Argthtjtr

The tritone substitution has been discussed in several questions here, perhaps most notably What is tritone substitution? and Why is bII 7(b5) considered a dominant? (I believe my question is different, but I'd understand and respect the urge to mark this as a duplicate.)

My understanding has always been that "tritone substitution" means that we use a dominant seventh chord that also has the same tritone found in the regular V7 chord. In C, G–B–D–F is our normal V7 chord. But we can instead play D♭–F–A♭–C♭, because the B–F tritone of the G7 becomes the F–C♭ tritone of the D♭7.

But the answers in the linked questions all emphasize that the chords have a root a tritone away from each other, and that these "usually" involve dominant seventh chords; it's only mentioned later (although not always) that they also happen to share the same tritone.

I ask because—and here's why I think my question is not a duplicate—if "tritone substitution" means the first definition above, then it must be used with dominant seventh chords. But if the definition is the second definition, then we can use any chord qualities. Needless to say, a proper understanding of this definition could prevent some major confusion regarding (and incorrect usage of) tritone substitutions, and I don't believe the current questions clarify this distinction.

Another way of asking this question would be: does the term "tritone substitution" refer to the interval shared between two chords, or the root distance between them?

My understanding has been that 'tritone' in tritone substitution refers to both preserving the shared tritone (B and F in this example) and the fact that the roots will be a tritone apart.

So, when part that together the sub will be a minimum of...

Db F ? Cb (enharm. B)

If we use either Ab or Abb for the chord fifth we get either Db7 or Db7b5.

I suppose we could use A natural for a Db7#5.

So they aren't all dominant seventh chords, but include altered versions of a dominant seventh.

I've never tried the #5 but I have tried the b5, but I imagine it would work just fine. The A natural could be held for resolving to a C6.

Anyway, my understanding is a two part meaning: common tritone & roots a tritone apart.

No, it doesn't have to be a dominant 7th. But it does have to have a dominant function.

A tritone substitution substitutes the tritone found in one chord for the same tritone in another chord. C7 contains the tritone E-Bb; F#7 contains the enharmonic tritone A#-E. When you make a tritone substitution, the roots are also a tritone apart (F# is a tritone from C), but you couldn't use an F#m7 instead of F#7, because you will have changed the chord's function in the progression.

But retaining the function (and the internal tritone) does not require the substitution also be a dominant 7th chord. It could be Gb7+, or F#7b9, or any other altered or extended chord with a dominant function and a tritone between its third and seventh.

Tritone substitution is one chord swapped for another, whose root is a tritone away. As in C7 and F♯7.

In C7 there is a tritone between E and B♭, (M3 and m7), which get reversed in the tts of F♯7,, where it's A♯ and E, (M3 and m7.

So, if I understand correctly, the chords themselves are a tritone apart, and both contain a tritone which changes round (M3>m7 and m7>M3), making a full tts.

I understand the development of the tritonus substition as a derivation of the following chord construction: (my explanation is in major-C)

• V7b5 (G,B,Db,F) and its 2nd inversion (Db,F,G,B) - the so called augmented 34 chord (relating to the 4th Db-G)



• the augmented 34 Db,F,G,B is enharmonic identically with Db7b5, the tritonus substitution of G7b5, (namely Db,F,Abb,Cb)




• the 2 chords G7b5 and its tritonus substitution Db7b5 are distanced by definition a tritonus and are built by definition of the same tones.




• Nod in jazz also the chord of the normal dominant G7b9 (G,B,D,F,Ab) or natural Dom.7b9 (natural because of the natural fifth in G7) has been substituted by Db7b9 (Db,F,Ab,Cb,Ebb) - the Dom.7b9 of the tritonus. (Cb,Eb => B,D)




• The substitution of natural dominants (V7) allows a chromatic downwards progression of secondary dominants (V7) in steps of a minor 2nd instead of chains of secondary 5ths.




• This will lead to all kind of variations of steps by a minor 2nd or a 5th. But the tetrades are basically all (V7) or extended chords of (V7) or V7b5 and their function is one of a secondary dominante as far they follow the rule above (chromatic down-step or circle of 5th.

Now I think that Richard proposes that we can substitute any chord by (a same chord?) in distance of a tritonus.

Why not? This would be nothing else but the logical development of the process described above!

If we imagine a progression of a normal chain of (ii7-V7) progression following the circle of 5ths it would be obvious that also the IIm7 chords can be replaced by their tritonus substitution. All jazz chaps can tell whether this is usual. I would be surprised if it’s not.

The textbook answer actually can differ from how this is approached in practice. I'll give the textbook answer first. A tritone substitution is defined to have these characteristics:

1. you're substituting in one dominant 7th chord for an existing dominant 7th chord


2. the original chord and the substituted chord have roots that are a tritone away


3. the 3rd and 7th of the original chord and the 3rd and 7th of the substituted chord are enharmonically equivalent (e.g., B and F form the 3rd and 7th of both G7 and D♭7).

Most textbook definitions I've seen include stipulation #1 alongside either #2 or #3. However, I have actually encountered a definition that only cited stipulation #3! (It essentially listed #1 and #2 as corollaries!) Stipulation #3 is perhaps the most important factor of them all, because it's the reason why a tritone substitution works so well and sounds so good. This emphasis on the two chords sharing the same 3rd & 7th is well-justified because the 3rd and 7th notes define the chord quality:

• M3 + M7 → major 7th chord


• m3 + m7 → minor 7th chord


• M3 + m7 → dominant 7th chord

This certainly isn't a comprehensive list, but it covers the vast majority of chord qualities that one encounters in jazz. (And you can think about other chords like half-diminished or altered dominant as fitting into one of these three chord qualities.)

So for this question, G7, G7♯5, G7♯9, G7♭9, G7♭13, etc. can all be treated the same, because (a) they all contain the same 3rd and 7th, (b) their roots are all a tritone away from D♭7, and (c) they all share the same 3rd and 7th as D♭7.

What about other chord qualities besides dominant 7th--like minor 7th or major 7th? The textbook definition says that these don't qualify as tritone substitutions. For example, you can't substitute Dmin7 for A♭min7, since their 3rd's and 7th's aren't enharmonically the same. (Dmin7 has F and C as its 3rd and 7th, while A♭min7 has C♭ and G♭ as its 3rd and 7th. Those are not enharmonically equivalent, and thus this isn't a textbook tritone substitution.)

But in practice, this requirement isn't always obeyed, and it's not terribly uncommon to hear a tritone substitution that only follows stipulation #2 from above--that the roots are a tritone away. Here's the general evolution that occurred:

| Dmin7 | Dmin7 | G7     |  G7    | Cmaj | Cmaj |

| Dmin7 | Dmin7 | Db7    | Db7    | CMaj | CMaj |

| Dmin7 | Dmin7 | Abmin7 | Db7    | CMaj | CMaj |

| Dmin7 | Dmin7 | Abmin7 | Abmin7 | CMaj | CMaj |

The final version essentially performs the tritone substitution only using the ii chords, and entirely bypasses the V7 chords. This sort of thing can allude to a V7sus sound, or it can serve as something unique in its own right. I believe the final version is more frequently found in fusion jazz (a la Chick Corea). Perhaps because of this evolution, the emphasis has shifted from stipulation #3 to stipulation #2 when defining the tritone substitution.