Why do tritone substitute dominants have tensions 9 #11 13?

Question

Secondary dominants take upper tensions from the key of the piece.

Diminished 7ths take upper tensions from the key of the piece.

Makes sense.

But substitute Vs (which are a form of secondary dominant) take upper tensions from the key of the chord. Why?

E.g. Db 7th will have an Eb G Bb on top (9, #11, 13). But sometimes they'll also take a #9 - which is not in the key of the chord. How were these tensions derived?

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Update

Some of the comments and answers amount to "you can add alterations however it sounds good". But my first year jazz theory teacher said the alterations are used because of the underlying mode. For instance, the V7 of a major key will not have altered tensions (e.g. G7 in C major will not have Ab), but in a minor mode they will (e.g. G7 in C harmonic minor will have Ab).

Below you can see all the available tensions in each mode in this chart in orange:

Gurney's answer that we use the alterations for a tritone sub's chord's key, rather than the song's key seems most correct: "It is harder to make the listener aware that you are using a tritone substitution."

But that doesn't explain why you may use a #9 only in subV/I, subV/IV, and subV/V (when you are resolving to a major key), and not the minors. I feel there is still an underyling principle here that could be explained faster and more elegantly.

Answer 1

Consider G7 in the key of C major = > G B D F (all in the C major scale). You will normally have tensions 9, #11, and 13 (A, C#, and E which are in the C major scale, except C#).

Now substitute G7 for Db. You get:

• Db: same note as G7's #11, out of the C major scale
• F: same note as G7's 7, inside the C major scale
• Ab: not part of G7 9 #11 13, out of the C major scale
• Cb (a.k.a. B): same note as G7's 3

If you go for extensions:

• Db's 9 is Eb: this is a b13 for G7, out of the C major scale
• Db's #11 is G: root of G7
• Db's 13 is Bb: this is the #9 of G7

So, if you go for these extension, you get a bigger color change compared to an unsubstituted G7, with more notes outside the C major scale, meaning that a melodic line will have more ways of indicating a substitution.

OTOH if you use b9/#9 and b13 over Db, you get

• b9: D, which is 5 of G7
• augmented 9: E, which is 13 of G7
• b13: A, which is 9 of G7

=> it is harder to make the listener aware that you are using a tritone substitution in the melody.

Conversely, in C minor, G7 normally has extensions b9 / #9 and b13. If you make a tritone substitution, you will generally use Db7 9 #11 13 in that context.

Answer 2

But substitute Vs (which are a form of secondary dominant) take upper tensions from the key of the chord. Why?

Well first, think about in minor scale harmony, the V chord is almost always major which is borrowed (at its core) from the fact that the leading tone should rise to the root and, ideally, the 4th should fall to the 3rd, yielding both the harmonic and melodic minor scales (that is, both are scales with a raised 7th and a natural 4th). But as far as further borrowing, the fact that we now add various "extras" (#9ths and #5ths and so on) has to do with the fact that, as pointed out in Tim's comment, generally something interesting is first found and then explained afterwards. If you listen to older jazz and blues, the flat 3rd/sharp 9 is ubiquitous (as it still is today) because they sound good. However, extensions are generally explained to students of Jazz in a few ways as to where they "come from" and how to apply them.

Let's take G7#9 (G B D E F Bb/A#) for example. It can be explained as the following:

1. The result of a harmonized diminished scale (i.e., the scale that produces G7b9 also produces G7#9, as well as G7#9#11)
2. Sometimes it implies the altered chord, which would be derived (here) from Ab melodic minor (here the actual chord would be G7#9#11 or G7b5#9)
3. Can be constructed from a triad pair, here being a G triad (G B D) and a Bb triad (Bb D F). You'll notice that, viola, these are the exact notes in the G7#9 chord with the D natural being in both chords. Many times upper structures (i.e., 9ths, 11ths, 13ths) will be construed as a triad placed above the "lower" chord (so for example, a Cmaj13#11 can be construed as a D major triad (D F# A) above a Cmaj7 (C E G B)).

The reason for this is that it makes it easier to improvise over a complex sound when you have a scale or some structure to reference. Triad pairs are particularly interesting to study because they open up unconventional sounds while being very simple in construction.