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In the book that I am reading, the author says that

secondary dominant's root is diatonic whereas its tritone substitute's root is chromatic.

And therefore tritone substitute's tensions need to "agree to the chord(diatonic to the root of the chord?) and clarify its function. The dissonance produced by b9 and b13(effective in primary and secondary dominants) ... lead the ear toward outside of the key and do not work at all as an enhancement of subV(tritone substitute)."

Does this mean any chords with chromatic roots(not only subV's) need to have tensions diatonic to the root of the chord and non-diatonic to the key?

If so, how does "lead(ing) the ear toward outside of the key" occur?

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  • As presented, this doesn't make sense. What is important about being a secondary dominant? And "diatonic" to what: the original key or the secondary key? Until those are clarified, it's unclear why b9 and b13 would be non-diatonic — that is, non-diatonic to which key?
    – Aaron
    Commented May 24 at 2:46
  • Difference between secondary dominant and tritone substitute is that secondary dominant's root is diatonic to the key of the song, while tritone substitute's root is chromatic. Because tritone substitute's root is chromatic, it cannot use dissonant tensions b9, b13 (because they lead the ear toward outside of the key of the song). So Lydian b7 is used for tritone substitute, while secondary dominant is free to use (alt) tension set
    – Sean
    Commented May 24 at 7:11
  • That just restates your question. It's not true that a secondary dominant's root is diatonic to the key of the song. The secondary dominant's root is diatonic to the key it is leading to — which could be any key — but may or may not be diatonic to the song's main key. What my question was meant to get across was: why does it have to be a secondary dominant (in which case the premise about being diatonic is not always true) as opposed to just a regular dominant of the main key?
    – Aaron
    Commented May 24 at 7:23
  • firstly, I meant primary/secondary dominant because their roots are all diatonic to the original key. Secondary dominant is chromatic 'chord' to the original key, but the root is diatonic.
    – Sean
    Commented May 24 at 9:19
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    If you were to show the author’s actual text instead of paraphrasing, your questions would be easier to understand and answer. Commented May 24 at 15:40

3 Answers 3

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So say you are playing II-V-I in C and sub the V with the tritone sub:

Dm-Db7-Cmaj

your b9 and b13 tensions are D and A so literally the root and the fifth of the II chord. So essentially they are not tensions anymore in relation to the actual (not substituted) dominant. If you play II-V-I and on change to V will play these notes they would be probably the worst possible note choices as they are grounding the previous chord and don't "present" the change. The b5 tension on the other hand this is the root of the primary dominant (G in this case) so it fits the II-V change pretty well. That's why the author suggests using Db lydian dominant in this case. Altered scale of tritone substitute of dominant is just a pretty incoherent set of notes.

so now to answer your specific questions:

Does this mean any chords with chromatic roots(not only subV's) need to have tensions diatonic to the root of the chord and non-diatonic to the key?

this is more of a general and frankly quite obvious observation that if we are substituting chords, their alterations are simply loosing its context and meaning. For me this is just an example like this type of "chord theory" explanations make obvious relations very convoluted and hard to grasp.

If so, how does "lead(ing) the ear toward outside of the key" occur?

Here again I have an impression that the author is very casual with the meaning of the words he is using, such as "key". In our example of II-V-I the tensions of the tritone sub are in the key of C but the problem with them is they imply II and therefore sticking on them don't push the harmony forward through II-V change. The musical effect is literally like beginner still struggling through the changes and playing C major scale throughout the whole II-V-I.

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I think he's just saying that you need to be careful about using altered extensions in chromatically-rooted chords, lest it all gets a bit too 'outside'.

(Isn't F♯7 a secondary dominant in C major?)

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  • yeah... but the author doesn't really accept it as secondary dominant because it does not fit to "secondary dominants having diatonic roots"... besides VII-7b5 is so unstable that it is meaningless to be a target chord.
    – Sean
    Commented May 24 at 10:18
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TL;DR

Based on the current presentation of the problem, the only time b9 and b13 extensions on tritone substitutions for secondary dominants are problematic is on subV/iii and subV/vi.


Summary

  1. Piece in key of C
  2. Possible roots of secondary dominants: C D E F (G) A B (G being primary)
  3. Roots of possible subV's: F# G# A# B C# D# E#=F
  4. b9 extensions: G A B C D E F#
  5. b13 extensions: D E F# G A B C#
  6. All b9 and b13 are diatonic to the original key (C major) except subV/iii and subV/vi.

Full explanation

The author's statement, as presented here, is ambiguous (at best) and depends on specifically which chord(s) he's discussing.

Consider a piece in C major.

Since the author limits secondary dominant chords to those whose root is diatonic to, in this case, C major, the possible roots are the notes of the C major scale:

C D E F G A B

This means that the possible target keys (of the secondary dominant) are:

F G A Bb C D E (Of course, the G-dominant to C-tonic isn't a "secondary" case, but that won't matter for this discussion.)

And since we're really discussing tritone substitutions, then instead of dominant chords rooted on C D E F G A B, we have as possible roots

F#       G#      A#       B          C#      D#       E#=F
subV/IV  subV/V  subV/vi  subV/bVII  subV/I  subV/ii  subV/iii

Given those roots for tritone subs, the b9 and b13 chord extensions (considered enharmonically) would be

G A B  C D E F# (b9)
D E F# G A B C# (b13)

In all but two cases (B-F# and F#-C#) these are diatonic to the original key of C major.

Thus, b9 and b13 are diatonic to the original key (C major) for every secondary dominant's tritone substitution except subV/vi and subV/iii.

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