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Thread: Augmented triad and the "Tristan Chord"

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    Default Augmented triad and the "Tristan Chord"

    I've started listening to Wagner, recently, and I must say I've been pleasantly surprised so far. I had mostly avoided him as he was mainly known for his opera work, and I must admit I'm not much of an opera fan... he does have some impressive symphonic work too, though, which I stumbled upon almost by chance, and this started opening a new world.

    In particular, I found myself listening to his "Siegfried Idyll" symphonic poem more than once in a row, and really loving it. There's a specific theme that really moved me, specifically the one starting at ~5:10 in this recording available on YouTube: tinkering with my guitar, I identified it as an E chord that moves to a G chord with a D# instead of D in there. I found out that's called an "augmented triad", as it does indeed increase the 5th to create a beautiful effect, but was surprised to read that it was not common at all in classical music, especially considering how powerful it sounds: the Wikipedia page for the pattern lists the Siegfried Idyll and Liszt's Faust as relevant examples (and you can indeed hear it very well in the slow cello arpeggios that start the work), but not much more.

    I then found that a similar pattern is used (even though in a different chord, and a different bass note) in the so-called "Tristan Chord" that Wagner is also famous for: you can hear it very well in the Tristan und Isolde overture (and across the whole opera I guess, which I haven't listened to yet), but I actually had heard it once before in the beautiful arrangement for orchestra Franco Mannino did of Wagner's Elegy in A-flat major, for the movie Ludwig. In both those occurrences they contribute to creating very moving progressions.

    Are there other examples of this kind of chords in classical music, in Wagner or otherwise? I'm mostly interested in 19th century music, as while I love how the occasional dissonance can create a powerful moment in a romantic score, when the dissonances become the sole purpose of the work just for the sake of experimentation (as it unfortunately happened way too often in the 20th century music) I personally just find them inpleasant.

    Thanks!

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    Liszt was fond of the augmented triad for its vagueness and ambiguity; Wagner used it but was less apt to dwell on it. It's a natural product of the whole tone scale, and Debussy used it in parallel progressions. Composers influenced by the Wagner-Liszt and impressionist styles used it liberally; Puccini's operas feature it prominently.

    Augmented sixth chords are commoner than pure augmented triads in Romantic music; along with diminished sevenths, they're the handiest of pivots for remote modulations. The "Tristan chord" is most easily read as an augmented (French) sixth momentarily obscured by an appoggiatura.
    Last edited by Woodduck; Feb-18-2020 at 20:04.

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    Quote Originally Posted by Woodduck View Post
    Liszt was fond of the augmented triad for its vagueness and ambiguity; Wagner used it but was less apt to dwell on it. It's a natural product of the whole tone scale, and Debussy used it in parallel progressions. Composers influenced by the Wagner-Liszt and impressionist styles used it liberally; Puccini's operas feature it prominently.

    Augmented sixth chords are commoner than pure augmented triads in Romantic music; along with diminished sevenths, they're the handiest of pivots for remote modulations. The "Tristan chord" is most easily read as an augmented (French) sixth momentarily obscured by an appoggiatura.
    I'll definitely have to study the different sixth chords out there, especially considering there seems to be one called the "Neapolitan sixth": I'm from Napoli, in Italy, and I should be ashamed I never heard of it

    Thanks for the thorough explanations you've given so far on both posts, they're really appreciated!
    Last edited by lminiero; Feb-19-2020 at 11:21.

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    I heard some augmenteds in Holst's "The Planets." To me, they create a sense of vertigo, like everything is expanding.
    Last edited by millionrainbows; Feb-19-2020 at 12:47.

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    Quote Originally Posted by millionrainbows View Post
    I heard some augmenteds in Holst's "The Planets." To me, they create a sense of vertigo, like everything is expanding.
    I agree, and in fact they're very much there when you listen at the title theme of Hermann's "Vertigo", where they give exactly that kind of feeling On an only marginally related note, I recently read somewhere (maybe in a post here? not sure) that in the score of "Vertigo" you can hear some inspiration from Wagner: even though IIRC it was mostly in the love theme, rather than the title, and more in general on his use of leitmotifs.
    Last edited by lminiero; Feb-19-2020 at 14:11.

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    Quote Originally Posted by lminiero View Post
    I recently read somewhere (maybe in a post here? not sure) that in the score of "Vertigo" you can hear some inspiration from Wagner
    Definitely. Tristan, specifically.

    https://www.youtube.com/watch?v=ObbHRxvpLJ4

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    The augmented triad repeats itself every major third, and it has a certain symmetry. Its intervals are M2, M3, and tritone. As such, it is "recursive," meaning that it's one of those constructs which cycles through the octave (4X3=12) based on the M3, and reconnects with itself within an octave, unlike fourths & fifths which must go "outside the octave" 5 cycles (5X12=60) and 7 cycles (7X12=84) of octaves before reconnecting.
    Diminished sevenths are 3X4=12, based on the m3, so these two (M# & m3) divide the octave symmetrically in interesting ways. The other recursive intervals, m2, M2, and tritones, are less interesting, don't build triads, are more chromatic, and are included in the dim & aug triads anyway.
    The emergence of diminished and augmented triads shows that tonality, based on root movements of fourths and fifths, was beginning to "go inward" into the smaller recursive intervals, and more obvious symmetries, and was becoming more chromatic.
    Last edited by millionrainbows; Feb-20-2020 at 16:26.

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    Here's my take on the "origin", or whatever you want to call it, of the Tristan chord:

    This analysis assumes parallel major/minor key shifts to be part of the idiom (so below there's a momentary shift to thinking in A major).

    The opening bar melody of the Tristan and Isolde theme establishes the tonic note A (it's in A minor), then leaps straight to gypsy appoggiatura note F, which resolves down to E. The A minor key is established at this point, not only by musical tradition, but also by the inclusion of a Tonic note (A), a Subdominant note (F), and a Dominant note E.

    Then the Tristan chord appears: the notes (bottom to top) being F, B, D#, G#. This chord has been called all sorts of things, with some theorists even changing the notes in order to squeeze the chord into a preconceived functional pigeonhole. But here we'll stick with the notes as they sound to the ear, which only seems fair.

    The Tristan chord has been called an F half-diminished chord, which it is, but what has a flat VI half diminished chord got to do with standard classical harmony? Not much. Calling it an unresolved N6 chord (unresolved Bb) seems like a stretch. And I can't see any way to make this chord fit the standard definition of an Augmented 6 chord, whether it's Italian, French, Blue Cheese, or whatever, without changing out the notes for other notes.

    Another way of looking at the chord is as a "resolved" minor 7 chord, or simply put, a minor 6 chord. So we can see the Tristan chord as a G#min6 chord, stacking the notes: G#, B, D#, F. It may seem overly simple to call this merely a chromatic move from Amin to G#min, but the notes are there on the page, and it's exactly what the melody is telling us. After the gypsy note resolves down to sol, it drops again to se, just as the chord (and tonality) drops a half step. It's this half step drop that makes the chord sound "tragic" in the Beethovean sense. If you want to make a minor tonality even sadder, dropping it down a half step is a pretty good solution. So the temporary tonality while sitting on the Tristan is G# minor, with an added 6 implying the melodic minor mode.

    Minor 6 chords can be substituted for a dominant 7th chord a P5 below (they contain the same tritone), so the point is that the ear can hear this as a C#7 chord, with added 9th (nothing strange about a 9th at this point in musical history). The chromatic melody note from G# to A sounds like merely a passing tone, though it does throw the mind for a short moment into whole tone lala-land. But functionally what is really happening is that the C#7 chord is slipping up a minor 3rd to an E7 chord (with #11 appoggiatura), which is nothing more than a 90 degree shift around the Dominant merrygoround. Put another way, it's a III7 shifting to a V7, which can be seen as a momentary shift to the key of F#, or simply a III dominant being changed out for a V dominant (thinking for a moment in A major). Again, it's exactly what the melody is telling us; as it moves chromatically to rest a minor 3rd above se to la, the chord and tonality move up the coresponding minor 3rd.

    The idea of a III dominant chord is nothing new in classical music, and it often resolves to I rather than the usual VI (Schumann's Kinderscenen #1 bar 12 is an example). What gives it the strange sense of vertigo is the tritone moving up a minor 3rd, as the dominant function is transfered from the III to the V. Oh yeah, and that momentary whole tone chord adds more vertigo to the mix, and creates enough smoke for the magician to pull off his trick, as it were.

    So functionally the Tristan chord acts as a pivot chord, functioning first as a G# minor chord when arrived at from a half step above, but then becoming, almost in retrospect when we hear the E7, a C#7 chord that morphs from III7 (C#7) to V7 (E7).

    In order to accept this explanation one must be cool with the idea of the melody and the functional root moving in parallel 5ths, as the melody in the case of both the C37 chord and the E7 chord is on the 5th. But by this point in history the parallel 5th prohibition was regular flouted, and the relaxing of that older voice leading rule from time to time by progressive composers was one of the things that allowed the music of late 19th century to become so interesting.

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    Not sure how to edit the post above, but the last paragraph should read "C#7" not "C37", and the 4th from the last paragraph should read "ti to re" not "se to la". It was late...

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    Here's my take on the "origin", or whatever you want to call it, of the Tristan chord:

    This analysis assumes parallel major/minor key shifts to be part of the idiom (so below there's a momentary shift to thinking in A major).

    The opening bar melody of the Tristan and Isolde theme establishes the tonic note A (it's in A minor), then leaps straight to gypsy appoggiatura note F, which resolves down to E. The A minor key is established at this point, not only by musical tradition, but also by the inclusion of a Tonic note (A), a Subdominant note (F), and a Dominant note E.

    Then the Tristan chord appears: the notes (bottom to top) being F, B, D#, G#. This chord has been called all sorts of things, with some theorists even changing the notes in order to squeeze the chord into a preconceived functional pigeonhole. But here we'll stick with the notes as they sound to the ear, which only seems fair.

    The Tristan chord has been called an F half-diminished chord, which it is, but what has a flat VI half diminished chord got to do with standard classical harmony? Not much. Calling it an unresolved N6 chord (unresolved Bb) seems like a stretch. And I can't see any way to make this chord fit the standard definition of an Augmented 6 chord, whether it's Italian, French, Blue Cheese, or whatever, without changing out the notes for other notes.

    Another way of looking at the chord is as a "resolved" minor 7 chord, or simply put, a minor 6 chord. So we can see the Tristan chord as a G#min6 chord, stacking the notes: G#, B, D#, F. It may seem overly simple to call this merely a chromatic move from Amin to G#min, but the notes are right there on the page, and it's exactly what the melody is telling us. After the gypsy note resolves down to sol, it drops again to se, just as the chord (and tonality) drops a half step. It's this half step drop that makes the chord sound "tragic" in the Beethovenian sense. If you want to make a minor tonality even sadder, dropping it down a half step is a pretty good solution. So the temporary tonality while sitting on the Tristan is G# minor, with an added 6 implying the melodic minor mode.

    Minor 6 chords can be substituted for a dominant 7th chord a P5 below (they contain the same tritone), so the point is that the ear can hear this as a C#7 chord, with added 9th (nothing strange about a 9th at this point in musical history). The chromatic melody note from G# to A sounds like merely a passing tone, though it does throw the mind for a short moment into whole tone lala-land. But functionally what is really happening is that the C#7 chord is slipping up a minor 3rd to an E7 chord (with #11 appoggiatura), which is nothing more than a 90 degree shift around the minor 3rd chain of Dominants. Put another way, it's a III7 shifting to a V7, which can be seen as simply a III Dominant being changed out for a V Dominant. Again, it's exactly what the melody is telling us; as it moves chromatically to rest a minor 3rd above ti to re, the chord and tonality move up the corresponding minor 3rd.

    The idea of a III Dominant chord is nothing new in classical music, and it often resolves to I rather than the usual VI (Schumann's Kinderscenen #1 bar 12 is an example). What gives it the strange sense of vertigo in Tristan is the tritone moving up a minor 3rd, as the Dominant function is transfered from the III to the V. Oh yeah, and that momentary whole tone chord adds more vertigo to the mix, and creates enough smoke for the magician to pull off his trick, as it were.

    So functionally the Tristan chord acts as a pivot chord, functioning first as a G# minor chord when arrived at from a half step above, but then becoming, almost in retrospect when we hear the E7, a III7 Dominant chord that morphs from III7 (C#7) to V7 (E7).

    In order to accept this explanation one must be cool with the idea of the melody and the functional root moving in parallel 5ths, as the melody in the case of both the C#7 chord and the E7 chord is on the 5th. But by this point in history the parallel 5th prohibition was regular flouted, and the relaxing of that older voice leading rule from time to time by progressive composers was one of the things that allowed the music of late 19th century to become so interesting.
    Last edited by Wes Lachot; Aug-16-2020 at 03:49. Reason: re-posted and simplified for clarity

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    ^^^Your theory of the chord is original, is it not? It's new to me, anyway, and I have to say that I can only follow it about halfway. Where you lose me is with your assertion that the ear can hear the Tristan chord as a C#7 with added ninth. My ear can certainly hear the chord in isolation as a C#9 with missing root, but a C# chord seems completely irrelevant in the context of the Tristan prelude, and my ear doesn't hear anything in the chord or its context as implying such a thing.

    Reading the chord as a G# minor sixth chord is more plausible, although of course it's still remote from A minor by classical functional criteria. My problem with reading it as "functional" is that we don't really have a clear sense of A minor before the chord is sounded. The first note A of the piece is a short anacrusis, not suggesting a tonic, and the real emphasis is on the long F, which at first hearing seems more likely to be a tonal center. It's hard to perceive a G#m6 as functional in terms of A minor when we don't really have A minor in our heads, and I think Wagner would have given us a stronger sense of A minor at the outset if he'd wanted us to perceive a meaningful half-step drop such as you speak of (maybe more like the opening of Reger's tone poem "The Isle of the Dead"). A G# minor chord certainly doesn't make much sense in relation to F major either, so we're left, as far as I'm concerned, with an anomaly.

    From my reading so far I've found all theories of this chord unsatisfactory, and I've more or less decided that that's as it should be. But I'd still have to hold that the "augmented 6th with an appoggiatura on G#" interpretation is the most elegant and least problematic way to think of it, and the one that sits most easily inside the theoretical context that Wagner himself would have understood in 1859.
    Last edited by Woodduck; Aug-16-2020 at 20:09.

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    Quote Originally Posted by Wes Lachot View Post
    But by this point in history the parallel 5th prohibition was regular flouted, and the relaxing of that older voice leading rule from time to time by progressive composers was one of the things that allowed the music of late 19th century to become so interesting.
    In this though, I particularly like how Wagner skillfully avoids parallel fifths:
    Last edited by hammeredklavier; Aug-17-2020 at 01:37.

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    Quote Originally Posted by Woodduck View Post
    ^^^Your theory of the chord is original, is it not? It's new to me, anyway, and I have to say that I can only follow it about halfway. Where you lose me is with your assertion that the ear can hear the Tristan chord as a C#7 with added ninth. My ear can certainly hear the chord in isolation as a C#9 with missing root, but a C# chord seems completely irrelevant in the context of the Tristan prelude, and my ear doesn't hear anything in the chord or its context as implying such a thing.

    Reading the chord as a G# minor sixth chord is more plausible, although of course it's still remote from A minor by classical functional criteria. My problem with reading it as "functional" is that we don't really have a clear sense of A minor before the chord is sounded. The first note A of the piece is a short anacrusis, not suggesting a tonic, and the real emphasis is on the long F, which at first hearing seems more likely to be a tonal center. It's hard to perceive a G#m6 as functional in terms of A minor when we don't really have A minor in our heads, and I think Wagner would have given us a stronger sense of A minor at the outset if he'd wanted us to perceive a meaningful half-step drop such as you speak of (maybe more like the opening of Reger's tone poem "The Isle of the Dead"). A G# minor chord certainly doesn't make much sense in relation to F major either, so we're left, as far as I'm concerned, with an anomaly.

    From my reading so far I've found all theories of this chord unsatisfactory, and I've more or less decided that that's as it should be. But I'd still have to hold that the "augmented 6th with an appoggiatura on G#" interpretation is the most elegant and least problematic way to think of it, and the one that sits most easily inside the theoretical context that Wagner himself would have understood in 1859.
    Wooduck: Yes, this analysis is original--thanks for noticing.

    I agree that there will never be a final consensus on the Tristan chord; it would sort of take the fun out of it if there was, right? I also agree that you have zeroed in on the turning point in my analysis that may need more work in order to make the argument convincing. It's just an ear thing for me that comes from being a jazz player and hearing in chord scale terms. The fact that the G3min6 chord and the C#7/9 chord share all the same notes except for the missing root, and that the tonality shifts down a half step is the "ear" part I'm talking about. But I get your point.

    Thanks for taking the time to analyze my analysis and make meaningful criticisms.

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    Hammeredklavier--That was cool. Is it difficult to post stuff from youtube the way you just did?

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