Bach's BWV 846 need help with harmonic analysis

[aznviolet]

Hi everyone!  just found this forum and i think it's great!

anyway, i've been trying to figure out how the b diminished 7th chord fits in mm.14 (if it's a b diminished 7th chord at all).

i was thinking maybe the chord in mm. 14 is just a b diminished (vii) which flows nicely to I in mm. 15 and maybe the a-flat is just a chromatic passing tone between mm.13 and 15.

am i thinking too hard?

[xvimbi]

am i thinking too hard?

With JSB, one can never think too hard.

However... are you talking about the Prelude in C major? If so, I don't see no chords in measures 13-15. What gives?

[aznviolet]

They are broken chords, not solid chords...

[allchopin]

Assuming you mean melodic chords, in measure 13 it is on the second scale degree and in measure 15 it is in the first.  The only acceptable tonal progressions from ii -> I are through V or vii (if he obeys these rules), and since G is not in measure 14 it must be a vii, thus a vii^o43.  I am curious how to interpret fully diminshed 7ths though, because any inversion brings it to a different possible 7th.

[xvimbi]

Assuming you mean melodic chords, in measure 13 it is on the second scale degree and in measure 15 it is in the first.  The only acceptable tonal progressions from ii -> I are through V or vii (if he obeys these rules), and since G is not in measure 14 it must be a vii, thus a vii^o43.  I am curious how to interpret fully diminshed 7ths though, because any inversion brings it to a different possible 7th.

I'm still confused. Are we talking about the upper staff, DAD in measure 13, DFB in measure 14, and CGC in measure 15? Except for DFB, those are not "normal" triads. I want to learn something here, so please elaborate Thanks!

[bernhard]

Here is the harmonic analysis for the first 19 bars. Just play the arpeggios as chords, and this is what you have:

Bar 1: CEGCE – C major chord – underlying key: C major – I
Bar 2: CDADF – D minor seventh chord – underlying key C major – II7
Bar 3: BDGDF – G seventh chord – underlying key C major – V7
Bar 4: CEGCE – C major chord – underlying key: C major – I
Bar 5: CEAEA – A minor chord – UK: C major (or G major) – VI (or II)
Bar 6: CDEF#AD – D seventh chord – UK: G major V7
Bar 7: BDGDG – G major chord – UK: G major  – I
Bar 8: BCEGC – C major seventh chord – UK: G major - IVmaj7
Bar 9: ACEGC – A minor seventh chord – UK: G major II7
Bar 10: DADF#C – D seventh chord – UK: G major  - V7
Bar 11: GBDGB – G major chord – UK: G major – I
Bar 12: GBbEGC# - C# diminished 7th chord – UK: D minor  – VIIdim7
Bar 13: FADAD – D minor chord – UK: D minor (or C major) – I (or II)
Bar 14: FAbDFB – B diminished chord  – UK: C minor – VIIdim7
Bar 15: EGEGC – C major chord – UK: C major – I
Bar 16: EFACF – F major seventh chord – UK: C major – IVmaj7
Bar 17: DFACF – D minor seventh chord – UK: C major – II7
Bar 18: GDGBF – G seventh chord – UK: C major – V7
Bar 19: CEGCE – C major chord: UK: C major - I


Homework: Complete the harmonic analysis and answer the following questions:

1.   What sort of cadence is there on the final chord?
2.   Where (which bar) does the end of this piece begins?
3.   Where (which bar) does the beginning of this piece ends?
4.   What is the harmonic importance of bars 20 – 23. Or to put in other words: Explain why bars 20 – 23 are the most intense bars in the whole piece, both polyphonically and harmonically?

Leave on my desk by the end of next week.

Best wishes,
Bernhard.

[allchopin]

I'm still confused. Are we talking about the upper staff, DAD in measure 13, DFB in measure 14, and CGC in measure 15? Except for DFB, those are not "normal" triads. I want to learn something here, so please elaborate Thanks!

Why are these not normal triads?  Each contains notes of their respective scale degrees (though they may be inverted), which in m. 13 is a ii⁶, in m. 14 is a vii^o4₃, and in m. 15 a I⁶. 

[xvimbi]

Why are these not normal triads?  Each contains notes of their respective scale degrees (though they may be inverted), which in m. 13 is a ii⁶, in m. 14 is a vii^o4₃, and in m. 15 a I⁶. 

I am sure you are right. I simply meant "normal" triad as one that contains three different notes.

[allchopin]

I am sure you are right. I simply meant "normal" triad as one that contains three different notes.

Most measures do contain three different notes - though some notes may be doubled (such as D and A in m. 13) or inverted such as a C major triad beginning on E or G (E would make it a ⁶, G would make it a ⁶₄).  If each measure does contain more than three different types of notes they would be considered sevenths, such as the measure in question, #14 which is why it is a vii^o4₃.
Bernhard, what does UK stand for.. is this some kind of acronym to describe key modulations?

[xvimbi]

Most measures do contain three different notes - though some notes may be doubled (such as D and A in m. 13) or inverted such as a C major triad beginning on E or G (E would make it a ⁶, G would make it a ⁶₄).  If each measure does contain more than three different types of notes they would be considered sevenths, such as the measure in question, #14 which is why it is a vii^o4₃.

Yes, yes, yes, thank you. I simply wasn't aware of the fact that one would have to include the first two notes in each measure in the harmonic analysis. Without that it is a bit difficult to make the analysis just from the chord outline (such as DA), although even this is probably possible, but I havn't had formal training in that area (harmonic analysis in Baroque pieces, that is; if we were talking about Jazz, then it would be completely different). Anyway, thanks for clearing this up.

Bernhard, what does UK stand for.. is this some kind of acronym to describe key modulations?

I venture to say it means "underlying key" as he spelled it out for measure 1-4.

[anda]

Bernhard, what does UK stand for.. is this some kind of acronym to describe key modulations?

united kingdom

[aznviolet]

Here is the harmonic analysis for the first 19 bars. Just play the arpeggios as chords, and this is what you have:

Bar 1: CEGCE – C major chord – underlying key: C major – I
Bar 2: CDADF – D minor seventh chord – underlying key C major – II7
Bar 3: BDGDF – G seventh chord – underlying key C major – V7
Bar 4: CEGCE – C major chord – underlying key: C major – I
Bar 5: CEAEA – A minor chord – UK: C major (or G major) – VI (or II)
Bar 6: CDEF#AD – D seventh chord – UK: G major V7
Bar 7: BDGDG – G major chord – UK: G major  – I
Bar 8: BCEGC – C major seventh chord – UK: G major - IVmaj7
Bar 9: ACEGC – A minor seventh chord – UK: G major II7
Bar 10: DADF#C – D seventh chord – UK: G major  - V7
Bar 11: GBDGB – G major chord – UK: G major – I
Bar 12: GBbEGC# - C# diminished 7th chord – UK: D minor  – VIIdim7
Bar 13: FADAD – D minor chord – UK: D minor (or C major) – I (or II)
Bar 14: FAbDFB – B diminished chord  – UK: C minor – VIIdim7
Bar 15: EGEGC – C major chord – UK: C major – I
Bar 16: EFACF – F major seventh chord – UK: C major – IVmaj7
Bar 17: DFACF – D minor seventh chord – UK: C major – II7
Bar 18: GDGBF – G seventh chord – UK: C major – V7
Bar 19: CEGCE – C major chord: UK: C major - I


Homework: Complete the harmonic analysis and answer the following questions:

1.   What sort of cadence is there on the final chord?
2.   Where (which bar) does the end of this piece begins?
3.   Where (which bar) does the beginning of this piece ends?
4.   What is the harmonic importance of bars 20 – 23. Or to put in other words: Explain why bars 20 – 23 are the most intense bars in the whole piece, both polyphonically and harmonically?

Leave on my desk by the end of next week.

Best wishes,
Bernhard.

Thank you, Bernhard for the harmonic analysis. 

ok, i'm confused with something... well a lot of things... but let's start with this.  from bars 1 to5 we're in the key of C+ and the chord progression is
 
bars 1-5   : I - ii - V - I - vi (C major)

then we modulate to G+ in bars 5 to11
bars 5-11 : ii - V - I - IV - ii - V - I (G major)

ok this is where i get lost, Bach throws in a C# diminished 7th chord which is vii of D minor in bar 12, bar 13 is a D minor chord.  then he throws in bar 14 a B diminished 7th chord which belongs to C minor.  then happily in bar 15 we're back to a C major chord.  i don't understand the chord progression from bars 11-15.

so we modulate back to C major in bar 11
bars 11 : V
bars 12 : vii of ii
bars 13 : ii
is that chord progression right?  V - ii?  am i looking at this wrong?  please, broaden my mind!

the b diminished 7th chord in bar 14 comes from C minor not C major, but if we label the Ab as a chromatic passing tone in the tenor the chord becomes b diminished (vii) and that progression makes sense to me, because bar 15 is I (C major.)
bars 14 : vii
bars 15 : I

ok... i have more but i have to go to a basketball game.  please, help me.  thank you in advance.

[richard w]

so we modulate back to C major in bar 11
bars 11 : V
bars 12 : vii of ii
bars 13 : ii
is that chord progression right?  V - ii?  am i looking at this wrong?  please, broaden my mind!

Your analysis of these bars is very pertinent. To me it doesn't seem that we ever 'modulated' to D minor. I think your secondary dominant suggestion is the best fit.

In fact you could have got this far without ever having modulated, by using the secondary dominant in the analysis, thus:

In C major:
Bar 1 - I
Bar 2 - II 642
Bar 3 - V 65
Bar 4 - I
Bar 5 - VI 6
Bar 6 - V 642 of V
Bar 7 - V 6
Bar 8 - I 642
Bar 9 - VI
Bar 10 - V7 of V
Bar 11 - V
Bar 12 - V °643 of II
Bar 13 - II 6
Bar 14 - V °643
Bar 15 - I 6

the b diminished 7th chord in bar 14 comes from C minor not C major, but if we label the Ab as a chromatic passing tone in the tenor the chord becomes b diminished (vii) and that progression makes sense to me, because bar 15 is I (C major.)
bars 14 : vii
bars 15 : I

You don't need to consider the A flat as a chromatic passing tone. The chord consisting of B, D, F and A flat is a perfectly acceptable way of implying the dominant harmony in C major. Think of this chord as a dominant minor ninth with no root - hence, why I have used the symbol V °643 instead of VII.

Is that any help?



Richard.

[aznviolet]

Thank you, Richard, that helps me a lot.  I haven't analyzed music in 6 years.  I have forgotten a lot, but it's slowly coming back to me!

ok, I must go and I will continue my analysis later.

[aznviolet]

here's the rest of my analysis:

bar 20 - V ^b7 of VI
bar 21 - IV ⁷
bar 22 - ii ^b7 of V (?)
bar 23 - vii ^b4₂
bar 24 - V ⁷              G pedal point starts
bar 25 - I ⁶₄
bar 26 - V ¹¹ (?)
bar 27 - V ⁷
bar 28 - ii ^b7 of V (?)
bar 29 - I ⁶₄
bar 30 - V ¹¹  (?)
bar 31 - V ⁷             G pedal point ends
bar 32 - I ^b7  (?)      C pedal point begins
bar 33 - IV - ii ⁴₂
bar 34 - V ⁷
bar 35 - I                      C pedal point ends

i'm not sure of what bars 22, 26, 28, 30, 32 are supposed to be.

1.   What sort of cadence is there on the final chord?

Perfect cadence

2.   Where (which bar) does the end of this piece begins?

Bar 24

3.   Where (which bar) does the beginning of this piece ends?

Bar 4

4.   What is the harmonic importance of bars 20 – 23. Or to put in other words: Explain why bars 20 – 23 are the most intense bars in the whole piece, both polyphonically and harmonically?

I will attempt to answer this question soon, Bernhard!

Thanks!