Key relationship?

[amanfang]

I noticed tonight while I practicing the 3rd mvmt of Beethoven's Op. 110, that the arioso is in a-flat minor, but the key sig indicates e-flat minor.  Why didn't he just add the extra flat into the key signature?  It is the parallel minor of the A-flat major tonic.  Does it have anything to do with beginning of the movement opening in b-flat minor?

[pianistimo]

it looks like g minor to me.  am i missing something?  at measure 116 the lh has a g minor chord.  he is making a chromatic key relationship here.  it is so miraculous!  he just adds in chromaticism to the fuga (using that as the basis for transition) and just does what he wants.

look at measure 113 - it is EbM7 to suddenly g minor at measure 114 - moving up in rh and down in lh.  very unusual and very chromatic.

[amanfang]

You're looking at the second time the arioso comes in.  It's before the first fugue subject statement.

[pianistimo]

same thing on the first arioso.  you have a losing key area in the 'adagio ma non troppo' where it is written as the key signature of Db major - but you are actually playing a Db major third above a bass note of Bb - so it sounds like Bb minor.  and to add to that - the seventh is sharped (A natural) which confirms Bb minor MORE than Db major.

then using that assumed key - we move into the recitative through chromatic means (adding the Cb and Fb in measure 2 and cancelling the Gb) to the supposed key of Db major - but NOW hearing Eb major and using the Db as the 5th of the Eb major chord.

then suddenly we move from Eb major to E major - using a very UNSTABLE 4th in the adagio.  the meno adagio  (UNSTABLE aug 5th) and last adagio before the adagio non troppo back to Eb - and then to using that as the fifth again for Ab major chord.  very unstable stuff goes on in that arioso (G natural and Fb).

besides chromaticism he is utilizing fourth and fifth relationships in ways that use the top note of the chord and not the tonic.  really crazy.  like turning a page upside down.  the second adagio ma non troppo seems to work down and backwards.  Eb's then Eb-C  then Eb - C- Ab  FINALLY we know what the key is.  sort of.

[ramseytheii]

same thing on the first arioso.  you have a losing key area in the 'adagio ma non troppo' where it is written as the key signature of Db major - but you are actually playing a Db major third above a bass note of Bb - so it sounds like Bb minor.  and to add to that - the seventh is sharped (A natural) which confirms Bb minor MORE than Db major.

Oh my goodness.  First of all: what is a "losing" key area?  I won't even try to guess.  Next thing: if a piece with 5 flats opens with a b-flat in the bass, and a "Db major third" above that, that's not the key of "Db major" that is b-flat minor.  Unless you would also like to argue that op.57 is in A-flat major, because it has 4 flats and opens with an "Ab major third." 

then using that assumed key - we move into the recitative through chromatic means (adding the Cb and Fb in measure 2 and cancelling the Gb) to the supposed key of Db major - but NOW hearing Eb major and using the Db as the 5th of the Eb major chord.

I disagree with just the last part but wish to write this in a clearer way.
At the end of the first bar, Beethoven is already modulating towards E-flat minor (circle of fifths); by introducing the D-natural, the bass becomes the dominant, and then on the last beat, a typical cadential 6-4 chord in E-flat minor; the C-flat comes from being the relative major to E-flat minor. 

We would seem to be in C-flat major because the whole second bar is a I-IV-V cadence, but this is also deceptive because he in turn uses C-flat major as the Major III of a-flat minor. 

Bar 3 is preparing the a-flat  minor cadence, it's not in E-flat, the E-flat is a cadential chord, but in an original stroke of genius the resolution is achieved by a transformation of the traditional Classical cadenza, into a dissolved, fantasy recitativo, which does in fact resolve the dominant.

Finally, D-flat can never be a "fifth" to E-flat, since it is a whole step below.  Did you mean 7th?

then suddenly we move from Eb major to E major - using a very UNSTABLE 4th in the adagio.  the meno adagio  (UNSTABLE aug 5th) and last adagio before the adagio non troppo back to Eb - and then to using that as the fifth again for Ab major chord.  very unstable stuff goes on in that arioso (G natural and Fb).

Here you are letting the apperance on the page get the better of your ear.  First of all the key was never E-flat major, the E-flat was clearly the dominant to a-flat minor.  Second of all E major is to be udnerstood here as F-flat major; in other words, the relative major of A-flat minor. 

This is not a bizarre key change - look at the chords in the andante.  Here are they in terms of a-flat minor: VI, Neapolitan in first inversion, III⁷ which is the dominant of VI.  OF course we can't spell out F-flat major, which is VI in a-flat minor, so enharmonically it becomes E major.

I don't disagree that it is unstable, and that he is establishing the key (a-flat) in a roundabout way, but wanted to point out the inherent, impeccable logic of it all.

As far as the arioso, I don't call the appearance of sharp'd or flat'd notes unstable.  There are explanations for them.  And definitely, a G-natural in A-flat minor is not unstable, it's the leading tone.  The F-flat doesn't play a part in changing the flow of harmony, so I also don't call it unstable.  It's a poignant, dissonant suspension, which recalls in my mind the words from the Te Deum, "thou hast overcome the sharpness of death."


BUT, all this blather doesn't address the original question, but I think I can answer it.  Why does Beethoven not write the arioso with an a-flat minor key signature?  That's a great question and I never even noticed that until you mentioned.  I think the reason is because he was being deliberately archaic.  If you look at early Baroque music, minor signatures are always minus one flat.  G minor is in one flat, C minor has two, et cetera.  I can't exlpain that convention, hopefuly someone can, but I believe Beethoven was imitating this, or at least calling to mind this learned tradition.

There are other elements of recalling the past in this sonata, for instance, the repeated A's, which clearly simulate the Bebung effect of the Clavichord on the modern piano that Beethoven was composing for.  Also the apperance of the fugue, and the conspicuous inversion, stretto, augmentation and diminution. 

Walter Ramsey

Walter Ramsey

[amanfang]

Walter Ramsey,

Thanks for your thoughts.  I decided not to try to sort through the other.  I did see that b-flat minor was the resolution of the picardy third F Maj. chord that preceeded it from the second movement, and it is fleeting, moving to F-flat, before finally reaching A min.  I was not aware of minor key signatures missing a flat.  And it is definitely minor and not dorian mode?  If the pieces were dorian, they would be missing a flat.  Perhaps it was as tonality was emerging and there was still some transitioning(?).  Interesting.

[ramseytheii]

Walter Ramsey,

Thanks for your thoughts.  I decided not to try to sort through the other.  I did see that b-flat minor was the resolution of the picardy third F Maj. chord that preceeded it from the second movement, and it is fleeting, moving to F-flat, before finally reaching A min.  I was not aware of minor key signatures missing a flat.  And it is definitely minor and not dorian mode?  If the pieces were dorian, they would be missing a flat.  Perhaps it was as tonality was emerging and there was still some transitioning(?).  Interesting.

Your suggestion of Dorian mode fascinates me, after all in quartet op.132 Beethoven wrote a movement titled, "Holy Song of Thanksgiving to the Deity by a Convalscent, in the Lydian Mode."  I don't know my modes but looked up Dorian on wikipedia, which said it was based on the tetrachord of two whole tones and a semitone.  Well these are of course the very intervals which make up the opening notes of the arioso (also Bach's aria from St. John, "Es ist vollbracht," "it has been fulfilled.")

But this was the Greek definition, and apparently there was some confusion.  The definition Beethoven would have known of Dorian also may apply: put simply it can be thought of as a major scale, played from the second note of the scale, up the octave to the second note of the scale again.  So in C major, a scale starting on D - but with C major key signature.  A Dorian scale in G would have the F major key signature - one flat, and the arioso does lack the one flat it needs to be A-flat minor.  BUT, the reprise of the aria is in strict g minor key signature, so maybe none of this applies.

Walter Ramsey

[pianistimo]

dear walter ramseytheii,

as i see it, in measure 1 of the adagio ma non troppo - things are not as easy as they appear or seem.  if you consider a sudden shift of key on measure 2 (not using notes within the Bb minor scale) - then you are entirely correct.

BUT, if you consider that immediately even on the last beat of measure 1 that there is an Ab added back in.  you are moving chordally to measure 2 to a chord which is definately part of Db Major scale. 

otherwise you would be moving from a Bb minor key - chord i to a Cb Major chord (out of the key of Bb minor) - and making a move from i to flatted ii.   

if you entertain the possibility that all is not as it seems - if you consider you are looking at an illusion - this is what it looks like:

truly in Db Major (despite indications for the first three beats)  - moving from I - VII in the natural key of Db major.  now when he adds the Cb and Fb , he is kind of saying 'bet you don't know what key you are in.'  until finally on the recitativo at measure 4 - we are in the II key (which is not in the key of Db major - or the key of Bb minor as that chord would normally be iv instead of IV).  so he does this back and forth thing - making you unsure as to which key you are really following because of the chords used. 

the second adagio is definately - without a doubt starting in a context of E Major (noting key change at the end of measure 4) and yet you don't realize because it sounds like B Major until measure 6.

now - if we are moving from Bb minor to B Major - this is a chromatic modulation.  if we are moving from the key of Db Major to B Major - this is a aubmented 6th modulation.  BOTH are extreme i guess. 

interesting what you say about the dorian mode!  i think it well could have been a little of using remote keys (therefore, still in tonality) and modal thinking (so it sounds a bit modal). 

[pianistimo]

i read in my hanning book on 'the concise history of western music' that the dorian mode focused on the first and fifth (tonic and dominant) or 'tenor' and is exactly as mr. ramseytheii says - moving in the key of C from D to D.  we would have a pattern of W 1/2WWW1/2 W steps. 

so - following this pattern of scale we can make up the chords that would be part of that mode:

in Bb minor = Bb to C = W    C to Db = 1/2  Db to Eb = W 

[ramseytheii]

Once again pianitisimo I am going to have to disagree with about 99.9% of what you write.  I hope you find these discussions as enjoyable as I do.

dear walter ramseytheii,

as i see it, in measure 1 of the adagio ma non troppo - things are not as easy as they appear or seem.  if you consider a sudden shift of key on measure 2 (not using notes within the Bb minor scale) - then you are entirely correct.

Try this: play the first bar as written, then, instead of playing bar 2, play an e-flat minor 6-4 chord, followed by a B-flat major chord, then resolve it to e-flat minor 5-3.  With the last beat of measure 1, Beethoven is suggesting one of those ultra-compact modulations that he does that are over in a second (like in opus 109), but frustrates it even before going to the cadential chords, because he moves from the 6-4 e-flat minor (last beat of bar 1) to its relative major (which would have been the outcome of a deceptive cadence), C-flat major.

It's not really possible to say that the opening of this movement is "in" b-flat minor, but nor is it acceptable to say there is a "d-flat major triad that just happens to have a b-flat in the bass."  But there nothing to suggest D-flat major in the opening bar, or in the second bar, or actually in the third bar either.

BUT, if you consider that immediately even on the last beat of measure 1 that there is an Ab added back in.  you are moving chordally to measure 2 to a chord which is definately part of Db Major key. 

I'm not sure what you mean: "you are moving chordally.." etc.  Do you mean, "it would seem we are moving chordally to D-flat , but then Beethoven changes it;" or do you mean, "measure 2 is definitely part of D-flat major."  The second case: no it's not.  C-flat major has no place in D-flat major.  What we have here is III/a-flat minor.  The first case: there are no indications the harmonies will go to D-flat major.  If you try my exercise again from the beginning, you will see it could easily cadence to e-flat minor (minor V/a-flat minor).  Nothing suggests D-flat major, unles you insist that a 5-flat key signature means D-flat major no matter what.

otherwise you would be moving from a Bb minor key - chord i to a Cb Major chord (out of the key of Bb minor) - and making a move from i to flatted ii.   

And yet this is more probable than saying C-flat major is a part of D-flat major, since it would have to be a flat major VII.   Flat major II is the Neapolitan, and that's totally normal; but in this case, it's not the Neapolitan, since it frustrates a possible cadenc in e-flat minor, but the VI of e-flat, or the III of a-flat.

if you entertain the possibility that all is not as it seems - if you consider you are looking at an illusion - this is what it looks like:

truly in Db Major (despite indications for the first three beats)  - moving from I - VII in the natural key of Db major.  now when he adds the Cb and Fb , he is kind of saying 'bet you don't know what key you are in.'  until finally on the recitativo at measure 4 - we are in the II key (which is not in the key of Db major - or the key of Bb minor as that chord would normally be iv instead of IV).  so he does this back and forth thing - making you unsure as to which key you are really following because of the chords used. 

Except it oesn't move to VII in the "natural key" of D-flat, because there's no c-flat in the D-flat key signature.  So nothing suggests D-flat in these two bars.
Recitativo: is on an E-flat seventh chord.  That is not in the "natural" key of D-flat, but it is the dominant to the dominant, so it is not far off.  Now, this is not "II," this is V/a-flat minor.  It's a seventh chord, with an e-flat in the bass, and it resolves, before the andante, into a-flat minor.  Yes you are unsure, but the Recitativo is an extended dominant, so you can be pretty sure after that.

the second adagio is definately - without a doubt starting in a context of E Major (noting key change at the end of measure 4) and yet you don't realize because it sounds like B Major until measure 6.

Your ears are deceiving you.  How can it sound like B major if the chord in measure 6 is a dominant seventh on B?  That is obvoiusly the dominant to E majr, which in this case, is the enharmonic spelling of F-flat major, the relative major of a-flat minor.  His modulation to E is beautiful, its striking, its unforgettable, but it isn't remote to the main key.  In fact it is one of the closest posible harmonies.

now - if we are moving from Bb minor to B Major - this is a chromatic modulation.  if we are moving from the key of Db Major to B Major - this is a aubmented 6th modulation.  BOTH are extreme i guess. 

Well we agreed already that we can't say the piece is "in" b-flat minor.  However let us now agree that it never goes to B major.  The only B major chord is a seventh chord, making it a dominant to E major, or in other words F-flat major, which is the relative major to a-flat minor, the tonic.  Anyways, E major, or F-flat major, is only appearing for... three eight notes?  It moves right along, using diminished seventh chords, to the tonic, a-flat minor.  So nothing even goes to E major.  It all goes to the tonic.

Walter Ramsey

[amanfang]

WR,
I sort of understand what you are thinking of as dorian mode.  You look at the major key signature at then begin the scale on the second degree.  I think of it as a minor scale with a raised 6.  And perhaps in early Baroque, as tonality was emerging rather than modality, they kept the dorian key signature and flatted the 6, producing a form of the natural minor, then perhaps raising the 7th as a leading tone. 
It is hard to say if that's what Beethoven had in mind.  That full use of key signatures in a tonal sense rather than modal had surely been established by that time. 

[pianistimo]

dear ramseytheii,

yes.  you are correct.  well, maybe both of us are in certain instances - but, i entirely agree with you consensus on the Cb (why didn't i see that?).  and, of course, the B chord the V7 of E.  seems that you and amanfang have hit on the III/ whatever idea - that he's using a lot of related thirds and changing sixths/sevenths a lot - to make the keys very remote and uncertain. 

you know he's being very 'wierd' if you want to call it that - when he uses a double flat on B at the end of measure 4 and then uses the A-natural in the B major chord to say - this is what i was intending all along.  (he's using the seventh of a five chord to modulate on).
 i think he's combining techniques of moving chromatically - with moving in harmonic manner with thirds AND seconds (modal).  measure 4 includes a dramatic chromatic modulation from the lower note of Db on the second beat (seventh again! of that chord of Em7) to D natural dim7 -which is about as remote as one can get in the key of either Gb major or Eb minor (excepting that it would be the seventh of Eb minor). 

we don't know where the Eb is leading at the 12/16 at measure 7 until measure 8 -last two beats (where suddenly it is now the 5th of the chord).  normally sevenths resolve to the I chord?  but here - he hangs on to the sevenths and doesn't move towards anything reliable.

perhaps he was testing the boundaries of tonality by picking remote relationships.

ps ramseytheii- yes i am enjoying this.  although, i'm double and triple checking everything and somehow you've messed up my mind with this theory stuff.

[ramseytheii]

 i think he's combining techniques of moving chromatically - with moving in harmonic manner with thirds AND seconds (modal).  measure 4 includes a dramatic chromatic modulation from the lower note of Db on the second beat (seventh again! of that chord of Em7) to D natural dim7 -which is about as remote as one can get in the key of either Gb major or Eb minor (excepting that it would be the seventh of Eb minor). 

I think you should be more careful with the way you use words; a "modulation" doesn't mean a chord progression, but the result of that progression.  In other words, "modulating," the verb, refers to the functioning chords in a progression, and a "modulation" refers to the arrival point.  So you don't modulate to a diminished seventh, because that's not the end; the modulation is from VI (E major, enharmonically replacing F-flat major as the relative major, or VI, of the tonic, a-flat minor), to i, at the Adagio ma non troppo.

Also I don't see this in measure 4, but I think you are refering to measure 6?

Also I am not sure where you are getting: Em7, G-flat major or E-flat minor.

we don't know where the Eb is leading at the 12/16 at measure 7 until measure 8 -last two beats (where suddenly it is now the 5th of the chord).  normally sevenths resolve to the I chord?  but here - he hangs on to the sevenths and doesn't move towards anything reliable.

Here the E-flat is never a seventh of anything, but already at the smorzando that precedes the introduction the arioso, we can hear clearly a-flat minor.  The E-flat can still change the direction obviously, and a certain amount of tension follows its additive descent to the a-flat, but it doesn't sound dissonant (as a seventh would). 

perhaps he was testing the boundaries of tonality by picking remote relationships.

If you look at the main harmonies in terms of a-flat minor in this opening dream-scape, you will find: ii (b-flat minor), III (C-flat major), V7 (E-flat major, 7), V7/VI (B major, 7, enharmonically replacing C-flat major).  Nothing is remote, and yet the way he juxtaposes the harmonies is striking, and unforgettable.  Sorry to be annoying about this, but I think that calling these kind of progressions remote, and relating them to a futuristic context, is actually overlooking the accomplishment which he achieved.  He uses closely related harmonies (related to the tonic), which would seem to be limited in scope, to conjure an amazing sense of destitution, melancholy, Sehnsucht. 

I think you are letting yoru eye deceive your ear.  Although it looks modernistic, with 6 flats going to four sharps, double accidentals, always changing accidentals, it all fits within the key.  Try transposing the music into a more conventional key, like c minor.  It will look much more rational, but sound essentially the same.

Walter Ramsey

[pianistimo]

dear ramseytheii,

i feel, as you indicate, that the modulations take place at key changes - but the preparation for these changes occurs more and more towards the beginning of the piece - in 'preparation'  if you can call it that.  you see a lot of accidentals and thing 'ok - we're going here - and then suddenly - nope - we're just modulating down chromatically at the key change.  so, it's not a typical harmonic modulation.

i don't think you understand what i mean about remote chords.  each scale - for instance the Bb minor scale - has a pattern of notes from which ALL the chords are pulled.  but, in this case - beethoven isn't following the minor chord scale pattern and many of the chords are more purposely chromatic or diminished. for instance, on the first beat of the second measure we already have a Cb!  this is a half step up from Bb and certainly not part of the Bb minor scale (nor Bb major, as you say!).  but, we do have Bb, Db, Fb Ab chord on second beat of third measure that makes the Bb chord diminished 7.