Tritone Substitutions

reed:

.... about tritone substitutions.

These are even in Bach's music.

The basic idea is that if you take any dominant chord, say C7 and look
at it you have:

C  E  G Bb.

Now within that chord we have a tritone interval, namely E and Bb.

This is a very unstable and strong interval. It is also a tritone no
matter which note you start on. I.e. Bb is a tritone above E and E is a
tritone above Bb.

Thus E is the third and Bb the seventh in a C7 chord. In Gb7 (a chord
with a root a tritone away), E (Fb) is the seventh and Bb is the third.

Because of the dominating nature of the tritone, this interval pretty
much overrides the rest of chord.

[E Bb] is going to resolve to either [F A] or [Eb Cb]

The [F A] corresponds to F major and [Eb Cb] to Cb major.

Thus C7 can be substituted for Gb7 and vice versa because they both have
the same tritone.

This concept is used over and over again in reharmonization.

Now what gets even more interesting is that the root substitutions can
be applied beyond dominant seventh chords.

I.e. sometimes an Abmaj7 can be used in place of a D7 even though
technically Ab7 would be the tritone sub.

For example instead of |C D7 | G7 | we might have |C Abmaj7| G7.

In other words the idea comes from dominants but players have learned to
stretch the concept.

[end reed]

Marc (context is Stella):

> In this key Ab7 is the dominant, so it is a diatonic chord in that key.
> Thus we are borrowing a chord from the parallel minor to use in a
> progression
> for the major scale (a common technique from classical music).
> 
> Then you are saying that the viio7 of Bb would be Adim7 (which can
> function
> as the V of Bb). In this case Ab7b9 == Adim7.

Yes, although in general, classical theory teaches you that any borrowed
chord can substitute for the corresponding scale degree of the original
key.  It's just coincidence that it happens to yield a common substitution
in this case.  Normally, I don't give much credence to classical analysis
of non-diatonic chords, because it seems artificial, but in this case, it
does make more sense to me to think of it this way.

Note another place where classical theory tries to explain something that
is obvious to most jazzers is the tritone sub.  As someone mentioned, it is
used in Bach and elsewhere, but they'd never call it that.  Depending on
how it was used, it would be a Neapolitan, German Sixth, French Sixth, or
Italian Sixth, and it would be spelled with all sorts of weird enharmonics
so you wouldn't recognize it as a seventh chord at all.  But that's all
these things are.

> > I tend to use Eb7alt - D7alt a lot here, sometimes walking the alt
chords
> > down to Bb7alt which I would use in place of the expected Bbmaj7.  The
> > Bb7alt can actually be used as a pedal of sorts over the next several
> > measures.
> >
> 
> So you are saying that beginning with bar 7 you use:
> 
> |Eb7alt D7alt| Bb7alt ..... |  with the Bb7 alt as a pedal for a few
> measures.

No, when I say "walk it down", I mean all steps in between.  That is, a bar
of Eb7alt in place of the Ebmaj7, then a beat each of D7alt, Db7alt, C7alt,
and B7alt in place of the Ab7, then landing on the Bb7alt for a while in
place of the Bbmaj7 and what follows.  That's just one device.  I also use
an F pedal over this whole section sometimes.

[end marc]

reed:

Re: Stella, again - Augmented sixth chords

[weird names for tritone subs.....]

Yes, this is an important point as far as nomenclature goes.

Because of voice leading considerations, the tritone sub is
called an augmented sixth chord in classical music.

For example consider Db7 -> C as a tritone sub for G7 ->C

If we wrote Db7 as a dominant seventh chord it would be:

Db F Ab Cb .

When a note resolves up a half step, you write it as a minor second from
the note you are resolving to. I think the reason why is because that
sound is basically the sound of a leading tone resolving to the root of
the scale. (In the key of C major, B is the leading tone and B->C). The
notation is trying to reflect the function of the two notes.

Thus:  E -> F,  F# ->G,  G#->A  .

In other words you don't write Ab-> A or Gb->G.

If  look at the notes as they would resolve in Db7->C you get:

Db     -> C
F      -> E
Ab     -> G
Cb     -> C

In order to satisfy the rules for notating voice leading you would want
the Cb->C to be B->C.  However B is not the seventh of Db but rather the
augmented 6th. In other words the sixth degree of Db is Bb so B is the
augmented sixth.

So technically the Db7 when substituted for G7 is a Db augmented sixth
chord.

If you read classical music, it is always notated like that. Especially
if you read Chopins Mazurkas or Waltzes you will see this all over the
place.

There are various flavors of augment sixth chords as Marc pointed out.

[end reed]

From: rinzler@cats.ucsc.edu (Paul Rinzler)
Subject: Stella, again - Augmented sixth chords

Reed Kotler wrote:

>Because of voice leading considerations, the tritone sub is
>called an augmented sixth chord in classical music.

=============
My summary of Reed's idea:
The Cb in a Db7 tritone sub for G7 in the key of C is really a B,
following the rule in classical theory that sharps resolve upward and
flats resolve downward, so B can resolve upward to C, whereas Cb wants
to resolve downward; so with a B you get an augmented 6th above Db.
=============

That's correct, except that in jazz a CM7 or Cm7 is "common practice"
(pun intended) after a G7, instead of C (triad), so the B doesn't have
to resolve to C anyway, but to B or Bb potentially.

The problem is that in order for the voice-leading that *defines* the
augmented 6th to work, you have to expand the augmented 6th to an
octave, and once you do that you're outside of common practice in jazz
because you now have a plain triad, rather than the standard 7th chord.

[end Paul Rinzler]

reed:

Paul,

I wasnt awake when I answered you earlier.

It doesnt really matter if the Db7 resovles to a Cmaj7.

In that case if you wrote a score, and B was the melody note over the
Db7 chord, how you would you write the chord?

I'll bet it would be Db F Ab B. Once you write a B it's not technically
a Db7 anymore, otherwise you would write a Cb. However had it been the
original G7 that we were subbing for, the B would have been fine.

Obviously for normal chord charts it doesnt matter at all but if you
write band charts, or piano arrangements out, by the way you are
notating things it is an augmented sixth chord in the case of Db7 as a
sub for G7.

The point is that the note B in that context is the leading tone of the
key of C (it doesnt matter if you actually resolve the note). Once you
use a B in the Db7 chord it's an augmented sixth chord.

[later]

One more point. Let's take a different key.

Let's say the D7 is a chord we use for a tritone sub.

What chord could the sub be for?  Could it be for Ab7?

Technically not because Ab7 = [Ab C Eb Gb] . If we wrote the notes D7 =
[D F# A C] then the F# would be mispelled. So technically D7 could only
be a tritone sub for G#7 .

(The tritone sub for Ab7 is Ebb7!!)

So G#7 is the dominant chord for C#. The note C in the key of C# is B#
so once again we have to spell D7 as D F# A B# when we are in that key
signature so we have an augmented sixth chord.

Anyway, in classical music it is always written this way and should be
in jazz big band charts but I don't know if it is always done properly.

My teacher Richard Hindman really drilled into my head these augmented
sixth chords (in jazz, as he is an amazing player [was Stan Getz's and
Richie Coles pianist for a while ]), as well as the minor plagal cadence
analysis that I've been discussing.

[end]