, Fr+6/I (Db F G B), or Gr+6/ii (Eb G Ab C#). In fact, you could have augmented sixth resolutions on any of the chord degrees, except probably VII, which is the exact same sort of system we have today with subV's, just with a different theoretical justification.

 

[tZer]

Wow... Pencil out... notes being taken...

 

[Richard Lindsey]

Except of course, when it doesn't pass through the cadential 6-4 chord and creates (gasp!) parallel fifths. Mozart was known to do this, and this sort of parallel fifth is know as the "Mozart Fifth" for that reason.

http://en.wikipedia.org/wiki/Consecutive_fifths#Mozart_fifths

It's interesting to note the parallels between the augmented sixth chords and tritone substitutions, although it wasn't until later on in the common practice that augmented sixth chords gained the flexibility that tritone subs have with jazz music today. Academia would have you believe that the only kinds of augmented sixths ever to exist were the German, Italian and French varieties which always resolved to some sort of dominant structure (or cadential 6-4). This would make them (roughly) enharmonic to subV/V. For example, the German augmented sixth chord in the key of C would be spelled Ab C Eb (D#) F#, which is enharmonic to Ab7. Ab7 is the tritone sub of D7, the V7 of V.

However, come the mid to late 19th centuries, composers started playing with this structure a LOT more, and no longer was it limited to resolving to the V7. You could have, say, Fr+6/I (Db F G B), or Gr+6/ii (Eb G Ab C#). In fact, you could have augmented sixth resolutions on any of the chord degrees, except probably VII, which is the exact same sort of system we have today with subV's, just with a different theoretical justification.

Nice one. I had entirely forgotten about the "Mozart fifth"!