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Thread: Beethoven's Razumovsky 3 Aug to N6 Magic Trick

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    Default Beethoven's Razumovsky 3 Aug to N6 Magic Trick

    In Beethoven's 3rd Razumovski quartet (his 9th quartet, op. 59) in the second movement he pulls off some real magic in bars 88-92 (not counting the repeat of bars 13-26--you may need to add 13 if your score counts these repeated bars). This is during the development of this exquisitely beautiful piece of "gypsy" inspired music in 6/8 time. The ear has been prepared for this moment (of course, with LVB) but I want to cut straight to the chase and describe how he uses Aug6 chords to modulate up a P5th.

    In the preceeding 6 bars he firmly establishes the temporary key of Bb- (the piece is in Amin; so tha's half way around the Circle of 5ths). Then in bar 86 he drops the bass note of the Bbmin chord to a G, making the chord a G half dim., leading to a C7 and then resolving to Fmin. This is a fairly standard way of getting the tonal center to shift up a P5th, going back to Bach. But then comes the cool part. He continues to work his way swimming upstream through the Circle of 5ths, but rather than doing the same old thing over and over, he cleverly disguises it (as he quickens the harmonic rhythm).

    At the top of bar 88 (3:55 on the Alexander Quartet version) he has just arrived at Fmin as described above, but then the viola moves to a B as the cello moves to Db, transforming the chord into a Db German Aug6 chord in Fmin at the top of bar 89 (Db, B, F, Ab). Nothing too unusual there, but here comes the magic part, involving LVB's total mastery and control of diminished chord symmetry. He slyly transforms the Db Aug6 chord (Db, B, F, Ab) into a D diminished chord on beat 3, then into a G7 chord on beat 6 as the cello moves down to G, then resolving to the key of Cmin at the top of bar 90.

    So in retrospect our ear tells us that, relative to the new key of Cmin, what we just heard was a N6 chord (Db7) resolving as it normally would to a G7 to Cmin. But going in, our ear heard the Db chord as an Aug6 chord in the old key of Fmin. This morphing between Aug6 function and N6 function to modulate up a 5th just sounds like pure magic to my ears, as if Beethoven knows a secret passageway through the Circle of 5ths, and then he does it again--the exact same moves, repeating the magic trick up a P5th. The Aug6 chord was in 1st inversion, by the way, the correct inversion for the ear to hear it as a N6 chord in retrospect.

    The Cmin chord at the top of bar 90 moves to Ab7 at bar 91 then Adim on beat 3 and D7 on beat 6. When this resolves to Gmin at bar 92 we realize that we've once again been snookerd into thinking the Aug6 chord (Ab7) in the key of Cmin was, well and Aug6 chord, only to find that it morphed into a N6 chord in the new key of Gmin.

    It all happens so fast, in the space of bars 4 bars of 6/8 time, that even the attentive listener who likes to keep up with the modulations can lapse into a sort of dream state, content to just let the magic happen, and to hell with what key we're in. To me it sounds like the sort of mystical experience that makes life worth living.

    This piece of music is one of my all time favorites. The first movement is awesome as well, starting off as it does with Beethoven's homage to the intro of Mozart's Dissonant Quartet. As usual for LVB, the diminished chords are again the key to his easy navigation from key to key, always with a sense of inevitability perfectly in balance with a countervailing sense of surprise. This tightly crafted balance of these two critical elements is what separates great music from merely good music, at least to my ear. Whether it's Beethoven, Bill Evans, The Beatles, or Brahms, this sort of magic doesn't happen by accident. It's always the carefully crafted balance of these two elements that keeps me coming back for more.

    Thanks for reading.
    Last edited by Wes Lachot; Aug-16-2020 at 19:31. Reason: clarity

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    I'd like to discuss this music but I must first renumber the bars in my score. (The old convention of not numbering bars when first and second endings are present really has to go. It's silly and has the obvious problem of leaving numberless bars.)
    Last edited by EdwardBast; Aug-16-2020 at 15:28.

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    Quote Originally Posted by EdwardBast View Post
    I'd like to discuss this music but I must first renumber the bars in my score. (The old convention of not numbering bars when first and second endings are present really has to go. It's silly and has the obvious problem of leaving numberless bars.)
    Edward, should I have included the repeat bars in my numbering? We would add 13 to the numbers in my post if that's the case. Would it be simpler if I renumbered the post for clarity? I'm working off of an old 19th century score that isn't numbered, so I'm having to count them anyway.

    I edited the post and added a caution about the bar numbering, but I can change the numbers in the post if that makes it easier.
    Last edited by Wes Lachot; Aug-16-2020 at 19:31.

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    No worries about the numbers. We just ended up four measures apart and I can easily use yours.*

    This movement is a favorite of mine as is the quartet. I agree it's unique and magical, and your analysis captures how this passage works pretty well. The only comment I'd make on your analysis is that I favor a less busy view of the harmonic structure. For example, I don't hear a diminished harmony in the last half of measure 89, but rather V7 of Cm with a suspended Ab resolving on beat 6. And the first half of the measure never sounds like an augmented 6th chord to me — I hear the the Neapolitan (or altered ii7) in Cm immediately. Mere quibbles in other words.

    The first movement has always struck me as a comic masterpiece, with the grandiloquent first violin part competing with the others and their obstinate obsession with a two note motive. The development is the story of how this short motive wanders off and runs amok in what sounds like a purposefully aimless progression until the imperial first part restores order with even more grandiloquent ruminations. And what a wonderful, rollicking finale!

    *The convention your score uses is traditional and widely accepted. But it makes no sense whatever. Under that convention the first ten notated measures of the Beethoven are numbered 1, 2, 3, 4, 5, 6, _, _, 7, 8. That is, two measures are, weirdly, left unnumbered. In the orchestra libraries where I've worked, any time a new set without bar numbers came in, we numbered every notated bar in order irrespective of repeats and first and second endings. It's unambiguous and thorough.
    Last edited by EdwardBast; Aug-16-2020 at 20:06.

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    Quote Originally Posted by EdwardBast View Post
    No worries about the numbers. We just ended up four measures apart and I can easily use yours.*

    This movement is a favorite of mine as is the quartet. I agree it's unique and magical, and your analysis captures how this passage works pretty well. The only comment I'd make on your analysis is that I favor a less busy view of the harmonic structure. For example, I don't hear a diminished harmony in the last half of measure 89, but rather V7 of Cm with a suspended Ab resolving on beat 6. And the first half of the measure never sounds like an augmented 6th chord to me — I hear the the Neapolitan (or altered ii7) in Cm immediately. Mere quibbles in other words.

    The first movement has always struck me as a comic masterpiece, with the grandiloquent first violin part competing with the others and their obstinate obsession with a two note motive. The development is the story of how this short motive wanders off and runs amok in what sounds like a purposefully aimless progression until the imperial first part restores order with even more grandiloquent ruminations. And what a wonderful, rollicking finale!

    *The convention your score uses is traditional and widely accepted. But it makes no sense whatever. Under that convention the first ten notated measures of the Beethoven are numbered 1, 2, 3, 4, 5, 6, _, _, 7, 8. That is, two measures are, weirdly, left unnumbered. In the orchestra libraries where I've worked, any time a new set without bar numbers came in, we numbered every notated bar in order irrespective of repeats and first and second endings. It's unambiguous and thorough.
    Edward: That's really wild! I wonder how on earth that convention got started? Is it like Bach's first prelude where an editor changed it somewhere along the way? I mean, bars 7 and 8 are the beginning of the repeat of the first theme; pretty strange to leave those unnumbered. But thanks--you are obviously quite familiar with this piece (understatement).

    I agree that the harmonic anaysis could be simpler, and that the diminished chords happen so fast they are hardly noticed. I guess I wanted to be as complete as possible, and also to point out that the difference between the Db7 chord and the target G7 chord, since they contain the same tritone (enharmonically of course--B and F), is that the root and 5th of the Db7 chord need to contract inward to a P4th for the G7 chord, and that by raising the Db to a D natural first, there is a diminished chord created for just a split second. But I agree that the simpler version would have made my analysis less long winded. It's amazing how a simple idea can end up being so many paragraphs...

    I agree with your points about the other movements as well, and without them the 2nd movement would have the needed context. Somehow that 2nd movement just transports me to another place; I think it may have been Rosen who referred to it as the "intellectual center of the Quartet" (paraphrasing). (I know it's sloppy to sort of quote someone, but I'm pretty sure it was Rosen, and I don't have a search engine that works for my dusty old books.)

    Thanks for your insights on this Quartet. Always looking to discuss Beethoven if you have any others to analyze or talk about. I like analyzing the string quartets of my favorite composers because the 4 voice writing is ripe fruit for analysis.

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    I've heard of augmented seventh chords, but not augmented sixths. Can you spell it?

    Also, you may want to read my post in the Need help understanding the neapolitan chord thread.

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    MR: In classical theory going way back, what we refer to in modern jazz terms as a tritone substitute for V/V, otherwise known as the bVI chord, was (is) called an Augmented 6 chord. There are 3 different versions, Italian, German, and French. The reason they are called Augmented 6 and not "7th", which is really how they sound, is because of voice-leading rules, and the historical background of the chord. And Aug 6th is really the same interval enharmonically, so you can call it either thing--it's the same sound. Historically they evloved from IV minor (Italian) and minor 6 (French) chords in 1st inversion, hence the name "Augmented 6".

    Without worrying right now about typical voice leading or doublings, the Italian version is spelled simply Ab, C, F#, and sounds like a root and tritone Ab7 chord, but is called an Aug6 instead because the F# normally voiceleads up to G for either the C tonic chord in 2nd inversion or the V chord proper.

    The French version also contains a D note or #11 (b5), so that would be spelled Ab, C, D, F#, and sounds like a dominant #11 chord. The interesting thing about the French version is it's symmetry: it can be viewed as either an Ab Aug6 or a DAug6. Play with it at the piano and you'll see for yourself.

    The German version simply replaces the D with an Eb. It's at this point that the classical way of describing these dominant 7th chords as "a rose by any other name" gets a little tenuous, but we're not here to argue about labels.

    A good musical example of a French Augmented 6 that most people have heard is the beautiful even sublime passage in bars 9 and 10 of Chopin's Prelude #20 (op. 28). The French Aug6 chord happens on beat 2 of bar 10. It happens to be in the key of C for ease of description. Check it out at the piano to get the sound in your head, and you'll notice that it's what we call a sub V of V nowadays.

    A more recent musical example of a French Augmented 6 that probably even more people can recall in their heads would be at the end of the bridge of Lennon/McCartney's "Oh! Darling", on the line "Well you know I nearly broke down and died" on "broke down". Just like in the Chopin example the melody note is on "re", a tritone from the root of the chord, which is pretty common.
    Last edited by Wes Lachot; Aug-19-2020 at 18:45. Reason: spelling

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    Quote Originally Posted by Wes Lachot View Post
    MR: In classical theory going way back, what we refer to in modern jazz terms as a tritone substitute for V/V, otherwise known as the bVI chord, was (is) called an Augmented 6 chord.
    So let me try to translate this: (key of C) a V of V is a D7, and the tritone sub for that is Ab7. So basically, this is a further reiteration (recurrence) of a dominant cycle of fifths.

    What throws me off is the term "augmented" which in my mind refers to a chord with a raised fifth, but in this case refers to an "augmented interval." Is that right? Correct me if I err.
    This needs to be made explicitly clear if any of the rest of the post is to make sense.

    There are 3 different versions, Italian, German, and French. The reason they are called Augmented 6 and not "7th", which is really how they sound, is because of voice-leading rules, and the historical background of the chord. And Aug 6th is really the same interval enharmonically, so you can call it either thing--it's the same sound.
    Ok, I think I get you here. The "aug" refers to an interval which is an enharmonic seventh, not a chord quality. And this is done to "protect" the diatonic context, I presume?

    Historically they evloved from IV minor (Italian) and minor 6 (French) chords in 1st inversion, hence the name "Augmented 6".
    You lost me again. Does "minor sixth" chord refer to an interval, or a minor chord with an added sixth? Why does being in first inversion make them "augmented sixths?"

    Without worrying right now about typical voice leading or doublings, the Italian version is spelled simply Ab, C, F#, and sounds like a root and tritone Ab7 chord, but is called an Aug6 instead because the F# normally voiceleads up to G for either the C tonic chord in 2nd inversion or the V chord proper.
    Okay, I think I get that; the voice leads to V or I, just like a dominant V-I leading tone F#-G.

    The French version also contains a D note or #11 (b5), so that would be spelled Ab, C, D, F#, and should like a dominant #11 chord.
    I don't call that a #11, though; to be a #11 (in jazz), there must be an unaltered fifth. So I'd call it a b5, since it is derived from a diminished seventh, in a tritone relationship (which is a "fifths" relation).

    The interesting thing about the French version is it's symmetry: it can be viewed as either an Ab Aug6 or a DAug6. Play with it at the piano and you'll see for yourself.
    Yes, the inherent symmetry in diminished sevenths, if that's what you mean. The "parent" diminished seventh chord is Ab-Cb-D-F, but I am puzzled that it doesn't work with Cb(B) or F as a root. So it must not be entirely derived from a diminished chord.

    The German version simply replaces the D with an Eb. It's at this point that the classical way of describing these dominant 7th chords as "a rose by any other name" gets a little tenuous, but we're not here to argue about labels.
    Well, it seems that this is all based on voice-leading principles, not harmonic factors, so it gets increasingly confusing to me.

    For me, the clearest way of seeing this is with a "parent" scale of F#-A-C-Eb. Then you can put a root of D or Ab under it. So this is like my "no. 2" dom7(b9) method.

    When you say the German version "replaces the D with an Eb," I need some reference: how is D functioning in the French, as a root or b5 of an A chord?
    ...and how does Eb function in the German, as a b9 of a D chord, or as a b5 of an Ab chord? Please spell the chords, and give their functions in the triad.

    A good musical example that most people have heard is the beautiful even sublime passage in bars 9 and 10 of Chopin's Prelude #20 (op. 28). The French Aug6 chord happens on beat 2 of bar 10. It happens to be in the key of C for ease of description. Check it out at the piano to get the sound in your head, and you'll notice that it's what we call a sub V of V nowadays.
    I'll look into that.
    Last edited by millionrainbows; Aug-19-2020 at 18:10.

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    Quote Originally Posted by millionrainbows View Post

    What throws me off is the term "augmented" which in my mind refers to a chord with a raised fifth, but in this case refers to an "augmented interval." Is that right? Correct me if I err.
    This needs to be made explicitly clear if any of the rest of the post is to make sense.
    Any interval can be "augmented", and in this case it's a major 6th being augmented into the equivalent of a minor 7th interval.

    I said above: "Historically they evolved from IV minor (Italian) and minor 6 (French) chords in 1st inversion, hence the name "Augmented 6".

    By this I mean that a minor IV chord in C, in 1st inversion, spells out as Ab, C, F. By raising the F to an F# it becomes an Italian Aug6 chord. "Italian" just means no 5th. And if you add the 6 to the 1st inversion IV chord before augmenting the 6 you get the French.

    I don't call that a #11, though; to be a #11 (in jazz), there must be an unaltered fifth. So I'd call it a b5, since it is derived from a diminished seventh, in a tritone relationship (which is a "fifths" relation).
    That's cool, but a lot of jazz guys don't make that distinction. It's just all one chord scale usually, and most charts aren't there to tell the pianist how to voice the chord, just what the tonality is. It is possible, FYI, so see #11 along with an altered 5th in the form of a flat 13. I've seen plenty of charts with the chord symbol C7b9/b13/#11, which is a nerdy way of writing out "Altered" which means the same thing (along with a #9). So many of us just use the term #11.

    Yes, the inherent symmetry in diminished sevenths, if that's what you mean. The "parent" diminished seventh chord is Ab-Cb-D-F, but I am puzzled that it doesn't work with Cb(B) or F as a root. So it must not be entirely derived from a diminished chord.
    That's actually not what I meant in this particular case. There of course is symmetry in what you're referring to, but I was speaking specifically of the French Aug6 chord, which has a peculiar trait that of being a sort of musical palindrome which reads the same intervals bottom to top as top to bottom. Again, I refer you to the piano, and check out how in either root position or 2nd inversion it's the same set of intervals.

    Well, it seems that this is all based on voice-leading principles, not harmonic factors, so it gets increasingly confusing to me.
    It's a combination of the two. I've seen you speak of this dichotomy on another thread as if it was a problem, but it's not generally viewed that way. Voice leading principles were created in order to keep the lyrical beauty and independence of the musical "parts" intact. Harmonic priciples were developed so that as those independent melodies collided with each other, acceptable, even beautiful harmonies resulted. They are not at war with each other, they just have to be taken into consideration about equally. For a genius like Bach, that's the fun of it--it's not easy or he would have moved on to something more intellectually challenging.

    For me, the clearest way of seeing this is with a "parent" scale of F#-A-C-Eb. Then you can put a root of D or Ab under it. So this is like my "no. 2" dom7(b9) method.
    I believe you are referring to the inherent symmetry of b9 chords. While this idea does open the doors of symmetrical thinking within the Circle of 5ths, it is just a part of that symmetry story, and if you want to look deeper into musical symmetry I would encourage you to look beyond the b9 chords that may have opened that musical door to begin with, since similar and fascinating symmetries exists for all sorts of other shapes and musical situations. The reason I mention this now, in this context, is that the bVI7 chord in question (Aug6 chord) is not a b9 chord. But it's got symmetry out the wazoo.

    When you say the German version "replaces the D with an Eb," I need some reference: how is D functioning in the French, as a root or b5 of an A chord?
    ...and how does Eb function in the German, as a b9 of a D chord, or as a b5 of an Ab chord? Please spell the chords, and give their functions in the triad.
    In the French Ab Aug6 chord (Ab, C, D, F#), the D is a #11 (or b5 if you prefer). The German version does not contain this note. It is just a straight triadically spelled 7th chord (Ab, C, Eb, F#), well except for the enharmonically spelled flat 7.

    Listening to those musical examples should make this wordy post make a lot more sense.
    Last edited by Wes Lachot; Aug-19-2020 at 19:50.

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    Quote Originally Posted by Wes Lachot View Post
    That's cool, but a lot of jazz guys don't make that distinction. It's just all one chord scale usually, and most charts aren't there to tell the pianist how to voice the chord, just what the tonality is. It is possible, FYI, so see #11 along with an altered 5th in the form of a flat 13. I've seen plenty of charts with the chord symbol C7b9/b13/#11, which is a nerdy way of writing out "Altered" which means the same thing (along with a #9). So many of us just use the term #11.
    Not for me in jazz; I distinguish between a chord with a flatted fifth (b5) and one which has a #11.

    A #11 indicates a color tone in the upper register, and does not refer to the fifth of the chord. An altered fifth changes the quality of a chord.

    A chord can have both, but the main triad is properly called a b5 chord. Example: C-E-Gb-Bb-D-F#-A, which I call a C13b5(#11).

    A ninth chord assumes a flatted seventh; in this case the seventh is indicated so as not to confuse the b9 with the main chord C as a Cb. I'd call it a C7b9(#11 b13), but this does not indicate a b5. Spelled out, it would be C-E-G-Bb-D-F#-Ab. The b13, in this chord, seems awkward to me.

    Quote Originally Posted by Wes Lachot View Post
    It's a combination of the two. I've seen you speak of this dichotomy on another thread as if it was a problem, but it's not generally viewed that way. Voice leading principles were created in order to keep the lyrical beauty and independence of the musical "parts" intact.
    If by "intact" you mean "remaining in-bounds of proper diatonic spelling," I see. It seems to me to be overly-accommodating to the diatonic system, while ignoring the chromatic aspect. After all, we are talking about (key of C) a root on Db, which is not diatonic.
    I'm a chromatic thinker, not diatonic, so that's the problem.
    Last edited by millionrainbows; Aug-19-2020 at 22:27.

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    MR: It can be any style--even completely atonal sounding. That's not the point. Let me try to put it a different way.

    Melodies are inherently linear, and harmonies are inherently verticle, right? But it's not so simple when you go to actually compose. You can't think of a chord as completely vertical, because after all it has to move to another chord, plus it had to come from somewhere--so now that's three chords just to discuss one chord, and so there is inevitably a melodic aspect creeping in. We can't just move to the next chord, we have to have it make sense, where each voice goes to it's natural conclusion, so if you sung that part alone in the shower it would sound good. That's harder than you think.

    It also works the other way. It's harder than you think to put two or three or four melodies together and have them make sense harmonically. So there's a chicken-and-egg thing going on where you can't start one puzzle without starting the other and vice-versa. That's what makes it so interesting for so many people.

    It's sort of like matter and energy to a physicist--you can't talk about one without talking about the other, and you can't affect one without affecting the other.
    Last edited by Wes Lachot; Aug-20-2020 at 00:48. Reason: sp

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    Quote Originally Posted by Wes Lachot View Post
    MR: It can be any style--even completely atonal sounding. That's not the point. Let me try to put it a different way.

    Melodies are inherently linear, and harmonies are inherently verticle, right? But it's not so simple when you go to actually compose. You can't think of a chord as completely vertical, because after all it has to move to another chord, plus it had to come from somewhere--so now that's three chords just to discuss one chord, and so there is inevitably a melodic aspect creeping in. We can't just move to the next chord, we have to have it make sense, where each voice goes to it's natural conclusion, so if you sung that part alone in the shower it would sound good. That's harder than you think.

    It also works the other way. It's harder than you think to put two or three or four melodies together and have them make sense harmonically. So there's a chicken-and-egg thing going on where you can't start one puzzle without starting the other and vice-versa. That's what makes it so interesting for so many people.

    It's sort of like matter and energy to a physicist--you can't talk about one without talking about the other, and you can't affect one without affecting the other.
    I'll grant you all that as true. The problem for me is the nomenclature, such as Aug6 as a name for a chord, when the name refers to voice leading. It doesn't make good sense to me.

    There are a lot of musical concepts which are based on the vertical and static, such as intervals and their ratios, and functions, and tonality. This is where all music started.

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