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Thread: Chromatic diminished 7ths in Beethoven rondo, how does this harmony work?

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    Senior Member caters's Avatar
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    Default Chromatic diminished 7ths in Beethoven rondo, how does this harmony work?

    Here is the passage I am talking about:

    Chromatic passage.png

    So starting at measure 291, there is a passage where 7th chords go up chromatically, and the majority of these 7th chords are diminished 7ths. The seventh chords only last for 2 bars until there is a break from them with a scale. So let me try to figure out the harmony here.

    A, C, D#, F#, this is an enharmonic respelling of Adim7 to better fit with the key signature of G major. And then that goes to an A#dim7. What scale comes after these 2 seventh chords? Well it starts on B and then goes up and it has 5 sharps. It must be B major. C and C# are skipped. D, F, G#, B, it is a Ddim7, again respelt to fit with the key signature better. That goes to D#dim7 which then lands on an E major scale. E and F are skipped.

    G, Bb, C#, E, it is a Gdim7 though here, it doesn't really fit with the key signature better than if the C# was written as Db. But that would mean spelling the E as Fb which doesn't fit with the key signature at all. As predicted it goes upwards to G#dim7. But here, Beethoven breaks the pattern of 2 diminished 7ths followed by a major scale. If he were to continue the pattern, it would end up on an A major scale. But it doesn't. We get our first resolution. G#dim7 goes to C minor. Beethoven sure loves his C minor.

    The resolution doesn't last for long though, he keeps going with the 7th chords. F, A, C, Eb, this is F7. I would expect it to resolve to Bb. So what does Beethoven give us? The unexpected is what he gives us. He gives us an Adim7 in third inversion. The Gb then goes back down to F giving us another F7. This time, it does resolve. Not only that but Bb is the temporary tonic note. It resolves to Bb minor.

    This then goes directly into Eb7 the same way that C minor went directly into F7. I would expect it to resolve to Ab. But, of course, Beethoven has to give us the unexpected. He gives us a Gdim7 respelt with an Fb instead of an E like the previous Gdim7. This then lands back on Eb7 and Beethoven gives us a scale. However, it isn't a major scale like the previous ones. No, it is Bb dorian where I would expect Eb major or Ab major. Then he finally resolves Eb7 to Ab without going to another 7th chord right after, ending this 20 measure long, chromatic passage. He then has to go back to G somehow but that isn't my focus here.

    So, yeah, it starts off with a pattern of 2 diminished 7ths a half step apart followed by a major scale. Then it deviates from this pattern with the first resolution to C minor. This then starts another pattern of root position dominant 7th, third inversion diminished 7th with root a third above the previous chord root, same root position dominant 7th, resolution chord which then ends with Ab major. So this way, Beethoven has practically brought us all the way up the chromatic scale using these 7th chords.

    But why does this work, this chromatic scale in the harmony? I think it has to do with not only the pattern and how it is deviated but also the circle of fifths.

    400px-Circle_of_fifths_deluxe_4.svg.png

    In both cases where it lands on a major scale, the second diminished 7th has the leading tone as the root and the first diminished 7th has the note 2 spaces on the circle of fifths flatter than the major scale as its root. And A to D itself is a circle of fifths motion. Likewise so is D to G. G# is where things deviate. But this still works because every note in the G#dim7 except for F is a half step away from a chord tone in the C minor chord. The C minor, as an unstable tonic sets us up for the second pattern of 7th chords. Via a motion to the major subdominant, we get F7, 1 space sharper on the circle of fifths than C minor. This then moves to the minor tonic, 3 spaces flatter on the circle of fifths. Again the tonic is unstable. This continues with another movement to the major subdominant. Then we finally get to a stable tonic with the Eb7 to Ab motion that ends the passage, a cadence in Ab. Summing this up, we move 9 spaces flatter on the circle of fifths than where we started.

    Is the circle of fifths the reason why this progression of 7th chords works?

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    Senior Member EdwardBast's Avatar
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    Could you please tell us what the piece is with an opus number or other reference?
    Last edited by EdwardBast; May-24-2019 at 22:13.

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    Senior Member TalkingHead's Avatar
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    Rondo a capriccio, Op.129

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    Senior Member EdwardBast's Avatar
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    Here is what's going on harmonically:

    Screen Shot 2019-05-24 at 7.25.40 PM.jpg

    Note that the harmony in mm. 10-11 of the example is a pivot chord, starting life as the vii7/V in D minor, becoming the vii4/2/ii in Bb minor.

    The Gb and Fb in mm. 14 and 18 respectively are just neighbor tones — the harmony really doesn't change.

    There is no Dorian mode. That scale is just Ab major, which is the scale of the local key.

    Caters, you tend to get bogged down in details in your analyses rather than looking at the big picture. The passage is mostly four measure units which are then transposed and repeated. If you have any questions don't hesitate to ask.
    Last edited by EdwardBast; May-25-2019 at 00:29.

    What greater comfort does time afford than the objects of terror re-encountered and their fraudulence exposed in the flash of reason?
    — William Gaddis, The Recognitions

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    Senior Member caters's Avatar
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    Why isn't the last scale of the passage an example of the Dorian mode? It starts and ends on Bb, which suggests to me that Bb is the root of the scale. Given that Bb minor has 5 flats and the scale in question only has 4 flats, it would make sense to me to call it Bb Dorian. I mean, if it was intended to be Ab major, wouldn't Beethoven have started the scale on Ab, like how he starts the B major scale on B and the E major scale on E?

    And what do the n's mean in your harmonic analysis? Does it mean that it is a chord based on the Neopolitan? Because those usually have a capital n in the analysis with 6 being the bass figure. Or does it mean that it isn't all that important harmonically and that the third inversion diminished 7th is really just a neighbor tone in the bass over a dominant 7th harmony?

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    Senior Member TalkingHead's Avatar
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    ^^^^ EdwardBast: may I ask what sofware you are using that enables you to take Cater's PNG image and figure it?
    That could be useful to me !!

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    Senior Member EdwardBast's Avatar
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    Quote Originally Posted by caters View Post
    Why isn't the last scale of the passage an example of the Dorian mode? It starts and ends on Bb, which suggests to me that Bb is the root of the scale. Given that Bb minor has 5 flats and the scale in question only has 4 flats, it would make sense to me to call it Bb Dorian. I mean, if it was intended to be Ab major, wouldn't Beethoven have started the scale on Ab, like how he starts the B major scale on B and the E major scale on E?
    The progression is just V7-I in Ab major. The V chord has an Ab major scale over it. Doesn't matter what note it starts on. The root of the scale is Ab. The simpler answer is: It's Beethoven! He's not writing in Dorian mode. There is nothing modal about this piece.

    Quote Originally Posted by caters View Post
    And what do the n's mean in your harmonic analysis? Does it mean that it is a chord based on the Neopolitan? Because those usually have a capital n in the analysis with 6 being the bass figure. Or does it mean that it isn't all that important harmonically and that the third inversion diminished 7th is really just a neighbor tone in the bass over a dominant 7th harmony?
    The n just means neighbor tone. The harmony in each case is V7 for three measures with the root moving to a neighbor tone for the second measure. The neighbor motion doesn't change the harmony. It is a linear phenomenon.
    Last edited by EdwardBast; May-25-2019 at 00:55.

    What greater comfort does time afford than the objects of terror re-encountered and their fraudulence exposed in the flash of reason?
    — William Gaddis, The Recognitions

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    Senior Member EdwardBast's Avatar
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    Quote Originally Posted by TalkingHead View Post
    ^^^^ EdwardBast: may I ask what sofware you are using that enables you to take Cater's PNG image and figure it?
    That could be useful to me !!
    I'm just really fast copying in Sibelius .

    What greater comfort does time afford than the objects of terror re-encountered and their fraudulence exposed in the flash of reason?
    — William Gaddis, The Recognitions

    Originality is a device untalented people use to impress other untalented people and to protect themselves from talented people.
    Basil Valentine

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    Quote Originally Posted by EdwardBast View Post
    I'm just really fast copying in Sibelius .
    Via MIDI keyboard input?

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    Quote Originally Posted by TalkingHead View Post
    Via MIDI keyboard input?
    Not in this case. Given the sequences involved and repeated figuration, it didn't take long: Cut-paste-transpose.

    Not sure how meaningful all the Roman numerals were, given the modulating sequential stuff.

    What greater comfort does time afford than the objects of terror re-encountered and their fraudulence exposed in the flash of reason?
    — William Gaddis, The Recognitions

    Originality is a device untalented people use to impress other untalented people and to protect themselves from talented people.
    Basil Valentine

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    Senior Member TalkingHead's Avatar
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    Quote Originally Posted by EdwardBast View Post
    Not in this case. Given the sequences involved and repeated figuration, it didn't take long: Cut-paste-transpose.

    Not sure how meaningful all the Roman numerals were, given the modulating sequential stuff.
    Well, that would be a lot of work for me (I use Finale), so thank you for making the effort.
    I think your Roman numerals were useful, though I might have a couple of little quibbles which I'll address later, nothing to get into a lather about, more to do with US/FR figured bass conventions, no sweat.

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    Senior Member EdwardBast's Avatar
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    Quote Originally Posted by TalkingHead View Post
    Well, that would be a lot of work for me (I use Finale), so thank you for making the effort.
    I think your Roman numerals were useful, though I might have a couple of little quibbles which I'll address later, nothing to get into a lather about, more to do with US/FR figured bass conventions, no sweat.
    Please give a critique! It was a fast job.
    Last edited by EdwardBast; May-25-2019 at 04:59.

    What greater comfort does time afford than the objects of terror re-encountered and their fraudulence exposed in the flash of reason?
    — William Gaddis, The Recognitions

    Originality is a device untalented people use to impress other untalented people and to protect themselves from talented people.
    Basil Valentine

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    Senior Member TalkingHead's Avatar
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    Quote Originally Posted by EdwardBast View Post
    Please give a critique! It was a fast job.
    For a fast job it was pretty good, I must say !!
    My quibbles really are very minor (you will call me a nit-picker !!).

    1) Figured bass conventions: you obviously are schooled in one way (VII°7) and me in another (VII7 with the 7 crossed out); sorry, I can't represent that in this forum programme, here is an image of what I mean:


    2) Concerning your point: The 'n' just means neighbor tone. The harmony in each case is V7 for three measures with the root moving to a neighbor tone for the second measure. The neighbor motion doesn't change the harmony. It is a linear phenomenon.
    I think they are more than just neighbour notes in bars 14 and 18; I see them as VII2, though I agree with you that the harmony doesn't really change fundamentally, they are just "dominant prolongations", if I can put it that way.

    3) At first I was going to take issue with your figuring at bar 11 (b-flat: vii4/2/ii) but on looking closer I see you are absolutely right! It took me a while to realize that Beethoven is using the chromatically altered supertonic II7 chord (in B-flat minor, with sharpened 3rd & 5th), but I was looking for an A-flat which is in fact present, though spelled as G# !! Bravo for that, I wouldn't have spotted that as quickly as you did.

    So finally, my only really little quibble is how we analyse the neighbour notes as explained in Point 2 above.
    Last edited by TalkingHead; May-25-2019 at 20:02.

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    Senior Member EdwardBast's Avatar
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    Quote Originally Posted by TalkingHead View Post
    For a fast job it was pretty good, I must say !!
    My quibbles really are very minor (you will call me a nit-picker !!).

    1) Figured bass conventions: you obviously are schooled in one way (VII°7) and me in another (VII7 with the 7 crossed out); sorry, I can't represent that in this forum programme, here is an image of what I mean:


    2) Concerning your point: The 'n' just means neighbor tone. The harmony in each case is V7 for three measures with the root moving to a neighbor tone for the second measure. The neighbor motion doesn't change the harmony. It is a linear phenomenon.
    I think they are more than just neighbour notes in bars 14 and 18; I see them as VII2, though I agree with you that the harmony doesn't really change fundamentally, they are just "dominant prolongations", if I can put it that way.

    3) At first I was going to take issue with your figuring at bar 11 (b-flat: vii4/2/ii) but on looking closer I see you are absolutely right! It took me a while to realize that Beethoven is using the chromatically altered supertonic II7 chord (in B-flat minor, with sharpened 3rd & 5th), but I was looking for an A-flat which is in fact present, though spelled as G# !! Bravo for that, I wouldn't have spotted that as quickly as you did.

    So finally, my only really little quibble is how we analyse the neighbour notes as explained in Point 2 above.
    As for figured bass conventions, I wasn't going for anything so ambitious as figured bass. I was doing whatever could easily be done with a normal typeface.

    What greater comfort does time afford than the objects of terror re-encountered and their fraudulence exposed in the flash of reason?
    — William Gaddis, The Recognitions

    Originality is a device untalented people use to impress other untalented people and to protect themselves from talented people.
    Basil Valentine

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