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Imagine the following progression:

C F D♭7 C

We typically just explain that third chord as a tritone substitution—and we stop there!—but this must be maddening for beginners, because we aren't actively explaining what it's a tritone substitution of.

Is there a common labeling system that explains what's being substituted? Instead of just labeling that chord, say, "TTS," are there any systems in place that would clarify this as a TTS of a G7?

I'm looking to use a system in my own teaching, and I'm curious if such a system already exists. In the absence of no other solutions, I'm currently leaning towards something like TTS(G7).

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    FWIW: In all my jazz playing from middle school through conservatory and freelance playing — nor in any jazz method book, chart, or fake book I've read — I've never encountered any notation (let alone a standard one) to specify a tritone substitution.
    – Aaron
    Aug 17, 2021 at 0:15
  • @Aaron I'm glad to hear that I'm not the only one that's sensed this. This seems like a major pedagogical oversight!
    – Richard
    Aug 17, 2021 at 0:17
  • As far as I know, tts is a direct substitution of a particular chord for another particular chord. I.e. V7 is changed for bII7. That's the ony alternative. It works using the 3 and 7 of one for the 7 and 3 of the other, so nothing else is in the frame. And the tritone bit involves the roots thereof. To me, that's a good clear explanantion, and one my students understand and use. Maybe just accept the fact, like we accept that dogs go 'woof' and don't go 'moo'.
    – Tim
    Aug 17, 2021 at 7:14
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    @Richard but secondary dominant isn't really analogous, because it refers to a relative function rather than a substitution. A better analogy might be the similar function of ii and IV or of vi and I. But we don't label these every time we see them, we just learn that they have a similar function. We certainly don't label ii as vi/IV without some reason to think we've moved to a different tonal center. The analogy you raise perhaps argues for calling E♭7 in C major "sub(V)/ii" or "TTS/ii" because it is a substituted secondary dominant of D.
    – phoog
    Aug 17, 2021 at 20:54
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    I thought you were arguing for TTS(G7). That seems to be analogous to calling d minor RMS(F), where RMS means "relative minor substitution."
    – phoog
    Aug 18, 2021 at 3:22

4 Answers 4

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This is often notated as sub(V), spoken as "sub five". The "sub" is short for "substitution", and it is understood as specifically the tritone substitution of the chord. The chord in (sometimes omitted) parentheses is the chord which is being replaced by the substitution, as in "sub of five" or "substitution for the dominant". Just like applied dominants, it can also be imagined like a programming or mathematical function notation - "apply the tritone substitution function to the V7 chord", in plain letters.

C F Db7 C would then be I IV sub(V7) I in RNA. This can be done in secondary positions as well, so Ab7 Db7 Cmaj7 would come out as sub(V7/V) sub(V7) I.

This is mainly useful for analysis purposes; I would wager that a majority of musicians would prefer bII7 over sub(V7) for the practicality of performance. However, it is a nice instructive tool for understanding the justification behind certain harmonies (in the same way that bVI7 is easier to play from than the pedagogical Ger+6 notation). It is also clearly not meant to cover the Neapolitan 6th chord N6, though the two are extremely similar.

As far as I am aware, this is already a standard convention for Roman Numeral Analysis, or at least a widely accepted symbol in jazz analysis. I have seen this notation before, and a cursory search found me a number of websites using this nomenclature: simplifyingtheory.com, The Jazz Resource, Chris Fitzgerald, this answer here on Music: Practice and Theory, this Reddit thread, Jazz Guitar Online, and ZOTZin Guitar Lessons all demonstrate this subV labelling principle. I have no doubt many other sources using this convention could be dug up as well!

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    Are you proposing a notation, or have you seen this in use somewhere? If the latter, please post the citation.
    – Aaron
    Aug 17, 2021 at 1:24
  • @Aaron Observed in use (see edit).
    – user45266
    Aug 17, 2021 at 1:48
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    Now that is an answer! :-) Much appreciated. The notation is entirely new to me.
    – Aaron
    Aug 17, 2021 at 2:36
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    I’ve used subV for analysis for years (but no parentheses on the V). I learned it at Berklee College of Music in 19XX.
    – John Belzaguy
    Aug 17, 2021 at 3:13
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    Another example of the basic idea books.google.com/…
    – Michael Curtis
    Aug 17, 2021 at 15:39
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We label a secondary dominant as V of V or V/V. I suppose we could label the TTS as TTS/V. Or maybe V(TTS).

If using absolute chord names rather than functional labels, and you felt explanation of an 'outside' chord was necessary, 'D♭7' could be annotated '(TTS of G7)'.

(later)

But if, as @user45266 informs us, there is already a 'sub(V7)' convention in use, I guess we join in!

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In analysis (and, at least for me, during improvisation and composition), there's a difference in some seemingly identical chords. The pattern (in equal or recirculant temperament) Ab-C-Eb-F# acts (and is notated as) a German Sixth when the resolution of the augmented sixth is outward: Ab-C-Eb-F# -> G-C-Eb-G -> G-B-D-G or something similar. It's a tritone substitution when it resolves as Ab-C-Eb-Gb to Db. Beethoven (and I think Schumann among others) liked to proceed to the chord in one way and leave in another. It's useful to have lots of choices.

(As mentioned in another answer) the Neapolitan Third doesn't seem to act this way. The other Augmented Sixth chords can be entered and resolved as tritone substitutions.

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  • Truth indeed on the Augmented 6th being different from the tritone substitution. I must ask, though, what do you propose for the question of how to label tritone substitutions? I must be missing it, sorry...
    – user45266
    Aug 18, 2021 at 5:53
  • Paul Harder (in his very good programmed learning books on harmony) discusses the use of Augmented Sixth chords on scale steps 2, 4, and 6 but has no particular name for this construction. He shows resolutions from the Aug Sixth on 6 to V and on 4 to step I and on 2 to I or I6. Classically, this is sufficient as the bass note is almost always given. (I think Steinke is the current author of the series.) Perhaps in line with some authors who us F, G, A, N for Sixth, a T would be sufficient if the tritone sub is a bII. or just bII7-I would work. Then ii-bII7-I would work.
    – ttw
    Aug 18, 2021 at 13:33
  • @ttw I think I'm misunderstanding you when you say "It's a tritone substitution when it resolves as Ab-C-Eb-Gb to Db." That would be viewed as a V7 of the Neapolitan, no?
    – Richard
    Aug 18, 2021 at 15:13
  • That's true. However if the approach to the Ab7 indicates a German Sixth, the alternate resolution is the tritone sub. It may not be a jazzy version, but the alternate resolutions of the Augmented Sixths do resolve the tritone in the "other" direction. It's hard to label something that's inherently ambiguous.
    – ttw
    Aug 18, 2021 at 15:37
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I discovered the tritone substitution this way:

going from dominant to the tonic (B7 to E)

  1. play the V7-circle B7-E7-A7-D7-G7-C7-F7-E
  2. play chroV7 chromatic scale downward: B7-Bb7-A7-Ab7-G7-Gb7-F7-E r.hand.
  3. same as version 2 in r.h. and bass B-E-A-D-G-C-F->e

this passage demonstrates that the chords are interchangeable, each second interval is a tritone and the chord is the tritone substitution. You don't need another name when a beginner knows triads and the terms third and fifth he will understand the diminished fifth and minor second and the tritone like the tritone substitution.

So the concept becomes evident by:

  1. playing, 2. listening 3. writing
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