# Augmented triad and the "Tristan Chord"



## lminiero

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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## Woodduck

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.


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## lminiero

Woodduck said:


> 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 :lol:

Thanks for the thorough explanations you've given so far on both posts, they're really appreciated!


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## millionrainbows

I heard some augmenteds in Holst's "The Planets." To me, they create a sense of vertigo, like everything is expanding.


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## lminiero

millionrainbows said:


> 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.


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## Woodduck

lminiero said:


> 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.


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## millionrainbows

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.


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## hammeredklavier




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## Wes Lachot

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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## Wes Lachot

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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## Wes Lachot

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.


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## Woodduck

^^^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.


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## hammeredklavier

Wes Lachot said:


> 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:


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## Wes Lachot

Woodduck said:


> ^^^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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## Wes Lachot

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


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## amfortas

Wes Lachot said:


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


Thanks for this post. Your music theory analysis left me feeling completely inadequate. Now, not quite so much.


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## Wes Lachot

Woodduck said:


> 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....


These are all fair points, but I wanted to explain a little more how the first three notes feel like a prolonged or "stressed" appoggiatura. When I hear it I'm actually reminded of the Brahms Piano Quintet in F minor (op. 34), that second theme that happens just under a minute in. The melody stresses le before resolving to sol, then back to another stressed le, then quickly le sol me fa sol. I'm not sure why I hear the Tristan theme in that same sort of way, in that tonality as it were, but I guess it's just I expect a dissonance out of Wagner at that point, a dissonance that needs resolving. *

So hearing it that way we call the notes "do le sol"; analyzed that way the ear gets to hear two notes of a tonic key plus a stressed appoggiatura. An alternate analysis I suppose would be to call the leap "sol me", then down to re, sort of a minor "My Bonnie" that then slides into the bII, and in that analysis the ear gets to hear two notes of the tonic chord as well, but neither of them is the root in this case (sol and me). In that version the stressed, elongated note is a consonant note, and I suppose we could ask the question whether at this point in musical history consonance or dissonance was more likely to be stressed. Since my ear refers back to the Brahms theme, I guess my subconscious pick must be dissonance (do to le to sol) as in my original analysis.

*(And in particular, throughout the century from LVB on, that particular note, what some call the "gypsy note", "le", was used a lot for that purpose. Beethoven leaned on that note a lot when he was cranking out the 3 Razumovskis, and he had to make sure they sounded Slavic enough to get paid for the gig.)


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## Wes Lachot

amfortas said:


> Thanks for this post. Your music theory analysis left me feeling completely inadequate. Now, not quite so much.


Hey Alan, I am so far behind the curve on some of this tech stuff it's ridiculous. I don't even do social media or any of that.


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## amfortas

Wes Lachot said:


> Hey Alan, I am so far behind the curve on some of this tech stuff it's ridiculous. I don't even do social media or any of that.


Nor do I, for that matter. As for embedding a YouTube video, it's actually quite easy. When writing a post, put your cursor where you want to insert the video, click on the "Link" button above (the little globe), and paste the URL of the appropriate YouTube page. Hours of fun!


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## Wes Lachot

Okay, thanks for the tip. I see the globe and I get it.


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## mikeh375

Having read Wes' take on this, another way to read that chord sprang to mind, a chromatic supertonic in A minor. It's not that simple of course but to use jazz parlance, the chord can be conceived as a B dom13 with a flattened 5th (f in the bass or second inversion). The 13th simply resolves up to the 7th of the chord and the chord itself functions as a a secondary dominant to E. There is no need to import a new bass note in this interpretation. 

Admittedly this proposed secondary dominant is an extravagant one and has probably been suggested before, but it does hold up as a theoretical possibility imv. It also relates more immediately to the key (if that is deemed important), and reflects Wagner's spelling of an F natural rather than an E sharp, which would be more appropriate for a Gsharp min 6th chord.

However with this chord especially, ymmv.


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## Woodduck

mikeh375 said:


> Having read Wes' take on this, another way to read that chord sprang to mind, a chromatic supertonic in A minor. It's not that simple of course but to use jazz parlance, the chord can be conceived as a B dom13 with a flattened 5th (f in the bass or second inversion). The 13th simply resolves up to the 7th of the chord and the chord itself functions as a a secondary dominant to E. There is no need to import a new bass note in this interpretation.
> 
> Admittedly this proposed secondary dominant is an extravagant one and has probably been suggested before, but it does hold up as a theoretical possibility imv. It also relates more immediately to the key (if that is deemed important), and reflects Wagner's spelling of an F natural rather than an E sharp, which would be more appropriate for a Gsharp min 6th chord.
> 
> However with this chord especially, ymmv.


The anomaly of the "Tristan chord" confronts us with the question of what analysis is for and what we're hoping to accomplish by it. All attempts to analyze the opening bars of _Tristan und Isolde_ start by acknowledging that the passage is harmonically "ambiguous." What does this mean? It means that, in the moments that the music's tones strike the ear, our brains cannot fit them into any single, expected or immediately comprehensible tonal scheme. What do we hope to achieve by applying tonal analysis to this music? Do we hope that by giving names to things we can overcome our initial impression of ambiguity and from then on hear a definite tonal progression as the music unfolds? If that's our objective, I think we can achieve it to some extent, but never entirely. Wagner wants us to feel the ambiguity, and regardless of how we analyze the passage we can't and shouldn't lose entirely the sense of surprise and mystery that's written into the music. Hence, my feeling about the "Tristan chord" is that it isn't possible to describe fully in analytical terms what we hear in it, and that we shouldn't think we have to do so. This needn't be a bad thing. The chord is supposed to create a sense of strangeness and mystery. It doesn't have to have a name or a single "function."

That said, we can certainly look at this passage of music in terms of its style and period, and describe what its harmony is doing with clear reference to terms its composer would probably have understood. However far-reaching Wagner's harmonic idiom could be at times, he was thoroughly grounded in and attentive to his inherited tonal language and to the laws of harmonic and melodic motion as they were understood in his day. I think it makes sense to approach the Tristan chord through the expectations inherent in those laws before considering anything more esoteric. In light of that, I think your reading of "the chord" as a modified secondary dominant is correct and, once we "get" it, rather obvious.

The underlying progression of the entire three-bar phrase in A minor is simple: i - V7/V - V7. The chord has, basically, a dominant-of-the-dominant function; it's presented in second inversion, the expected F# is modified to F, and the troublesome G# is a non-chord tone with a clear melodic function. In exploring this I've found it interesting to play the passage with certain chord tones omitted. Leave out the top melody line - the G# and its chromatic ascent up to B - and the basic commonness of the progression emerges clearly. Play only the top line without the lower voices, and among possible harmonizations none seems more logical than i - V/V - V (the G# readable as either a melodic appoggiatura or part of a B13) except possibly the even simpler i - i - V (the G# as the leading tone to the tonic A). My own favorite view of the progression regards the V7/V with flatted F as an augmented (French) sixth and the G3 as an appoggiatura ascending through the expected A to an A# appoggiatura over the following V7.

I haven't found that an understanding of the basic harmonic movement of this passage deprives the famous chord of any of its magic. The sense of ambiguity is still there; the home key of A minor is not very clearly announced even before we're hit with an altered chord that seems initially to come out nowhere and requires that we hear and absorb its resolution even to partially sense its tonal function. Because the chromatic alterations of the V/V chord as it first strikes the ear obscure its underlying function, I have some sympathy with attempts to "explain" the chord in more far-fetched ways, but I really don't find any of them capable of explaining the chord's effect, which will surely, and properly, remain a mystery.


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## mikeh375

Your interpretation is eloquent WD and may well be the best one. The magic of that chord also comes from the scoring of course, the plaintive, searching, questioning reeds following a searing crescendo on the cellos intense A string.


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## millionrainbows

> ...I really don't find any of them capable of explaining the chord's effect, which will surely, and properly, remain a mystery.



Then the only conclusion is that the notes we hear are lines, not chords with function. 
If the "Tristan" chord is not harmonically analyzable as a chord, then it is simply a coincidence if moving lines. 
The key context is ambiguous, too, so we can't really say what key area it is with absolute certainty.
So to fully "appreciate" the Tristan chord, we need to stop thinking of it as a chord.


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## mikeh375

millionrainbows said:


> Then the only conclusion is that the notes we hear are lines, not chords with function. If the "Tristan" chord is not harmonically analyzable as a chord, then it is simply a coincidence if moving lines.


Me, WD and Wes have viably analysed it as a chord, which it is. It comes in as one sound, right?


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## millionrainbows

mikeh375 said:


> Me, WD and Wes have viably analysed it as a chord, which it is. It comes in as one sound, right?


Oh, pardon me; I thought that it was a mystery.


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## Woodduck

millionrainbows said:


> Then the only conclusion is that the notes we hear are lines, not chords with function.
> If the "Tristan" chord is not harmonically analyzable as a chord, then it is simply a coincidence if moving lines.
> The key context is ambiguous, too, so we can't really say what key area it is with absolute certainty.
> So to fully "appreciate" the Tristan chord, we need to stop thinking of it as a chord.


This isn't a necessary conclusion. Having a single function as a chord and being "simply" a coincidence of moving lines are not the only options. An underlying progression of i - V7/V - V7 is clearly audible and not merely visible on the page, at least once we're alerted to it. The altered chord tones obscure this progression initially and create a "mixed" effect, meaning an effect of ambiguity, but ambiguity isn't nonexistence; we don't know in the moment of hearing where the chord comes from or where it will go, but, as it resolves, its source and meaning become evident in retrospect. Besides, three of the chord's four notes haven't "moved" from anywhere!

The tonal plan of the _Tristan_ prelude is so strong and lucid that there's no chance Wagner just happened upon it in the course of writing counterpoint.


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## DavidA

The Tristan Chord has been accorded the mystique usually associated with Newton's first law or Einstein's Special Theory of Relativity but of course it was not Wagner who used it. Liszt had been using this chord and many others of its ilk before Wagner wrote it into Tristan.


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## Woodduck

DavidA said:


> The Tristan Chord has been accorded the mystique usually associated with Newton's first law or Einstein's Special Theory of Relativity but of course it was not Wagner who used it. Liszt had been using this chord and many others of its ilk before Wagner wrote it into Tristan.


Do you know where the Tristan chord occurs in the music of Liszt, and how it's used? I can recall you making this point before more than once, but I've seen no indication that you understand anything about the music you're referring to, or even know what it is.

I have more than a suspicion that your real objective is your usual one of trying to diminish the significance of something that others find significant. It's a curious occupation, the appeal of which escapes me.


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## millionrainbows

Woodduck said:


> Do you know where the Tristan chord occurs in the music of Liszt, and how it's used? I can recall you making this point before more than once, but I've seen no indication that you understand anything about the music you're referring to, or even know what it is.
> 
> I have more than a suspicion that your real objective is your usual one of trying to diminish the significance of something that others find significant. It's a curious occupation, the appeal of which escapes me.


RE: the thread title; does it have anything to do with augmented chords?


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## DavidA

No need for us to get uptight about this. People have reckoned they find echoes of this in works by Mozart (Dissonance quartet K.428), Beethoven (op.31 no.5), Spohr (Concerto for two violins, Quartet op.4 no.1), Gottschalk (The Last Hope), Chopin (op.68 no.4), Liszt ("Die Loreley", "Ich möchte hingehen") and other composers. Why the problem? Whether they are right or wrong depends on the musical scholarship . In any case there is nothing new under the sun.


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## Woodduck

millionrainbows said:


> RE: the thread title; does it have anything to do with augmented chords?


Liszt was extremely fond of augmented triads. Wagner used them but was less enamored of them. Listen to the beginning of Liszt's _Faust Symphony:_






Between the augmented and diminished triads, there's hardly anything with an unambiguous tonal direction. The _Faust Symphony_ slightly precedes Wagner's work on _Tristan_ and shows Liszt to be running neck and neck with Wagner, and maybe slightly ahead of him, in progressive harmony. The difference between them is that Liszt liked ambiguity and strangeness for its own sake and did things Wagner, who was focused on integrating dramatic with musical structure, wouldn't do. Liszt's late piano pieces live in a cloud of morbid ambiguity that Wagner would have found unusable and probably personally unsatisfying.

There's a real difference in musical purpose between this






and this


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## Woodduck

DavidA said:


> No need for us to get uptight about this. People have reckoned they find echoes of this in works by Mozart (Dissonance quartet K.428), Beethoven (op.31 no.5), Spohr (Concerto for two violins, Quartet op.4 no.1), Gottschalk (The Last Hope), Chopin (op.68 no.4), Liszt ("Die Loreley", "Ich möchte hingehen") and other composers. Why the problem? Whether they are right or wrong depends on the musical scholarship . In any case there is nothing new under the sun.


There are new things under the sun. The innovation in the _Tristan_ chord was not in the notes themselves but in the unprepared use of the chord at the beginning of the piece, the way it relates to its surroundings and to the tonality of the piece. That's what the hoopla is really all about.


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## Wes Lachot

Woodduck, You gave me a lot to think about. Dealing with the death of a close friend today so I'm a little out of it. I am using thinking about this as a distraction though, so I will weigh in shortly.

-Wes


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## amfortas

Wes Lachot said:


> Woodduck, You gave me a lot to think about. Dealing with the death of a close friend today so I'm a little out of it. I am using thinking about this as a distraction though, so I will weigh in shortly.
> 
> -Wes


Sorry to hear about your loss, Wes. I hope the conversations here provide at least a bit of relief.


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## Wes Lachot

Woodduck,

FYI, my ideas below hinge on the concept of the ear always being aware of a tonality or chord scale ("mood"), meaning though we may only be hearing 3 or 4 notes, our minds fill in the blanks to create a chord scale based on the musical context. Of course this is tricky with Tristan... Also, though I address this to you I am writing to the group, so I may explain some things you don't necessarily need to have explained. Also, I am not necessarily looking for a "final answer", really just enjoying the conversation. 

I did try out your ideas at the piano, and it was illuminating, and helped me to sharpen my ideas. (Hopefully the reverse will also be true.) Your analysis certainly works from a jazz perspective, if you invert the Tristan notes, although it works better if you add some more notes to the voicing. Bear with me and try at the piano voicing the original Tristan chord simply moving the B down an octave to try your idea that this is the root of the chord. First simply play the chord in this inversion and listen, then play it again adding an "A" a 7th above the B root. This is a modern jazz chord, and a really nice one (B7/13/#11) because this voicing still leaves a bit of ambiguity as to the chord scale, because the 9th has been left out. The two possible chord scales are these, one with a natural 9 and one with a flatted 9. Possibility one: Adding the flatted 9 (middle C) creates another common jazz chord (B7/b9/13/#11) that usually implies the symmetric diminished chord scale (half/whole, starting on B in this case). 

The other possibility is a C# note instead of a C (try playing the chord, bottom up, B, A, C#, D#, F, G#). This is another great jazz chord (simply B7#11) that calls for the lydian flat 7 (lydian dominant) chord scale starting on B. There's a strong argument to be made for this chord scale (tonality) for a couple of reasons, not only because of the #11 and the 13, but because I think the C# note is a much more likely candidate than C, even given that the key is A minor. 

So sticking with enharmonic spelling for the F, the chord scale for B7/13/#11 is: B, C#, D#, F, F#, G#, A. But the Tristan chord doesn't contain the requisite tritone for a B7 chord, not until the melody note moves up, and it seems that the original chord is held for so long that any viable analysis should take the chord at face value.

Getting back to the C#7 possibility I advocated for in my original analysis, the Tristan chord does contain the tritone for this chord, right from the start. Delving a bit further, the actual notes, inverted as they occur in the Tristan chord, are harmonics 5, 7, 9, and 12 of the overtone series for C# (rounding--this post is not about micro-tuning). There is a known psychoacoustic phenomenon, that our "ears" fill in missing fundamentals from upper partials. So if we allow for a second that it's possible our ears are hearing the C#7 lydian b7 tonality, those notes would be C#, D#, F, G, G#, A#, B. Five of the seven notes are the same as the B7 #11 chord scale, the F# and A being raised chromatically to G and A# in the latter case. 

There is a distinction to be made between the chord scale theory of the lydian flat 7 tonalities and the scientific overtone series theory. The overtone series contains all of the notes of the lydian flat 7 chord scale except for "la"--there is no musical sounding 13th in the overtone series until you go way up past where it matters. So looking at the six notes that the lydian b7 scale has in common with the overtone series we have 1, 3, 5, b7, 9, #11.

So let's compare the lydian b7 tonality for the two options, B7#11 and C#7#11, in root position stacking 3rds:

1) B, D#, F#, A, C#, F 

2) C#, F, G#, B, D#, G

In the first case, that of the naturally occuring B tonality, 3 of the 4 notes of the Tristan chord are present, but the D# and the the F are both in the wrong octave with respect to the overtone series (the 11th harmonic, F, being transposed down an octave and the 5th harmonic up an octave). So the ear would not be able to sort this out from a psychoacoustic perspective (not that that is the be all and end all, but it matters since the chord is pretty isolated).

On the other hand, in the second case, that of the naturally occurring C# tonality, all 4 of the Tristan notes are present, and they are stacked in the Tristan chord exactly as they are in the overtone series, F, B, D#, and G# being harmonics 5, 7, 9, and 12 as stated earlier. Plus, the other 2 notes, C# and G, would be harmonics 4 and 11 of the C#7 harmonic series. 

You don't have to invert the notes from the Tristan chord for this version, you can just "hear them at face value". The 4 notes are there, 2 of them make up the tritone critical for a dominant chord. 
The two possibilities we're boiling it down to--B7 and C#7, share many notes of their respective whole tone rows, and jazz musicians use this fact a lot to creat ambiguity between, say, the bVI chord and the bV chord of a key. So we are definitely in the land of ambiguity, as you pointed out.

Also, Lydian b7 chord scale can generate three other chord scales: Locrian #2 starting on the 3rd degree; Altered, starting on the #11 degree, and Melodic minor (ascending), starting on the 5th degree. This last one would be my G#min6 tonality. You can make great chords with each of the roots, and the G7 Altered one is pretty "Wagnerian" sounding too. But next to the root position C#7 chord, I think the G# minor tonality the the easiest to discern, because the ear can fill in the 3rd overtone partial of the harmonic series about as easily as it can the 4th to hear it as a G#minor. This is at the first of the piece, sinking down from the A minor tonality along with the melody. So there is a certian "ambuguity" down there that is important, since I am asking you to indulge me in this weakest part of my theory, which you pointed out earlier--the jump from calling the tonality G#minor totaling it C#7 tonality. I'm not saying that all minor chords immediately suggest to the ear the dom7th chord a 5th below, only that minor chords with an added 6 tend more to sound that way. And isn't it all the same tonality anyway? 

Thanks for the critique--I'll take more if you got it!


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## Wes Lachot

Thanks Alan. I'm pretty freaked out right now and this is helping. -Wes


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## DavidA

Wes Lachot said:


> Thanks Alan. I'm pretty freaked out right now and this is helping. -Wes


Sincere condolences Wes.


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## Woodduck

Sorry to hear about your friend, Wes.



Wes Lachot said:


> Woodduck,
> 
> FYI, my ideas below hinge on the concept of the ear always being aware of a tonality or chord scale, meaning though we may only be hearing 3 or 4 notes, our minds fill in the blanks to create a chord scale based on the musical context. Of course this is tricky with Tristan...


True that chords can be incomplete, with the missing notes implied.



> I did try out your ideas at the piano, and it was illuminating, and helped me to sharpen my ideas. (Hopefully the reverse will also be true.) Your analysis certainly works from a jazz perspective, if you invert the Tristan notes, although it works better if you add some more notes to the voicing.


And those notes are...



> Bear with me and try at the piano voicing the original Tristan chord simply moving the B down an octave to try your idea that this is the root of the chord. First simply play the chord in this inversion and listen, then play it again adding an "A" a 7th above the B root.


The A that would make this more clearly a V7/V is what the G# will resolve to before moving to V7 of A minor, so adding an A to "the chord" is fine by me.



> The other possibility is a C# note instead of a C (try playing the chord, bottom up, B, A, C#, D#, F, G#).


Its' a very nice chord.



> There's a strong argument to be made for this chord scale (tonality) for a couple of reasons, not only because of the #11 and the 13, but because I think the C# note is a much more likely candidate than C, even given that the key is A minor. (You will remember that C was the one tonic note Wagner left out of the original 3 note motive, and also that my original analysis hinged on the C# note. I will return to that C# note shortly.) So sticking with enharmonic spelling for the F, the chord scale for B7/13/#11 is: B, C#, D#, F, F#, G#, A. Let's take note that it contains an A, which strengthens your case since A minor is the key. But it's a stretch how we got to this tonality from the opening 3 notes, because in a minor tune I've never heard Evans or Jarrett or anybody use that tonality on the supertonic. It's used on all of these degrees in major: I, bII, II, bIII, IV, bV, V, bVI, BVII. It is not a great tonality for the II in minor, and I've never heard it used that way. So that's a problem. (The B7 lydian b7 tonality is also not a naturally occuring phenomenon in the relative major of C, which ties into the "bias against the VII" discussed in another thread.) *And there is also the fact that the Tristan chord doesn't really contain the requisite tritone to be talking about a B7 chord, not at least until the melody note moves up, and it seems that the original chord is held for so long that any viable analysis should take the chord at face value.*


"Taking the chord at face value" is exactly what we can't do. The whole essence of harmonic ambiguity is that a chord can't be taken at face value, since it "faces" in more than one direction. I see no reason for assuming that the underlying tonality must include all the notes presented in the chord. We recognize such things as "altered chords" and "substitutions." In this case the F# of the V/V is altered to F, which gives the chord its augmented sixth aspect (F to D#) and is superbly logical in that the movement of the F to E in the next bar exactly mimics the F to E melodic movement in the first bar. As for the "missing" tritone created by the delayed A, I have no problem waiting for it.



> So getting back to the C#7 possibility, I would like to point out a few considerations. The first is that the Tristan chord does contain the tritone for this chord, right from the start. Delving a bit further, the actual notes, inverted as they occur in the Tristan chord, are harmonics 5, 7, 9, and 12 of the overtone series for C# (this post is not about micro-tuning). So I'm not saying everything is music has to be constantly justified by the overtone series, but I do think that when a chord is heard in isolation as the Tristan chord is (well, almost in isolation) it is reasonable to bring the overtone series into it, since it's a proven psychoacoustic phenomenon that our "ears" fill in missing fundamentals from upper partials. (My day gig is acoustics, and I can provide more info if needed.) So if we allow for a second that it's possible our ears are hearing the C#7 lydian b7 tonality, those notes would be C#, D#, F, G, G#, A#, B. Five of the seven notes are the same as the B7 #11 chord scale, the F# and A being raised chromatically to G and A# in the latter case.


I think there's a bit of rationalizing going on here...



> So you're probably thinking the presence of the A# sinks my argument, but I want to point out a distinction between the chord scale theory of the lydian flat 7 tonalities (as taught at Berklee and North Texas, etc.) and the scientific overtone series version. The overtone series contains all of the notes of the chord scale except for "la"--there is no musical sounding 13th in the overtone series until you go way up past where it matters. (That fact would seem to weaken your argument, since the melody begins on what would in that case the 13th of a B7 chord which has yet to acquire it's 7th). So looking at the six notes that the lydian b7 scale has in common with the overtone series we have 1, 3, 5, b7, 9, #11.


Ibid.



> So let's compare the lydian b7 tonality for the two option, B7#11 and C#7#11, in root position stacking 3rds:
> 
> 1) B, D#, F#, A, C#, F
> 
> 2) C#, F, G#, B, D#, G


You are clearly hooked on the idea of an implied C#. It makes a lovely chord in both your examples, but in option 1 it's unnecssary to define the tonality, and in option 2 it feels stylistically wrong for Wagner. He simply would not have imagined a C# chord here. He does use dominant 9ths a lot, but this voicing, with the fifth on top, is not characteristic of his style in _Tristan_ - a curious fact, since the Tristan chord can certainly be heard in other contexts as a dominant 9th minus its root. But despite the frequent occurrence of the chord throughout the opera, it is never, to my knowledge, given that dominant function, but always carries with it the ambiguous, darkly mysterious, minor-ish quality it possesses in the prelude.

Perhaps an even greater problem for the C#9 hypothesis is the chord's position between the A minor first bar and the V7 of A minor third bar. The whole progression - A minor to C#9 to E7 - is interesting, but though It's hard for me to give you evidence as to why, I just don't believe Wagner would have thought of it.

A third objection is that when the entire passage is reiterated in bars 4-7 at a higher pitch, your reading of the Tristan chord would result in an undesirable progression in which the (assumed) root of the chord, this time an E, would be the same as the implied root of the bar before it.You'll have to go play the passage with the added roots to hear why this falure to change roots undermines the effect of the Tristan chord, but I'm sure you'll agree that it does and that Wagner, or any good composer, wouldn't have done it that way.



> What I notice is that in the first case, 3 of the 4 notes of the Tristan chord are present, so that's cool, but I would point out that the D# and the the F are both in the wrong octave with respect to the overtone series (the 11th harmonic, F, being transposed down an octave and the 5th harmonic up an octave). So the ear would not be able to sort this out from a psychoacoustic perspective (not that that is the be all and end all, but it matters since the chord is pretty isolated).
> 
> On the other hand, in the second case all 4 of the Tristan notes are present, and they are stracked in the Tristan chord exactly as they are in the overtone series, F, B, D#, and G# being harmonics 5, 7, 9, and 11 as stated earlier. Plus, the other 2 notes, B and F#, would be harmonics 4 and 6 of the C#7 chord scale. So the ear doesn't have to sort out anything at all.
> 
> So I think that's my strongest argument, and it's also how I hear it. You don't have to invert the notes from the Tristan chord for this version, you can just "hear them at face value". The 4 notes are there, 2 of them make up the tritone critical for a dominant chord. Thanks for the critique--I'll take more if you got it!
> 
> P.S. The two possibilities we're boiling it down to--B7 and C#7, share many notes of their respective whole tone rows, and jazz musicians use this fact a lot to creat ambiguity between, say, the bVI chord and the bV chord of a key. So we are definitely in the land of ambiguity, as you pointed out.
> 
> Also, they teach you at Berklee that the Lydian b7 chord scale can generated three other chord scales: Locrian #2 starting on the 3rd degree; Altered, starting on the #11 degree, and Melodic minor (ascending), starting on the 5th degree. This last one would be my G#min6 tonality. While the other two (Locrian #2 and Altered) have nothing to do with this conversation, I think it's reasonable to say that the ear can also fill in the 3rd overtone partial of the harmonic series about as easily as it can the 4th. So there is a certian "ambuguity" down there that is important, since I am asking you to indulge me in this weakest part of my theory, which you pointed out earlier--the jump from the sinking feeling to a tonality of G#minor to the C#7 angle on the tonality. I'm not saying that all minor chords immediately suggest to the ear the dom7th chord a 5th below, only that minor chords with an added 6 tend more to sound that way.
> 
> I know this post is a bit longwinded, but any serious discussion of the Tristan chord deserves to be, right? I would just ask you to consider that, despite my ineloquence and longwindedness, at the end of the day *it is a pretty simple idea that the harmonic series contains the answer.* I'll have to work on a condensed version.


I don't see any need to appeal to the harmonic series.



> *In my Wild Theory system, this lydian flat 7 tonality, which is the tonality of the overtone series, sits chromatically above every diatonic chord degree as a sort of "Neapolitan tonality of each degree", and without getting too philosophical right this minute, I think of it as the generator of all tonality. But that's a whole other story, a very long one we won't get into right now, and hence the footnote. But I guess you could infer that *my analysis boils down to the Tristan chord being the "Neapolitan tonality of the relative major".*


I can't see the Neapolitan of C Major as having any relevance to this progression, since there is no suggestion anywhere of C Major. There is no such chord as the Neapolitan of an absent tonality. Moreover, I believe that the chord built on a flat supertonic is properly called a Neapolitan only in the right syntactic context; it isn't a Neapolitan simply by virtue of being on that scale degree.

My ultimate feeling about your theory is that it's rooted in your personal affinity for certain harmonies, probably based on your jazz background. I like those harmonies too, but I don't hear them as necessary here.


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## Wes Lachot

Woodduck,

Wow, thanks for taking so much time with my rambling post! As you can see I've tried to edit some of the superfluous nonsense out of it, some of which you've quoted, which is fine. I was writing "On The Road" style and probably could have boiled the whole thing down to this: I hear the tritone shfting by a minor third, and that's not usually how we hear tritones working when the root motion is cycle 5. So I guess I just hear the implied chords moving with the tritones and other chord tones (we can skip calling them harmonic partials). And importantly I hear the C#7 chord in 2nd inversion, meaning the G# minor tonality.

So if the tritone moves up a minor 3rd, and the melody moves up a minor 3rd, is it really such a stretch to say that the tonality moves up a minor 3rd? That's all I'm saying. 

So that it, really. And I'm not trying in any way to say that would be how Wagner composed it, only saying how it sounds.


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## Wes Lachot

Woodduck said:


> I can't see the Neapolitan of C Major as having any relevance to this progression, since there is no suggestion anywhere of C Major. There is no such chord as the Neapolitan of an absent tonality. Moreover, I believe that the chord built on a flat supertonic is properly called a Neapolitan only in the right syntactic context; it isn't a Neapolitan simply by virtue of being on that scale degree.
> 
> My ultimate feeling about your theory is that it's rooted in your personal affinity for certain harmonies, probably based on your jazz background. I like those harmonies too, but I don't hear them as necessary here.


Oh, that wasn't serious, just an aside--sorry. I agree with your by-the-book version of a proper N6 chord. I was just loosely talking of a Dominant tonality a m2nd above. I will try to be more exact with my descriptions.

You're probably right about my jazz background affecting that theory of a Lydian flat 7 tonality 1/2 step above every diatonic chord. Lydian flat 7 tonality is the one for all of the black key roots in the key of C, plus for C and F, so there is something to this observation, at least if you're looking at it from a jazz angle. It's a cool sound worth checking at the piano to see if you think there's anything there.

You can sit at the piano and play the B7 chord with all 4 Tristan notes or the C#7 chord with all 4 Tristan notes--that's the cool thing. I'm just saying that the way Wagner voiced them out, they resonate with the harmonic series of certain tonalities over others.

Thanks again for all of the time. I'm really appreciating the back and forth. Sorry I didn't reply to your post point by point--running out of mojo today. I will heed your suggestion to look at the following bars for more context.


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## Wes Lachot

Woodduck: I'll try to congeal and simplify my point even further:

The 4 notes that make up a G# minor6 chord, G#, B, D#, F, are on the page of the score and in the air, and I'm just saying I hear a G# minor6 chord. 

Can that really be wrong? Surely we can say this is at leaat a one valid interpretation, right?


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## Woodduck

Wes Lachot said:


> Woodduck: I'll try to congeal and simplify my point even further:
> 
> The 4 notes that make up a G# minor6 chord, G#, B, D#, F, are on the page of the score and in the air, and I'm just saying I hear a G# minor6 chord.
> 
> Can that really be wrong? Surely we can say this is at leaat a one valid interpretation, right?


That's the "trick," isn't it? That's the ambiguity. The chord, taken by itself, is indeed an inverted G# minor 6th. It IS one and, whatever else it is, it will always be one. But Wagner's use of it, and our perception of it, have long raised the question of whether that's ALL it is - just a surprise, an isolated chord in some key unrelated to the A minor tonality of the piece - or whether it can also be defined in terms of its _behavior_ in relation to the tonality of the piece. Are we naming things in isolation, or according to their context? Do we regard them as static entities, or as moments in a dynamic and evolving whole? If the latter, we can posit further that musical events should be understood in all three time dimensions: past, present, and future. We know what things are by where they've been (retrospectively) and where they're going as well as by what they appear to be in the moment. In the case of the Tristan chord, can we say with confidence that it is only what it sounds like when it first strikes our ear, or should we wait and see how it develops as it takes us from what comes before to what comes after? If we do the latter, and we are thus enabled to see it in retrospect, are we justified in applying a different name to it than the one we would apply if it were simply an isolated event? And if we are justified in doing that, might that name, which tells us how a chord is _functioning_, be at least as useful a name as one that identifies it merely as a static collection of tones?

Just askin'...


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## hammeredklavier

DavidA said:


> they find echoes of this in works by Mozart (Dissonance quartet K.428), Beethoven (op.31 no.5), Spohr (Concerto for two violins, Quartet op.4 no.1), Gottschalk (The Last Hope), Chopin (op.68 no.4), Liszt ("Die Loreley", "Ich möchte hingehen") and other composers.


lol, you accuse Wagner of taking stuff off others, yet you also did the same yourself, (the entire quote above was taken from this website): https://www.monsalvat.no/tristanchord.htm
Anyway, I find this website an interesting read, especially the part where it explains Wagner essentially derives his four Tristan chords from diminished seventh harmony:


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## mikeh375

Condolences Wes, I went through similar last year.


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## hammeredklavier

Woodduck said:


> There are new things under the sun. The innovation in the _Tristan_ chord was not in the notes themselves but in the unprepared use of the chord at the beginning of the piece, the way it relates to its surroundings and to the tonality of the piece. That's what the hoopla is really all about.


I can agree with this. There is a section in Chopin's ballade Op.23 where the same famous 4 note grouping is used in the same ordering. Although the way the voices move and the overall expression don't quite anticipate the "Tristan Chord", nevertheless the dramatic use of the half-diminished seventh chord is reminiscent of the "climax" of the Wagner prelude:
www.youtube.com/watch?v=nW5po_Z7YEs&t=6m








(Contrary to DavidA's accusations), nobody before Wagner had used "the Tristan chords" to express "unfulfilled desires" the way he did, by delaying the resolution til the end of a full-length opera. Btw, these days I find that the slow movement of Mozart's K.533 seems to anticipate the prelude in certain ways. I mean the part where it rises stepwise in chromatic chords to eventually climax with a dominant seventh on F, and then falls with an arpeggio to get to the reprise of the initial material: www.youtube.com/watch?v=fRu5f7BzdR4&t=5m5s


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## DavidA

hammeredklavier said:


> lol, you accuse Wagner of taking stuff off others, yet you also did the same yourself, (the entire quote above was taken from this website): https://www.monsalvat.no/tristanchord.htm
> Anyway, I find this website an interesting read, especially the part where it explains Wagner essentially derives his four Tristan chords from diminished seventh harmony:


So what? There was a question asked and I researched an answer. Any problems? It is what people do when asked a question. I did find quite a number of references on the internet and that appeared the most comprehensive. I had read in musical history books previously that others (including Liszt) has used the Tristan chord. It was also featured on a TV programme where the presenter (himself a composer) demonstrated them both. The chord may even go back to early music according to some, why people have written PhDs on it.


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## millionrainbows

If looked at in the context of diminished sevenths, the ambiguity of the "Tristan" chord is not as remarkable as it seems to some.


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## millionrainbows

There are "invisible" principles at play in chromatic music, which may defy analysis, and yet can still be determining factors in the use of a chord form. These underlying "invisible" principles can, when activated conceptually by the composer, determine principles of root movement, tonality, and function.

It may well be that Wagner was using "invisible" principles which were, especially at that time, unexplainable by conventional chord function and theory.


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## Woodduck

millionrainbows said:


> If looked at in the context of diminished sevenths, the ambiguity of the "Tristan" chord is not as remarkable as it seems to some.


Just how remarkable does its ambiguity seem to some?



> There are "invisible" principles at play in chromatic music, which may defy analysis, and yet can still be determining factors in the use of a chord form. These underlying "invisible" principles can, when activated conceptually by the composer, determine principles of root movement, tonality, and function.
> 
> It may well be that Wagner was using "invisible" principles which were, especially at that time, unexplainable by conventional chord function and theory.


What principles are "invisible"? Are they "invisible" to everyone?


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## Wes Lachot

Woodduck,

I am going to weigh in further on the Tristan chord and its musical context, but this time I'll gather my thoughts and edit my post before posting.

FYI, I do like the simplicity of your analysis, at least once the Tristan chord acquires it's French Augmented 6 character. I do think that there is virtue in pointing out the fact that the Aug6 chord can be seen as a "regular" resolution to the E7. But I think the analysis can be improved, from my perspective at least, and so I'd like for my version of the analysis to take into consideration the condition of the Tristan chord prior to aqcuiring this "French aspect" as you so colorfully referred to it. I'd also like for my version to take into consideration some other interesting elements of the voice leading, which I'll get to in my post.

May I ask, what is your Pistonian analysis of the next few bars? 

Thanks for the back and forth.


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## millionrainbows

Woodduck said:


> Just how remarkable does its ambiguity seem to some?


To your point, of it being a mystery. Sorry, but I'm not satisfied with that analysis.



> What principles are "invisible"? Are they "invisible" to everyone?


If you deem the Tristan chord to be a mystery and unanalyzable, then I think there is something which eludes conventional analysis, so whatever it is is "invisible" or unaccountable for in your view of it. I do think there is an answer.

Unless I'm wrong, and you have given an explanation, which seems to be Wes' assumption (above). Unless that is also wrong. God forbid I try to put words in your mouth.

You can see, can't you, how your responses seem to discourage discussion, I trust.


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## Woodduck

millionrainbows said:


> To your point, of it being a mystery. Sorry, but I'm not satisfied with that analysis.
> 
> If you deem the Tristan chord to be a mystery and unanalyzable, then I think there is something which eludes conventional analysis, so whatever it is is "invisible" or unaccountable for in your view of it. I do think there is an answer.
> 
> Unless I'm wrong, and you have given an explanation, which seems to be Wes' assumption (above). Unless that is also wrong. God forbid I try to put words in your mouth.
> 
> You can see, can't you, how your responses seem to discourage discussion, I trust.


My view of the Tristan chord, and of analysis in general, is simple. I think the idea that there must be a theoretical system that fully and definitively "explains" every musical phenomenon is mistaken, and the Tristan chord problem offers an excellent demonstration of that.

In post #12 I said: "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."

In post #22 I expanded on this: "The anomaly of the Tristan chord confronts us with the question of what analysis is for and what we're hoping to accomplish by it. All attempts to analyze the opening bars of Tristan und Isolde start by acknowledging that the passage is harmonically ambiguous. What does this mean? It means that, in the moments that the music's tones strike the ear, our brains cannot fit them into any single, expected or immediately comprehensible tonal scheme. What do we hope to achieve by applying tonal analysis to this music? Do we hope that by giving names to things we can overcome our initial impression of ambiguity and from then on hear a definite tonal progression as the music unfolds? If that's our objective, I think we can achieve it to some extent, but never entirely. Wagner wants us to feel the ambiguity, and regardless of how we analyze the passage we can't and shouldn't lose entirely the sense of surprise and mystery that's written into the music. Hence, my feeling about the Tristan chord is that it isn't possible to describe fully in analytical terms what we hear in it, and that we shouldn't think we have to do so. This needn't be a bad thing. The chord is supposed to create a sense of strangeness and mystery. It doesn't have to have a name or a single function."

I think that's clear enough. Your idea of "invisible principles," however, is anything but clear. You say that "there is an answer," but that it's "invisible." I think the claim to knowledge of "invisible answers" is presumptuous woowoo, exactly as your notion of the Neapolitan being "generated" by a diminished seventh when it clearly did not evolve out of a diminished seventh is woowoo. Instead of just looking at reality and accepting phenomena for what they are, you seem to need to "explain" everything with a "theory" or "principle," and you end up cavorting with unicorns.

People have been trying to analyze a single chord for a century and a half, arguing about what it "really is." I'm suggesting that the best we can do is look at its components, at the musical context in which it occurs, and at the composer's stylistic development and musical thinking insofar as we can understand them. If we do that, we can make some reasonable statements about the chord, and say that some descriptions make more sense than others. I believe that my description of what the chord is doing makes the best sense of any I've encountered on all these counts, but it doesn't pretend to describe _everything_ that the chord is doing. The fact remains that when the chord strikes the ear we do not immediately know where we are in the tonal universe, and I prefer to think that that's the way Wagner intended the chord to work on us, given that he generally seemed to have a pretty good idea of what he was doing.


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## millionrainbows

Woodduck said:


> My view of the Tristan chord, and of analysis in general, is simple. I think the idea that there must be a theoretical system that fully and definitively "explains" every musical phenomenon is mistaken, and the Tristan chord problem offers an excellent demonstration of that...In post #22 I expanded on this: "The anomaly of the Tristan chord confronts us with the question of what analysis is for and what we're hoping to accomplish by it. All attempts to analyze the opening bars of Tristan und Isolde start by acknowledging that the passage is harmonically ambiguous. What does this mean? It means that, in the moments that the music's tones strike the ear, our brains cannot fit them into any single, expected or immediately comprehensible tonal scheme.


The key word here is "tonal." What you say above might be true in the context of tonality, such as "the passage is harmonically ambiguous" and "our brains cannot fit them into any single, expected or immediately comprehensible tonal scheme," but IMHO, we are now in "chromatic" territory, and I mean that in a very "outside-the-box-of-tonality" way, not just as an adjunct to diatonic tonality. I know that this contradicts your view of Wagner as the ultimate tonalist.



> What do we hope to achieve by applying tonal analysis to this music? Do we hope that by *giving names to things* we can overcome our initial impression of ambiguity and from then on hear a *definite tonal progression *as the music unfolds?


No, I mean more than simply "naming chords" or "function" in a tonal sense.



> ...my feeling about the Tristan chord is that it isn't possible to describe fully in analytical terms what we hear in it, and that we shouldn't think we have to do so. This needn't be a bad thing. The chord is supposed to create a sense of strangeness and mystery. It doesn't have to have a name or a single function.


I don't believe I've ever said that the Tristan chord must "have to have a name or a single function."



> Your idea of "invisible principles," however, is anything but clear. You say that "there is an answer," but that it's "invisible." I think the claim to knowledge of "invisible answers" is presumptuous woowoo, exactly as your notion of the Neapolitan being "generated" by a diminished seventh when it clearly did not evolve out of a diminished seventh is woowoo.


I think the real problem is that you are not prepared to accept certain underlying ("invisible") conceptual principles of chromatic thinking (and hearing---no 'evolving' necessary, history notwithstanding).

Again, truly "chromatic" territory, and I mean that in a very "outside-the-box-of-tonality" way, not just as an adjunct to diatonic tonality. In order to re-orient yourself into a chromatic concept of music, there's a lot of diatonic ideation which you must be prepared to look past and even discard as inadequate to the task at hand.



> Instead of just looking at reality and accepting phenomena for what they are, you seem to need to "explain" everything with a "theory" or "principle," and you end up cavorting with unicorns.


A lot of other theorists have thought this way, including Schoenberg, and in his defense, he knew the tonal system inside and out, as is evidenced in his _Harmonielehre.
_


> People have been trying to analyze a single chord for a century and a half, arguing about what it "really is." I'm suggesting that the best we can do is look at its components, at the musical context in which it occurs, and at the composer's stylistic development and musical thinking insofar as we can understand them. If we do that, we can make some reasonable statements about the chord, and say that some descriptions make more sense than others. I believe that my description of what the chord is doing makes the best sense of any I've encountered on all these counts, but it doesn't pretend to describe _everything_ that the chord is doing. The fact remains that when the chord strikes the ear we do not immediately know where we are in the tonal universe, and I prefer to think that that's the way Wagner intended the chord to work on us, given that he generally seemed to have a pretty good idea of what he was doing.


I can agree with most of that, although I think there's a time to realize that, in that way of thinking, that most analysts are "beating their heads against a brick wall."

In closing, I'd like to plea with you, Woodduck, to refrain from calling my ideas "woowoo" and drop the "unicorns" references, and deal with the discussion in a more civil and respectful way.


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## hammeredklavier

The way to reach the dominant from i64, with the chromatic ascent C -> C# -> D, with the major second [ G, A ] on the top
(D -> C -> C# -> D | G -> F# | Bb -> A)
Dzmj8lRLHh0&t=16m50s sounds so eerie


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## hammeredklavier

Actually, this part with the non-chord tone E flat watch?v=Dzmj8lRLHh0&t=20m10s "V/iv - iv - *V* - VI - iv6 - V" may be a bit more appropriate as an example for this thread. But I think the example I posted earlier is also noteworthy, in the context of the discussion on "i - [something chromatic] - V(7)".


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## hammeredklavier




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## Woodduck

hammeredklavier said:


>


Nice, but where are the augmented triads and Tristan chords?


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## hammeredklavier

Woodduck said:


> where are the augmented triads


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## Woodduck

hammeredklavier said:


>


A dominant triad with a melodic embellishing tone? Seriously?


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## hammeredklavier

Woodduck said:


> A dominant triad with a melodic embellishing tone










Then whatabout this?:


hammeredklavier said:


>


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## Bwv 1080

Did 18th century practice recognize the augmented chord, rather than a chromatic embellishment? - i.e. is there a figured bass for it?


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## hammeredklavier




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## bagpipers

Not sure what is meant by "augmented triad" the "Tristan Chord" is more of a inverted G# minor VI chord

F-B-D#-G# so de-invert (G#-B-D#-E#)


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## EdwardBast

I always thought it's just a French augmented 6th chord with a G# appoggiatura.


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## Bwv 1080

bagpipers said:


> Not sure what is meant by "augmented triad" the "Tristan Chord" is more of a inverted G# minor VI chord
> 
> F-B-D#-G# so de-invert (G#-B-D#-E#)


You mean minor 6th chord - Jazz nomenclature for a 1st inversion half diminished chord? The Tristan chord enharmonically is just a plain old drop 2 half-diminished chord, but as Edward notes above, most think of the G# as an appoggiatura resolving to A which forms a French Augmented 6th chord (which has nothing to do with an augmented triad, A6 chords are tritone subs for the V/V, and the Fr6th is a dom 7 with a flat fifth degree)


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## bagpipers

Bwv 1080 said:


> You mean minor 6th chord - Jazz nomenclature for a 1st inversion half diminished chord? The Tristan chord enharmonically is just a plain old drop 2 half-diminished chord, but as Edward notes above, most think of the G# as an appoggiatura resolving to A which forms a French Augmented 6th chord (which has nothing to do with an augmented triad, A6 chords are tritone subs for the V/V, and the Fr6th is a dom 7 with a flat fifth degree)


You mean 6th chord? I said minor VI chord!

Not sure what a French 6th has to do with( Aflat-C-D-F#) 

With the F in the bass the chord ultimately has no tonal center,spin it all day how you want.


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## Bwv 1080

bagpipers said:


> You mean 6th chord? I said minor VI chord!
> 
> Not sure what a French 6th has to do with( Aflat-C-D-F#)
> 
> With the F in the bass the chord ultimately has no tonal center,spin it all day how you want.


that is why I was confused, what is a minor VI chord, and why is it enharmonically a half diminished chord? Not familiar with that nomenclature.
Also not sure what you mean about the significance of ‘no tonal center’ for the F - does it need one? It’s a Fr6, so I guess you could look at F as the root if you thought about it as a tritone sub. The French A6th is after the G# resolves upward to A:


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## bagpipers

Bwv 1080 said:


> that is why I was confused, what is a minor VI chord, and why is it enharmonically a half diminished chord? Not familiar with that nomenclature.
> Also not sure what you mean about the significance of ‘no tonal center’ for the F - does it need one? It’s a Fr6, so I guess you could look at F as the root if you thought about it as a tritone sub. The French A6th is after the G# resolves upward to A:
> 
> View attachment 170236


What is a minor VI chord? A-C-E-F# or A-C-E-F (often called minor flat 6th because theory revolves around the major)
If you diminish the perfect V and re-write the F# as Gflat (A-C-Eflat-Gflat) you have the Dim-VII chord

I would ask what the Hades is a Fr+6 chord? Never heard of that!

I do see the E maj French VI in the bar 4 though.Although in a French sixth chord you double shard the C not naturalize the D.

OK! I get it the Fr is for French and the +6 means augmented VI chord so hence; A French VI chord (I was confused a moment) I would just write French 6th or French VI (Fr +6) is confusing.Everyone knows the Italian,German and French VI chords are all augmented on step VI a non augmented 6th chord would not be called Italian,German or French


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## mikeh375

^ never really heard of a,c,e,f being called a minor flat 6th chord. I see that it could be that but to my thinking it's an F major 7th 1st inversion. Any minor 6th chord is understood to have the sharpened 6th, especially when it comes to chord symbols..


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## bagpipers

mikeh375 said:


> ^ never really heard of a,c,e,f being called a minor flat 6th chord. I see that it could be that but to my thinking it's an F major 7th 1st inversion. Any minor 6th chord is understood to have the sharpened 6th, especially when it comes to chord symbols..


Yes minor VI chords have a #'ined 6th so F# in A minor and that is why with a natural 6th step it's called "minor flat VI chord"
It could be an inverted Maj VII chord but with the minor triad in the bass it sounds minor and theory goes by the ear.


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## mikeh375

bagpipers said:


> Yes minor VI chords have a #'ined 6th so F# in A minor and that is why with a natural 6th step it's called "minor flat VI chord"
> It could be an inverted Maj VII chord but with the minor triad in the bass it sounds minor and theory goes by the ear.


...well maybe, vertical spacing, scoring and context all play their part in perception too so I wouldn't say it sounds minor period. We are undoubtedly both right but I can't say in practice that I've come across the minor flat 6th designation for a chord, even though I can see it is theoretically a possibility and exists.


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## bagpipers

mikeh375 said:


> ... but I can't say in practice that I've come across the minor flat 6th designation for a chord, even though I can see it is theoretically a possibility.


It is not very common at all because with the perfect V in the chord it gives you a parallel V coming back to a triad,plus the chord is very dark and sad.I love the chord but rarely even use it in my music.

The best example would be in "Leyenda" (Asturias) by Isaac Albanez with the G minor scale pattern G D E flat D Bflat A G with a tremolo on the octave D giving the flat vi through the back door.

It is a rare chord but a real chord non the less


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## mikeh375

It's funny how we perceive things slightly differently. I've played the piano version of Asturias in my time when I learnt the full Suite Espanola. Not for one moment have I thought of those e flats that impinge on the pedal octaves on D as anything other than thematic or riff like. The e flats to my ear do not define those opening bars as a minor flat6 chord. If it was so, one should also include the c that follows the e flat and think of the chord on beat 2 as some form of c minor ninth. It seems nonsensical to think like that, especially given the tempo along with the insistence of the D and downbeat G's.
I hear an emphatic G minor throughout the bar, with thematic ostinato type embellishments. Ymmv of course just as our ears do... 
Just for us composers we should say YTMV...your theory may vary, which should cover all our differences and sins...


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## Bwv 1080

bagpipers said:


> What is a minor VI chord? A-C-E-F# or A-C-E-F (often called minor flat 6th because theory revolves around the major)
> If you diminish the perfect V and re-write the F# as Gflat (A-C-Eflat-Gflat) you have the Dim-VII chord


 A-C-E-F# in jazz would be called a minor 6th chord, don't see that terminology in classical music, there it would be a first inversion half diminished and would serve a subdominant function. In Tristan, the F-B(Cb)-D#(Eb)-G#(Ab) is a drop 2 voiced half-diminished chord, not the minor 6th voicing. Another way to look at it, is the F-7b5 is a tritone away from the ii, sharing the B-F tritone. Wagner could have wrote a D natural, then you would have had a very conventional i-ii 6/5 - V7, treating the G# as a nonharmonic tone, so its the D# that really gives this passage its power


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## bagpipers

mikeh375 said:


> It's funny how we perceive things slightly differently. I've played the piano version of Asturias in my time when I learnt the full Suite Espanola. Not for one moment have I thought of those e flats that impinge on the pedal octaves on D as anything other than thematic or riff like. The e flats to my ear do not define those opening bars as a minor flat6 chord. If it was so, one should also include the c that follows the e flat and think of the chord on beat 2 as some form of c minor ninth. It seems nonsensical to think like that, especially given the tempo along with the insistence of the D and downbeat G's.
> I hear an emphatic G minor throughout the bar, with thematic ostinato type embellishments. Ymmv of course just as our ears do...
> Just for us composers we should say YTMV...your theory may vary, which should cover all our differences and sins...


Best example I could think of ,sorry


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## mikeh375

bagpipers said:


> Best example I could think of ,sorry


no need to apologise, we are all different, especially when it comes to music . Post some music in the Today's composers as it's always good to hear others work.... I'd be particularly interested to hear your bitonal music.


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## bagpipers

mikeh375 said:


> no need to apologise, we are all different, especially when it comes to music . Post some music in the Today's composers as it's always good to hear others work.... I'd be particularly interested to hear your bitonal music.


I'm not good with computers otherwise I'd have already posted.I have two good tonal recordings and two atonal recording my bi-tonal works have yet to be recorded.


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## bagpipers

Bwv 1080 said:


> A-C-E-F# in jazz would be called a minor 6th chord, don't see that terminology in classical music, there it would be a first inversion half diminished and would serve a subdominant function. In Tristan, the F-B(Cb)-D#(Eb)-G#(Ab) is a drop 2 voiced half-diminished chord, not the minor 6th voicing. Another way to look at it, is the F-7b5 is a tritone away from the ii, sharing the B-F tritone. Wagner could have wrote a D natural, then you would have had a very conventional i-ii 6/5 - V7, treating the G# as a nonharmonic tone, so its the D# that really gives this passage its power


I don't know jazz well honestly and your right I have never seen the minor VI chord in classical music l although I have played Bartok pieces or a piece with an inverted Dim VII chord.


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## EdwardBast

bagpipers said:


> It is not very common at all because with the perfect V in the chord it gives you a parallel V coming back to a triad,plus the chord is very dark and sad.I love the chord but rarely even use it in my music.
> 
> The best example would be in "Leyenda" (Asturias) by Isaac Albanez with the G minor scale pattern G D E flat D Bflat A G with a tremolo on the octave D giving the flat vi through the back door.
> 
> *It is a rare chord but a real chord non the less*


It's not a real chord in classical theory, nor, to my knowledge in jazz nomenclature, which, by the way, tends to have more to do with expediency than with theory—with getting the right notes under the fingers rather than reflecting any view of actual root motion. That is to say, many chords in jazz nomenclature, including most 6th chords, are named the way they are so the right note (one that is actually not the root) ends up in the bass. Essentially, it's like what would happen if one were told to convey the information in a figured bass using only letters, numbers, and accidentals.


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## bagpipers

EdwardBast said:


> It's not a real chord in classical theory, nor, to my knowledge in jazz nomenclature, which, by the way, tends to have more to do with expediency than with theory—with getting the right notes under the fingers rather than reflecting any view of actual root motion. That is to say, many chords in jazz nomenclature, including most 6th chords, are named the way they are so the right note (one that is actually not a root) ends up in the bass.


It is a very rare chord but I use it in my compositions but I write tonally progressive modern music and sort of try to break the rules.

You might see a "minor flat VI" in heavy metal for example


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## Bwv 1080

EdwardBast said:


> It's not a real chord in classical theory, nor, to my knowledge in jazz nomenclature, which, by the way, tends to have more to do with expediency than with theory—with getting the right notes under the fingers rather than reflecting any view of actual root motion. That is to say, many chords in jazz nomenclature, including most 6th chords, are named the way they are so the right note (one that is actually not the root) ends up in the bass. Essentially, it's like what would happen if one were told to convey the information in a figured bass using only letters, numbers, and accidentals.


But 6th chords in Jazz are not inversions - they function as written, a tonic maj 6th chord can be called a vi 6/5 but that is not how it functions, the 6th is just a color note. I guess someone could call it an add 13 if they wanted to be pedantic. 

The chord he is referring to in Asturias is an A6 if I remember the piece correctly


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## bagpipers

Bwv 1080 said:


> The chord he is referring to in Asturias is an A6 if I remember the piece correctly


The original piano was in G minor accept for the actually more performed guitar version in E minor


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## Bwv 1080

bagpipers said:


> The original piano was in G minor accept for the actually more performed guitar version in E minor


Sorry mean an Augmented 6th, not AC#EF#, but looking at it now, its C# Eb G Bb resolving to D, the outer voices are C# and Eb moving to an octave D - its upside down from the conventional aug 6th, but that is how I always thought about the chord


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## bagpipers

Bwv 1080 said:


> Sorry mean an Augmented 6th, not AC#EF#, but looking at it now, its C# Eb G Bb resolving to D, the outer voices are C# and Eb moving to an octave D - its upside down from the conventional aug 6th, but that is how I always thought about the chord


I thought the Leyenda scale pattern was; G D Eflat D Bflat A G against a octave D tremolo. I used to play in on guitar and it was E B C B G F# E against an octave B tremolo


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## Bwv 1080

bagpipers said:


> I thought the Leyenda scale pattern was; G D Eflat D Bflat A G against a octave D tremolo. I used to play in on guitar and it was E B C B G F# E against an octave B tremolo


im talking about the third rasgueado chord - with the C# in the bass in the piano version or A# in the guitar one. Alot of guitar transcriptions just do a C7 to B, the standard Phrygian flamenco thing, but if you want to follow the piano bassline, you need an A# in the bass, so a 4/2 voicing of the C7. Augmented 6th chords are dominant 7ths a half step above the V with particular voice leading


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## bagpipers

Bwv 1080 said:


> im talking about the third rasgueado chord - with the C# in the bass in the piano version or A# in the guitar one. Alot of guitar transcriptions just do a C7 to B, the standard Phrygian flamenco thing, but if you want to follow the piano bassline, you need an A# in the bass, so a 4/2 voicing of the C7. Augmented 6th chords are dominant 7ths a half step above the V with particular voice leading


Oh ok I understand
The previous post was on the "minor flat 6th" not the minor 6th.The B theme in Leyenda is a VII chord basically


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## hammeredklavier

Bwv 1080 said:


>


If we were to view it as "Fr+6 — V7", wouldn't the A have to go down to G#, not rise chromatically?
We can alternatively view the { F, B, D#, G# } as "viio(6#/4/2#)", and the A (instead of the G#) as a non-chord tone.


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## Bwv 1080

hammeredklavier said:


> If we were to view it as "Fr+6 — V7", wouldn't the A have to go down to G#, not rise chromatically?
> We can alternatively view the { F, B, D#, G# } as "viio(6#/4/2#)", and the A (instead of the G#) as a non-chord tone.


the aug 6th is F in the bass and D# in the alto, but instead of rising to an octave E, the D# descends by half step to form the V7 chord


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## Bwv 1080

on a related note


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## hammeredklavier

Bwv 1080 said:


>


@3:44, I'm intrigued by its discussion of Albrechtsberger's method from 1790. Btw, something intriguing from his childhood organist buddy, which too is _contemporaneous _with the Mozart minuet -


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## hammeredklavier




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