5

On my question Why does the French sixth sound more dissonant than the others?, I got this answer from Ben I.:

It's because the French 6th chord has an extra tritone.

If we take an A♭ Augmented 6th chord, we would have:

A♭ C D F♯

A♭ to D and C to F♯ are both tritones.

Caters had wrote this comment on Ben I.'s answer:

So, it is like a diminished 7th (which is also 2 overlapping tritones) but based on the major chord instead?

Both the Fr. 6 and dim7 are made of two overlapping tritones. The question is, are there any chords that are made of two overlapping tritones other than the dim7 and the Fr. 6?

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    The third option is 0167 (e.g. C C# F# G) and its inversion 056e (e.g. C F F# B), also called a "Z-Cell" and apparently used by Bartok in his 6th string quartet. – Your Uncle Bob Apr 11 at 9:09
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    Theoretically, if you kept adding degrees you could have infinite tritones, disregarding the key signature. – Nathan Tibbitts Apr 15 at 14:37
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The V7♭5 also has two overlapping tritones, but it and the French augmented-sixth chord are just enharmonic spellings of each other; in C, the V7♭5 is G–B–D♭–F, which is the same as the French in B (G–B–C♯–F).

From this, we also see that most extended dominant chords that involve the ♯11 will also have these two tritone (one between the root and ♯11, the other between the third and ♭7), but occasionally a voicing preference may remove one of the involved pitches.

You have Scriabin's Mystic chord, but really that's just an extended V7 chord just discussed in the prior paragraph.

And speaking of special "composer chords," the Petroushka chord is a polychord of two triads: C major and F♯ major. This means that there are actually three embedded tritones, each between the roots, thirds, and fifths of either triad.

Perhaps notably, the Tristan chord only has one tritone.

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    I was also thinking of Tristan, because Tristan and tritone would be a nice paranomasia. – Albrecht Hügli Apr 11 at 14:13
3

Apart from the diminished seventh chord and the dominant 7(b5) chord mentioned in other answers, another useful chord with two stacked tritones is the dominant 7 (#9 13) (usually played without the 5th). E.g., an E7(#9,13) would be played with the following notes:

E G# D G C#

where I've spelled out the #9 as a b10 (G). There's a tritone between G# and D, and between G and C#.

Note that the same chord with its root a tritone away from the original root (in our example a Bb7(#9,13) has the same upper structure (enharmonically):

Bb D Ab Db G

where the upper structure D Ab Db G is enharmonically the same as the upper structure G# D G C# of the E7(#9,13).

An appropriate chord scale for that chord is the half-whole octatonic scale.

  • +1, although those aren't "overlapping tritones" in the voicings you wrote. – user45266 Apr 13 at 5:41
  • @user45266: That's right, but they were not meant as voicings, just as a sequential list of chord tones. – Matt L. Apr 13 at 12:31
3

There are 6 possible tritones before we reach the inversion of the first one. This is what we get when overlapping each of them. They all COULD be described by a chord symbol. I'd say that B, C and D deserve an name rather than a description. For instance, A could be 'C(sus♭2)(add#11)' but that isn't really very useful! What do you think?

(We could extend into chords that INCLUDE two overlapping tritones rather than consisting of JUST two overlapping tritones of course...)

enter image description here

  • I really like how you show systematically how run all the possibilities for a definitive answer. Wish you added the example symbols so I could be lazy and do it myself :-) – Michael Curtis Apr 11 at 13:00
  • A could also be a (rather spicy) rootless voicing of A13♯9. You have a great list, but I think it leaves out the possibility of chords with more than 4 notes in them. +1 – user45266 Apr 13 at 5:40
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    Yes, I restricted myself to chords composed of JUST two overlapping tritones. And yes, I tend to lose interest in chord-labelling when '0mit root' becomes necessary! – Laurence Payne Apr 13 at 13:08
  • The first inversion of example E is identical to example A, transposed up a perfect fourth. I would be inclined to consider them as identical, just as the first inversion of example C, the diminished 7th chord, is enharmonically equivalent to itself transposed up a minor third. Perhaps unsurprisingly, the same symmetry exists between examples B and D. So in fact there's really only one additional chord to the two identified in the question. – phoog Apr 13 at 17:00
3

You can think of the French augmented sixth chord, in first inversion, as two whole steps separated by a tritone. This gives two overlapping tritones, one between the lower notes of the whole steps and one between the upper notes.

Similarly, a diminished seventh chord can be described as two minor thirds separated by a tritone. So we can try this with a smaller interval, and find that there is also a chord that is two half steps separated by a tritone (for example C, D-flat, F-sharp, G). I don't know how useful that will be, but it will certainly be more dissonant than the other two.

But if we try to use any larger intervals (and if we're considering inversions to be equivalent, and we're ignoring enharmonic respellings) we'll find that we are repeating ourselves, because a major third is a whole step smaller than a tritone. The chord that is constructed by placing two major thirds a tritone apart is equivalent to an inversion of the chord that comprises two whole steps a tritone apart. So (ignorimg inversions and respellings) there are only three such chords: the two you mentioned plus the one made from two half steps.

2

what about the V#579 ?

So,Ti,Ri,Fa,La (e.g. G-B-D#-F-A)

tritones=Ti-Fa and Ri-La (B-F and D#-A)

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    most English speakers won't be familiar with your sol-fa based nomenclature here, so it's better to use letter names instead (or use both), just a tip :) – Some_Guy Apr 11 at 14:13
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    @ Some-Guy: if they aren't familiar it would be time that they get there ;) – Albrecht Hügli Apr 11 at 14:14
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    Well, much as it might be a nice thing, unfortunately it's not often a feature of English language pedagogy, and as such, when used in English it's unlikely to be understood (and different Europeans use it in different ways so it also can cause confusion). Don't disagree with you though, it'd be nice if we did start using it! – Some_Guy Apr 11 at 19:30
  • Confusion as in whether Do=tonic or Do=C and also using vowel changes to indicate sharps and flats, I'm not sure there's a solid rule across different countries there (although I could be wrong). Anyway thanks for the edit to help us solfa illiterate Anglophones :) – Some_Guy Apr 11 at 19:36
  • Yes, thats why I will consequently use it: as movable doremi ;) – Albrecht Hügli Apr 11 at 19:56

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